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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":805,"body":1785,"description":7957,"extension":1952,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":7958,"navigation":1782,"path":806,"published":2028,"seo":7959,"stem":807,"__hash__":7960},"docs\u002Fen\u002Fplayground\u002F01-typstex.md",{"type":1786,"value":1787,"toc":7931},"minimark",[1788,1792,1796,1801,1813,1830,1835,1844,1848,1853,1857,1861,1865,1868,1871,1874,1877,1880,1883,1887,1890,1893,1909,1913,1916,1919,1923,1930,1933,1938,1948,2086,2090,2097,2505,2509,2512,2850,2854,2857,2861,3039,3170,3174,3177,3411,3552,3824,4318,4322,4328,4484,4680,4684,4688,4691,4988,4991,5370,5374,5377,5546,5549,5692,5696,5699,6046,6049,6214,6218,6221,6484,6487,6819,7014,7018,7021,7330,7670,7880,7906,7927],[1789,1790,805],"h1",{"id":1791},"typst-plugin-playground",[1793,1794,1795],"p",{},"This 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",[1839,1840],"typst-math",{"is-block":1841,"src64":1842},"false","MSArIDIgKyAzICsgZG90cyArIG4gPSAobihuKzEpKS8y"," in the text.",[1831,1845,1847],{"id":1846},"display-math-example","Display Math Example",[1839,1849],{"is-block":1850,"src64":1851,"font-size":1852},"true","XGludF8wXlxpbmZ0eSBlXnsteF4yfVwsZHggPSBcZnJhY3tcc3FydHtccGl9fXsyfQ==","18",[1831,1854,1856],{"id":1855},"mixed-formula-typst-syntax","Mixed Formula (Typst Syntax)",[1839,1858],{"is-block":1850,"src64":1859,"font-size":1860},"RSA9IG0gY14y","20",[1831,1862,1864],{"id":1863},"complex-expressions","Complex Expressions",[1793,1866,1867],{},"Quadratic formula:",[1839,1869],{"is-block":1850,"src64":1870,"font-size":1852},"eCA9ICgtYiBwbHVzLm1pbnVzIHNxcnQoYl4yIC0gNGEgYykpLygyYSk=",[1793,1872,1873],{},"Matrix representation:",[1839,1875],{"is-block":1850,"src64":1876,"font-size":1852},"bWF0KDEsIDI7IDMsIDQpIHZlYyh4LCB5KSA9IHZlYyg1LCA2KQ==",[1793,1878,1879],{},"Summation and limits:",[1839,1881],{"is-block":1850,"src64":1882,"font-size":1852},"c3VtXyhpPTEpXm4gaV4yID0gKG4obisxKSgybisxKSkvNg==",[1797,1884,1886],{"id":1885},"rendering-engine-comparison","Rendering Engine Comparison",[1793,1888,1889],{},"Let's compare the same formula rendered with three different engines.",[1793,1891,1892],{},"Target formula:",[1894,1895,1900],"pre",{"className":1896,"code":1897,"language":1898,"meta":1899,"style":10},"language-tex shiki shiki-themes github-light-high-contrast github-light-high-contrast github-dark-high-contrast","\\int_0^\\infty e^{-x^2}\\,dx = \\frac{\\sqrt{\\pi}}{2}\n","tex","title=\"LaTeX formula example\"",[1805,1901,1902],{"__ignoreMap":10},[1903,1904,1907],"span",{"class":1905,"line":1906},"line",1,[1903,1908,1897],{},[1831,1910,1912],{"id":1911},"_1-native-typst-typst-syntax","1. Native Typst (Typst Syntax)",[1793,1914,1915],{},"Using Typst's native syntax:",[1839,1917],{"is-block":1850,"src64":1918,"font-size":1852},"aW50ZWdyYWxfMF7iiJ4gZV4oLXheMikgZCB4ID0gc3FydCjPgCkvMg==",[1831,1920,1922],{"id":1921},"_2-typstmath-fallback-mathjax","2. TypstMath Fallback (MathJax)",[1793,1924,1925,1926,1929],{},"When configured with ",[1805,1927,1928],{},"latexEngine: 'mathjax'",", LaTeX-style input falls back to MathJax:",[1839,1931],{"is-block":1850,"src64":1851,"font-size":1852,"latex-engine":1932},"mathjax",[1934,1935,1937],"h4",{"id":1936},"overriding-the-engine-per-component","Overriding the Engine per Component",[1793,1939,1940,1941,1943,1944,1947],{},"The global plugin sets the default fallback engine, but you can override it for any ",[1805,1942,1811],{}," via the ",[1805,1945,1946],{},"latex-engine"," prop:",[1894,1949,1953],{"className":1950,"code":1951,"language":1952,"meta":10,"style":10},"language-md shiki shiki-themes github-light-high-contrast github-light-high-contrast github-dark-high-contrast","\u003CTypstMath\n  src=\"\\\\int_0^\\\\infty e^{-x^2}\\\\,dx = \\\\frac{\\\\sqrt{\\\\pi}}{2}\"\n  :is-block=\"true\"\n  latex-engine=\"katex\"\n  :fontSize=\"18\"\n\u002F>  \u003C!-- Force KaTeX -->\n\n\u003CTypstMath\n  src=\"\\\\int_0^\\\\infty e^{-x^2}\\\\,dx = \\\\frac{\\\\sqrt{\\\\pi}}{2}\"\n  :is-block=\"true\"\n  latex-engine=\"mathjax\"\n  :fontSize=\"18\"\n\u002F>  \u003C!-- Force MathJax -->\n","md",[1805,1954,1955,1961,1999,2005,2011,2017,2023,2030,2035,2064,2069,2075,2080],{"__ignoreMap":10},[1903,1956,1957],{"class":1905,"line":1906},[1903,1958,1960],{"class":1959},"s7iLA","\u003CTypstMath\n",[1903,1962,1964,1967,1971,1974,1976,1979,1981,1984,1986,1989,1991,1994,1996],{"class":1905,"line":1963},2,[1903,1965,1966],{"class":1959},"  src=\"",[1903,1968,1970],{"class":1969},"sklAV","\\\\",[1903,1972,1973],{"class":1959},"int_0^",[1903,1975,1970],{"class":1969},[1903,1977,1978],{"class":1959},"infty e^{-x^2}",[1903,1980,1970],{"class":1969},[1903,1982,1983],{"class":1959},",dx = ",[1903,1985,1970],{"class":1969},[1903,1987,1988],{"class":1959},"frac{",[1903,1990,1970],{"class":1969},[1903,1992,1993],{"class":1959},"sqrt{",[1903,1995,1970],{"class":1969},[1903,1997,1998],{"class":1959},"pi}}{2}\"\n",[1903,2000,2002],{"class":1905,"line":2001},3,[1903,2003,2004],{"class":1959},"  :is-block=\"true\"\n",[1903,2006,2008],{"class":1905,"line":2007},4,[1903,2009,2010],{"class":1959},"  latex-engine=\"katex\"\n",[1903,2012,2014],{"class":1905,"line":2013},5,[1903,2015,2016],{"class":1959},"  :fontSize=\"18\"\n",[1903,2018,2020],{"class":1905,"line":2019},6,[1903,2021,2022],{"class":1959},"\u002F>  \u003C!-- Force KaTeX -->\n",[1903,2024,2026],{"class":1905,"line":2025},7,[1903,2027,2029],{"emptyLinePlaceholder":2028},true,"\n",[1903,2031,2033],{"class":1905,"line":2032},8,[1903,2034,1960],{"class":1959},[1903,2036,2038,2040,2042,2044,2046,2048,2050,2052,2054,2056,2058,2060,2062],{"class":1905,"line":2037},9,[1903,2039,1966],{"class":1959},[1903,2041,1970],{"class":1969},[1903,2043,1973],{"class":1959},[1903,2045,1970],{"class":1969},[1903,2047,1978],{"class":1959},[1903,2049,1970],{"class":1969},[1903,2051,1983],{"class":1959},[1903,2053,1970],{"class":1969},[1903,2055,1988],{"class":1959},[1903,2057,1970],{"class":1969},[1903,2059,1993],{"class":1959},[1903,2061,1970],{"class":1969},[1903,2063,1998],{"class":1959},[1903,2065,2067],{"class":1905,"line":2066},10,[1903,2068,2004],{"class":1959},[1903,2070,2072],{"class":1905,"line":2071},11,[1903,2073,2074],{"class":1959},"  latex-engine=\"mathjax\"\n",[1903,2076,2078],{"class":1905,"line":2077},12,[1903,2079,2016],{"class":1959},[1903,2081,2083],{"class":1905,"line":2082},13,[1903,2084,2085],{"class":1959},"\u002F>  \u003C!-- Force MathJax -->\n",[1831,2087,2089],{"id":2088},"_3-markdown-it-typstex-fallback-katex","3. markdown-it-typstex Fallback (KaTeX)",[1793,2091,2092,2093,2096],{},"The same LaTeX formula parsed by the ",[1805,2094,2095],{},"markdown-it-typstex"," plugin, falling back to KaTeX when Typst fails:",[1903,2098,2101],{"className":2099},[2100],"katex-display",[1903,2102,2105,2183],{"className":2103},[2104],"katex",[1903,2106,2109],{"className":2107},[2108],"katex-mathml",[2110,2111,2114],"math",{"xmlns":2112,"display":2113},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[2115,2116,2117,2178],"semantics",{},[2118,2119,2120,2136,2155,2159,2162,2164,2167],"mrow",{},[2121,2122,2123,2127,2131],"msubsup",{},[2124,2125,2126],"mo",{},"∫",[2128,2129,2130],"mn",{},"0",[2132,2133,2135],"mi",{"mathvariant":2134},"normal","∞",[2137,2138,2139,2142],"msup",{},[2132,2140,2141],{},"e",[2118,2143,2144,2147],{},[2124,2145,2146],{},"−",[2137,2148,2149,2152],{},[2132,2150,2151],{},"x",[2128,2153,2154],{},"2",[2156,2157,2158],"mtext",{}," ",[2132,2160,2161],{},"d",[2132,2163,2151],{},[2124,2165,2166],{},"=",[2168,2169,2170,2176],"mfrac",{},[2171,2172,2173],"msqrt",{},[2132,2174,2175],{},"π",[2128,2177,2154],{},[2179,2180,2182],"annotation",{"encoding":2181},"application\u002Fx-tex","\\int_0^\\infty e^{-x^2}\\,dx = \\frac{\\sqrt{\\pi}}{2}",[1903,2184,2187,2363],{"className":2185,"ariaHidden":1850},[2186],"katex-html",[1903,2188,2191,2196,2269,2274,2343,2346,2349,2352,2356,2360],{"className":2189},[2190],"base",[1903,2192],{"className":2193,"style":2195},[2194],"strut","height:2.3262em;vertical-align:-0.9119em;",[1903,2197,2200,2206],{"className":2198},[2199],"mop",[1903,2201,2126],{"className":2202,"style":2205},[2199,2203,2204],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[1903,2207,2210],{"className":2208},[2209],"msupsub",[1903,2211,2215,2260],{"className":2212},[2213,2214],"vlist-t","vlist-t2",[1903,2216,2219,2255],{"className":2217},[2218],"vlist-r",[1903,2220,2224,2243],{"className":2221,"style":2223},[2222],"vlist","height:1.4143em;",[1903,2225,2227,2232],{"style":2226},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[1903,2228],{"className":2229,"style":2231},[2230],"pstrut","height:2.7em;",[1903,2233,2239],{"className":2234},[2235,2236,2237,2238],"sizing","reset-size6","size3","mtight",[1903,2240,2130],{"className":2241},[2242,2238],"mord",[1903,2244,2246,2249],{"style":2245},"top:-3.8129em;margin-right:0.05em;",[1903,2247],{"className":2248,"style":2231},[2230],[1903,2250,2252],{"className":2251},[2235,2236,2237,2238],[1903,2253,2135],{"className":2254},[2242,2238],[1903,2256,2259],{"className":2257},[2258],"vlist-s","​",[1903,2261,2263],{"className":2262},[2218],[1903,2264,2267],{"className":2265,"style":2266},[2222],"height:0.9119em;",[1903,2268],{},[1903,2270],{"className":2271,"style":2273},[2272],"mspace","margin-right:0.1667em;",[1903,2275,2277,2281],{"className":2276},[2242],[1903,2278,2141],{"className":2279},[2242,2280],"mathnormal",[1903,2282,2284],{"className":2283},[2209],[1903,2285,2287],{"className":2286},[2213],[1903,2288,2290],{"className":2289},[2218],[1903,2291,2294],{"className":2292,"style":2293},[2222],"height:1.0369em;",[1903,2295,2297,2300],{"style":2296},"top:-3.113em;margin-right:0.05em;",[1903,2298],{"className":2299,"style":2231},[2230],[1903,2301,2303],{"className":2302},[2235,2236,2237,2238],[1903,2304,2306,2309],{"className":2305},[2242,2238],[1903,2307,2146],{"className":2308},[2242,2238],[1903,2310,2312,2315],{"className":2311},[2242,2238],[1903,2313,2151],{"className":2314},[2242,2280,2238],[1903,2316,2318],{"className":2317},[2209],[1903,2319,2321],{"className":2320},[2213],[1903,2322,2324],{"className":2323},[2218],[1903,2325,2328],{"className":2326,"style":2327},[2222],"height:0.8913em;",[1903,2329,2331,2335],{"style":2330},"top:-2.931em;margin-right:0.0714em;",[1903,2332],{"className":2333,"style":2334},[2230],"height:2.5em;",[1903,2336,2340],{"className":2337},[2235,2338,2339,2238],"reset-size3","size1",[1903,2341,2154],{"className":2342},[2242,2238],[1903,2344],{"className":2345,"style":2273},[2272],[1903,2347,2161],{"className":2348},[2242,2280],[1903,2350,2151],{"className":2351},[2242,2280],[1903,2353],{"className":2354,"style":2355},[2272],"margin-right:0.2778em;",[1903,2357,2166],{"className":2358},[2359],"mrel",[1903,2361],{"className":2362,"style":2355},[2272],[1903,2364,2366,2370],{"className":2365},[2190],[1903,2367],{"className":2368,"style":2369},[2194],"height:2.1633em;vertical-align:-0.686em;",[1903,2371,2373,2378,2501],{"className":2372},[2242],[1903,2374],{"className":2375},[2376,2377],"mopen","nulldelimiter",[1903,2379,2381],{"className":2380},[2168],[1903,2382,2384,2492],{"className":2383},[2213,2214],[1903,2385,2387,2489],{"className":2386},[2218],[1903,2388,2391,2404,2415],{"className":2389,"style":2390},[2222],"height:1.4773em;",[1903,2392,2394,2398],{"style":2393},"top:-2.314em;",[1903,2395],{"className":2396,"style":2397},[2230],"height:3em;",[1903,2399,2401],{"className":2400},[2242],[1903,2402,2154],{"className":2403},[2242],[1903,2405,2407,2410],{"style":2406},"top:-3.23em;",[1903,2408],{"className":2409,"style":2397},[2230],[1903,2411],{"className":2412,"style":2414},[2413],"frac-line","border-bottom-width:0.04em;",[1903,2416,2418,2421],{"style":2417},"top:-3.677em;",[1903,2419],{"className":2420,"style":2397},[2230],[1903,2422,2424],{"className":2423},[2242],[1903,2425,2428],{"className":2426},[2242,2427],"sqrt",[1903,2429,2431,2480],{"className":2430},[2213,2214],[1903,2432,2434,2477],{"className":2433},[2218],[1903,2435,2438,2454],{"className":2436,"style":2437},[2222],"height:0.8003em;",[1903,2439,2443,2446],{"className":2440,"style":2442},[2441],"svg-align","top:-3em;",[1903,2444],{"className":2445,"style":2397},[2230],[1903,2447,2450],{"className":2448,"style":2449},[2242],"padding-left:0.833em;",[1903,2451,2175],{"className":2452,"style":2453},[2242,2280],"margin-right:0.0359em;",[1903,2455,2457,2460],{"style":2456},"top:-2.7603em;",[1903,2458],{"className":2459,"style":2397},[2230],[1903,2461,2465],{"className":2462,"style":2464},[2463],"hide-tail","min-width:0.853em;height:1.08em;",[2466,2467,2473],"svg",{"xmlns":2468,"width":2469,"height":2470,"viewBox":2471,"preserveAspectRatio":2472},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2474,2475],"path",{"d":2476},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1903,2478,2259],{"className":2479},[2258],[1903,2481,2483],{"className":2482},[2218],[1903,2484,2487],{"className":2485,"style":2486},[2222],"height:0.2397em;",[1903,2488],{},[1903,2490,2259],{"className":2491},[2258],[1903,2493,2495],{"className":2494},[2218],[1903,2496,2499],{"className":2497,"style":2498},[2222],"height:0.686em;",[1903,2500],{},[1903,2502],{"className":2503},[2504,2377],"mclose",[1831,2506,2508],{"id":2507},"_4-pure-typst-syntax","4. Pure Typst Syntax",[1793,2510,2511],{},"Using Typst's mathematical syntax:",[1903,2513,2515],{"className":2514},[2100],[1903,2516,2518,2620],{"className":2517},[2104],[1903,2519,2521],{"className":2520},[2108],[2110,2522,2523],{"xmlns":2112,"display":2113},[2115,2524,2525,2617],{},[2118,2526,2527,2530,2533,2536,2538,2541,2544,2547,2556,2558,2561,2563,2565,2567,2569,2572,2579,2581,2587,2590,2592,2594,2596,2599,2602,2604,2606,2608,2610,2612,2615],{},[2132,2528,2529],{},"i",[2132,2531,2532],{},"n",[2132,2534,2535],{},"t",[2132,2537,2141],{},[2132,2539,2540],{},"g",[2132,2542,2543],{},"r",[2132,2545,2546],{},"a",[2121,2548,2549,2552,2554],{},[2132,2550,2551],{},"l",[2128,2553,2130],{},[2132,2555,2529],{},[2132,2557,2532],{},[2132,2559,2560],{},"f",[2132,2562,2529],{},[2132,2564,2532],{},[2132,2566,2529],{},[2132,2568,2535],{},[2132,2570,2571],{},"y",[2137,2573,2574,2576],{},[2132,2575,2141],{},[2124,2577,2578],{"stretchy":1841},"(",[2124,2580,2146],{},[2137,2582,2583,2585],{},[2132,2584,2151],{},[2128,2586,2154],{},[2124,2588,2589],{"stretchy":1841},")",[2132,2591,2161],{},[2132,2593,2151],{},[2124,2595,2166],{},[2132,2597,2598],{},"s",[2132,2600,2601],{},"q",[2132,2603,2543],{},[2132,2605,2535],{},[2124,2607,2578],{"stretchy":1841},[2132,2609,2175],{},[2124,2611,2589],{"stretchy":1841},[2132,2613,2614],{"mathvariant":2134},"\u002F",[2128,2616,2154],{},[2179,2618,2619],{"encoding":2181},"integral_0^infinity e^(-x^2) d x = sqrt(π)\u002F2",[1903,2621,2623,2763,2818],{"className":2622,"ariaHidden":1850},[2186],[1903,2624,2626,2630,2634,2637,2640,2643,2647,2650,2705,2708,2712,2716,2719,2722,2752,2756,2760],{"className":2625},[2190],[1903,2627],{"className":2628,"style":2629},[2194],"height:1.185em;vertical-align:-0.247em;",[1903,2631,2633],{"className":2632},[2242,2280],"in",[1903,2635,2535],{"className":2636},[2242,2280],[1903,2638,2141],{"className":2639},[2242,2280],[1903,2641,2540],{"className":2642,"style":2453},[2242,2280],[1903,2644,2543],{"className":2645,"style":2646},[2242,2280],"margin-right:0.0278em;",[1903,2648,2546],{"className":2649},[2242,2280],[1903,2651,2653,2657],{"className":2652},[2242],[1903,2654,2551],{"className":2655,"style":2656},[2242,2280],"margin-right:0.0197em;",[1903,2658,2660],{"className":2659},[2209],[1903,2661,2663,2696],{"className":2662},[2213,2214],[1903,2664,2666,2693],{"className":2665},[2218],[1903,2667,2670,2682],{"className":2668,"style":2669},[2222],"height:0.8747em;",[1903,2671,2673,2676],{"style":2672},"top:-2.453em;margin-left:-0.0197em;margin-right:0.05em;",[1903,2674],{"className":2675,"style":2231},[2230],[1903,2677,2679],{"className":2678},[2235,2236,2237,2238],[1903,2680,2130],{"className":2681},[2242,2238],[1903,2683,2684,2687],{"style":2296},[1903,2685],{"className":2686,"style":2231},[2230],[1903,2688,2690],{"className":2689},[2235,2236,2237,2238],[1903,2691,2529],{"className":2692},[2242,2280,2238],[1903,2694,2259],{"className":2695},[2258],[1903,2697,2699],{"className":2698},[2218],[1903,2700,2703],{"className":2701,"style":2702},[2222],"height:0.247em;",[1903,2704],{},[1903,2706,2532],{"className":2707},[2242,2280],[1903,2709,2560],{"className":2710,"style":2711},[2242,2280],"margin-right:0.1076em;",[1903,2713,2715],{"className":2714},[2242,2280],"ini",[1903,2717,2535],{"className":2718},[2242,2280],[1903,2720,2571],{"className":2721,"style":2453},[2242,2280],[1903,2723,2725,2728],{"className":2724},[2242],[1903,2726,2141],{"className":2727},[2242,2280],[1903,2729,2731],{"className":2730},[2209],[1903,2732,2734],{"className":2733},[2213],[1903,2735,2737],{"className":2736},[2218],[1903,2738,2741],{"className":2739,"style":2740},[2222],"height:0.938em;",[1903,2742,2743,2746],{"style":2296},[1903,2744],{"className":2745,"style":2231},[2230],[1903,2747,2749],{"className":2748},[2235,2236,2237,2238],[1903,2750,2578],{"className":2751},[2376,2238],[1903,2753],{"className":2754,"style":2755},[2272],"margin-right:0.2222em;",[1903,2757,2146],{"className":2758},[2759],"mbin",[1903,2761],{"className":2762,"style":2755},[2272],[1903,2764,2766,2770,2800,2803,2806,2809,2812,2815],{"className":2765},[2190],[1903,2767],{"className":2768,"style":2769},[2194],"height:1.1141em;vertical-align:-0.25em;",[1903,2771,2773,2776],{"className":2772},[2242],[1903,2774,2151],{"className":2775},[2242,2280],[1903,2777,2779],{"className":2778},[2209],[1903,2780,2782],{"className":2781},[2213],[1903,2783,2785],{"className":2784},[2218],[1903,2786,2789],{"className":2787,"style":2788},[2222],"height:0.8641em;",[1903,2790,2791,2794],{"style":2296},[1903,2792],{"className":2793,"style":2231},[2230],[1903,2795,2797],{"className":2796},[2235,2236,2237,2238],[1903,2798,2154],{"className":2799},[2242,2238],[1903,2801,2589],{"className":2802},[2504],[1903,2804,2161],{"className":2805},[2242,2280],[1903,2807,2151],{"className":2808},[2242,2280],[1903,2810],{"className":2811,"style":2355},[2272],[1903,2813,2166],{"className":2814},[2359],[1903,2816],{"className":2817,"style":2355},[2272],[1903,2819,2821,2825,2828,2831,2834,2837,2840,2843,2846],{"className":2820},[2190],[1903,2822],{"className":2823,"style":2824},[2194],"height:1em;vertical-align:-0.25em;",[1903,2826,2598],{"className":2827},[2242,2280],[1903,2829,2601],{"className":2830,"style":2453},[2242,2280],[1903,2832,2543],{"className":2833,"style":2646},[2242,2280],[1903,2835,2535],{"className":2836},[2242,2280],[1903,2838,2578],{"className":2839},[2376],[1903,2841,2175],{"className":2842,"style":2453},[2242,2280],[1903,2844,2589],{"className":2845},[2504],[1903,2847,2849],{"className":2848},[2242],"\u002F2",[1797,2851,2853],{"id":2852},"markdown-it-typstex-plugin","markdown-it-typstex Plugin",[1793,2855,2856],{},"This plugin allows you to write math expressions directly in markdown.",[1831,2858,2860],{"id":2859},"inline-math","Inline Math",[1793,2862,2863,2864,3038],{},"Here's an inline formula: ",[1903,2865,2867,2917],{"className":2866},[2104],[1903,2868,2870],{"className":2869},[2108],[2110,2871,2872],{"xmlns":2112},[2115,2873,2874,2914],{},[2118,2875,2876,2879,2881,2884,2886,2888,2890,2893,2896,2903,2906],{},[2132,2877,2878],{},"L",[2124,2880,2166],{},[2128,2882,2883],{},"1",[2132,2885,2614],{"mathvariant":2134},[2128,2887,2154],{},[2132,2889,2543],{},[2132,2891,2892],{},"h",[2132,2894,2895],{},"o",[2137,2897,2898,2901],{},[2132,2899,2900],{},"v",[2128,2902,2154],{},[2132,2904,2905],{},"S",[2907,2908,2909,2912],"msub",{},[2132,2910,2911],{},"C",[2132,2913,2878],{},[2179,2915,2916],{"encoding":2181},"L = 1\u002F2 rho v^2 S C_L",[1903,2918,2920,2939],{"className":2919,"ariaHidden":1850},[2186],[1903,2921,2923,2927,2930,2933,2936],{"className":2922},[2190],[1903,2924],{"className":2925,"style":2926},[2194],"height:0.6833em;",[1903,2928,2878],{"className":2929},[2242,2280],[1903,2931],{"className":2932,"style":2355},[2272],[1903,2934,2166],{"className":2935},[2359],[1903,2937],{"className":2938,"style":2355},[2272],[1903,2940,2942,2946,2950,2953,2956,2959,2990,2994],{"className":2941},[2190],[1903,2943],{"className":2944,"style":2945},[2194],"height:1.0641em;vertical-align:-0.25em;",[1903,2947,2949],{"className":2948},[2242],"1\u002F2",[1903,2951,2543],{"className":2952,"style":2646},[2242,2280],[1903,2954,2892],{"className":2955},[2242,2280],[1903,2957,2895],{"className":2958},[2242,2280],[1903,2960,2962,2965],{"className":2961},[2242],[1903,2963,2900],{"className":2964,"style":2453},[2242,2280],[1903,2966,2968],{"className":2967},[2209],[1903,2969,2971],{"className":2970},[2213],[1903,2972,2974],{"className":2973},[2218],[1903,2975,2978],{"className":2976,"style":2977},[2222],"height:0.8141em;",[1903,2979,2981,2984],{"style":2980},"top:-3.063em;margin-right:0.05em;",[1903,2982],{"className":2983,"style":2231},[2230],[1903,2985,2987],{"className":2986},[2235,2236,2237,2238],[1903,2988,2154],{"className":2989},[2242,2238],[1903,2991,2905],{"className":2992,"style":2993},[2242,2280],"margin-right:0.0576em;",[1903,2995,2997,3001],{"className":2996},[2242],[1903,2998,2911],{"className":2999,"style":3000},[2242,2280],"margin-right:0.0715em;",[1903,3002,3004],{"className":3003},[2209],[1903,3005,3007,3029],{"className":3006},[2213,2214],[1903,3008,3010,3026],{"className":3009},[2218],[1903,3011,3014],{"className":3012,"style":3013},[2222],"height:0.3283em;",[1903,3015,3017,3020],{"style":3016},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1903,3018],{"className":3019,"style":2231},[2230],[1903,3021,3023],{"className":3022},[2235,2236,2237,2238],[1903,3024,2878],{"className":3025},[2242,2280,2238],[1903,3027,2259],{"className":3028},[2258],[1903,3030,3032],{"className":3031},[2218],[1903,3033,3036],{"className":3034,"style":3035},[2222],"height:0.15em;",[1903,3037],{}," for lift force.",[1793,3040,3041,3042,3169],{},"The famous Euler's identity: ",[1903,3043,3045,3080],{"className":3044},[2104],[1903,3046,3048],{"className":3047},[2108],[2110,3049,3050],{"xmlns":2112},[2115,3051,3052,3077],{},[2118,3053,3054,3060,3062,3064,3066,3068,3071,3073,3075],{},[2137,3055,3056,3058],{},[2132,3057,2141],{},[2124,3059,2578],{"stretchy":1841},[2132,3061,2529],{},[2132,3063,1793],{},[2132,3065,2529],{},[2124,3067,2589],{"stretchy":1841},[2124,3069,3070],{},"+",[2128,3072,2883],{},[2124,3074,2166],{},[2128,3076,2130],{},[2179,3078,3079],{"encoding":2181},"e^(i pi) + 1 = 0",[1903,3081,3083,3141,3160],{"className":3082,"ariaHidden":1850},[2186],[1903,3084,3086,3090,3120,3123,3126,3129,3132,3135,3138],{"className":3085},[2190],[1903,3087],{"className":3088,"style":3089},[2194],"height:1.138em;vertical-align:-0.25em;",[1903,3091,3093,3096],{"className":3092},[2242],[1903,3094,2141],{"className":3095},[2242,2280],[1903,3097,3099],{"className":3098},[2209],[1903,3100,3102],{"className":3101},[2213],[1903,3103,3105],{"className":3104},[2218],[1903,3106,3109],{"className":3107,"style":3108},[2222],"height:0.888em;",[1903,3110,3111,3114],{"style":2980},[1903,3112],{"className":3113,"style":2231},[2230],[1903,3115,3117],{"className":3116},[2235,2236,2237,2238],[1903,3118,2578],{"className":3119},[2376,2238],[1903,3121,2529],{"className":3122},[2242,2280],[1903,3124,1793],{"className":3125},[2242,2280],[1903,3127,2529],{"className":3128},[2242,2280],[1903,3130,2589],{"className":3131},[2504],[1903,3133],{"className":3134,"style":2755},[2272],[1903,3136,3070],{"className":3137},[2759],[1903,3139],{"className":3140,"style":2755},[2272],[1903,3142,3144,3148,3151,3154,3157],{"className":3143},[2190],[1903,3145],{"className":3146,"style":3147},[2194],"height:0.6444em;",[1903,3149,2883],{"className":3150},[2242],[1903,3152],{"className":3153,"style":2355},[2272],[1903,3155,2166],{"className":3156},[2359],[1903,3158],{"className":3159,"style":2355},[2272],[1903,3161,3163,3166],{"className":3162},[2190],[1903,3164],{"className":3165,"style":3147},[2194],[1903,3167,2130],{"className":3168},[2242],".",[1831,3171,3173],{"id":3172},"display-math-double-dollar-signs","Display Math (Double Dollar Signs)",[1793,3175,3176],{},"Maxwell's equations:",[1903,3178,3180],{"className":3179},[2100],[1903,3181,3183,3261],{"className":3182},[2104],[1903,3184,3186],{"className":3185},[2108],[2110,3187,3188],{"xmlns":2112,"display":2113},[2115,3189,3190,3258],{},[2118,3191,3192,3194,3196,3198,3200,3202,3204,3206,3208,3210,3212,3214,3217,3219,3221,3223,3225,3228,3230,3232,3234,3236,3238,3240,3242,3244,3246,3248,3250,3252],{},[2132,3193,2540],{},[2132,3195,2543],{},[2132,3197,2546],{},[2132,3199,2161],{},[2132,3201,2529],{},[2132,3203,2141],{},[2132,3205,2532],{},[2132,3207,2535],{},[2132,3209,2161],{},[2132,3211,2895],{},[2132,3213,2535],{},[2132,3215,3216],{},"b",[2132,3218,2895],{},[2132,3220,2551],{},[2132,3222,2161],{},[2124,3224,2578],{"stretchy":1841},[2132,3226,3227],{},"E",[2124,3229,2589],{"stretchy":1841},[2124,3231,2166],{},[2132,3233,2543],{},[2132,3235,2892],{},[2132,3237,2895],{},[2132,3239,2614],{"mathvariant":2134},[2132,3241,2141],{},[2132,3243,1793],{},[2132,3245,2598],{},[2132,3247,2529],{},[2132,3249,2551],{},[2132,3251,2895],{},[2907,3253,3254,3256],{},[2132,3255,2532],{},[2128,3257,2130],{},[2179,3259,3260],{"encoding":2181},"gradient dot bold(E) = rho \u002F epsilon_0",[1903,3262,3264,3333],{"className":3263,"ariaHidden":1850},[2186],[1903,3265,3267,3270,3273,3276,3279,3282,3285,3288,3291,3294,3297,3300,3303,3306,3309,3312,3315,3318,3321,3324,3327,3330],{"className":3266},[2190],[1903,3268],{"className":3269,"style":2824},[2194],[1903,3271,2540],{"className":3272,"style":2453},[2242,2280],[1903,3274,2543],{"className":3275,"style":2646},[2242,2280],[1903,3277,2546],{"className":3278},[2242,2280],[1903,3280,2161],{"className":3281},[2242,2280],[1903,3283,2529],{"className":3284},[2242,2280],[1903,3286,2141],{"className":3287},[2242,2280],[1903,3289,2532],{"className":3290},[2242,2280],[1903,3292,2535],{"className":3293},[2242,2280],[1903,3295,2161],{"className":3296},[2242,2280],[1903,3298,2895],{"className":3299},[2242,2280],[1903,3301,2535],{"className":3302},[2242,2280],[1903,3304,3216],{"className":3305},[2242,2280],[1903,3307,2895],{"className":3308},[2242,2280],[1903,3310,2551],{"className":3311,"style":2656},[2242,2280],[1903,3313,2161],{"className":3314},[2242,2280],[1903,3316,2578],{"className":3317},[2376],[1903,3319,3227],{"className":3320,"style":2993},[2242,2280],[1903,3322,2589],{"className":3323},[2504],[1903,3325],{"className":3326,"style":2355},[2272],[1903,3328,2166],{"className":3329},[2359],[1903,3331],{"className":3332,"style":2355},[2272],[1903,3334,3336,3339,3342,3345,3348,3351,3354,3357,3360,3363,3366,3369],{"className":3335},[2190],[1903,3337],{"className":3338,"style":2824},[2194],[1903,3340,2543],{"className":3341,"style":2646},[2242,2280],[1903,3343,2892],{"className":3344},[2242,2280],[1903,3346,2895],{"className":3347},[2242,2280],[1903,3349,2614],{"className":3350},[2242],[1903,3352,2141],{"className":3353},[2242,2280],[1903,3355,1793],{"className":3356},[2242,2280],[1903,3358,2598],{"className":3359},[2242,2280],[1903,3361,2529],{"className":3362},[2242,2280],[1903,3364,2551],{"className":3365,"style":2656},[2242,2280],[1903,3367,2895],{"className":3368},[2242,2280],[1903,3370,3372,3375],{"className":3371},[2242],[1903,3373,2532],{"className":3374},[2242,2280],[1903,3376,3378],{"className":3377},[2209],[1903,3379,3381,3403],{"className":3380},[2213,2214],[1903,3382,3384,3400],{"className":3383},[2218],[1903,3385,3388],{"className":3386,"style":3387},[2222],"height:0.3011em;",[1903,3389,3391,3394],{"style":3390},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1903,3392],{"className":3393,"style":2231},[2230],[1903,3395,3397],{"className":3396},[2235,2236,2237,2238],[1903,3398,2130],{"className":3399},[2242,2238],[1903,3401,2259],{"className":3402},[2258],[1903,3404,3406],{"className":3405},[2218],[1903,3407,3409],{"className":3408,"style":3035},[2222],[1903,3410],{},[1903,3412,3414],{"className":3413},[2100],[1903,3415,3417,3470],{"className":3416},[2104],[1903,3418,3420],{"className":3419},[2108],[2110,3421,3422],{"xmlns":2112,"display":2113},[2115,3423,3424,3467],{},[2118,3425,3426,3428,3430,3432,3434,3436,3438,3440,3442,3444,3446,3448,3450,3452,3454,3456,3458,3461,3463,3465],{},[2132,3427,2540],{},[2132,3429,2543],{},[2132,3431,2546],{},[2132,3433,2161],{},[2132,3435,2529],{},[2132,3437,2141],{},[2132,3439,2532],{},[2132,3441,2535],{},[2132,3443,2161],{},[2132,3445,2895],{},[2132,3447,2535],{},[2132,3449,3216],{},[2132,3451,2895],{},[2132,3453,2551],{},[2132,3455,2161],{},[2124,3457,2578],{"stretchy":1841},[2132,3459,3460],{},"B",[2124,3462,2589],{"stretchy":1841},[2124,3464,2166],{},[2128,3466,2130],{},[2179,3468,3469],{"encoding":2181},"gradient dot bold(B) = 0",[1903,3471,3473,3543],{"className":3472,"ariaHidden":1850},[2186],[1903,3474,3476,3479,3482,3485,3488,3491,3494,3497,3500,3503,3506,3509,3512,3515,3518,3521,3524,3527,3531,3534,3537,3540],{"className":3475},[2190],[1903,3477],{"className":3478,"style":2824},[2194],[1903,3480,2540],{"className":3481,"style":2453},[2242,2280],[1903,3483,2543],{"className":3484,"style":2646},[2242,2280],[1903,3486,2546],{"className":3487},[2242,2280],[1903,3489,2161],{"className":3490},[2242,2280],[1903,3492,2529],{"className":3493},[2242,2280],[1903,3495,2141],{"className":3496},[2242,2280],[1903,3498,2532],{"className":3499},[2242,2280],[1903,3501,2535],{"className":3502},[2242,2280],[1903,3504,2161],{"className":3505},[2242,2280],[1903,3507,2895],{"className":3508},[2242,2280],[1903,3510,2535],{"className":3511},[2242,2280],[1903,3513,3216],{"className":3514},[2242,2280],[1903,3516,2895],{"className":3517},[2242,2280],[1903,3519,2551],{"className":3520,"style":2656},[2242,2280],[1903,3522,2161],{"className":3523},[2242,2280],[1903,3525,2578],{"className":3526},[2376],[1903,3528,3460],{"className":3529,"style":3530},[2242,2280],"margin-right:0.0502em;",[1903,3532,2589],{"className":3533},[2504],[1903,3535],{"className":3536,"style":2355},[2272],[1903,3538,2166],{"className":3539},[2359],[1903,3541],{"className":3542,"style":2355},[2272],[1903,3544,3546,3549],{"className":3545},[2190],[1903,3547],{"className":3548,"style":3147},[2194],[1903,3550,2130],{"className":3551},[2242],[1903,3553,3555],{"className":3554},[2100],[1903,3556,3558,3669],{"className":3557},[2104],[1903,3559,3561],{"className":3560},[2108],[2110,3562,3563],{"xmlns":2112,"display":2113},[2115,3564,3565,3666],{},[2118,3566,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587,3590,3592,3594,3596,3598,3600,3602,3604,3606,3608,3610,3612,3614,3616,3618,3620,3622,3624,3626,3628,3630,3632,3634,3636,3638,3640,3642,3644,3646,3648,3650,3652,3654,3656,3658,3660,3662,3664],{},[2132,3568,2540],{},[2132,3570,2543],{},[2132,3572,2546],{},[2132,3574,2161],{},[2132,3576,2529],{},[2132,3578,2141],{},[2132,3580,2532],{},[2132,3582,2535],{},[2132,3584,2535],{},[2132,3586,2529],{},[2132,3588,3589],{},"m",[2132,3591,2141],{},[2132,3593,2598],{},[2132,3595,3216],{},[2132,3597,2895],{},[2132,3599,2551],{},[2132,3601,2161],{},[2124,3603,2578],{"stretchy":1841},[2132,3605,3227],{},[2124,3607,2589],{"stretchy":1841},[2124,3609,2166],{},[2124,3611,2146],{},[2124,3613,2578],{"stretchy":1841},[2132,3615,1793],{},[2132,3617,2546],{},[2132,3619,2543],{},[2132,3621,2535],{},[2132,3623,2529],{},[2132,3625,2546],{},[2132,3627,2551],{},[2132,3629,3216],{},[2132,3631,2895],{},[2132,3633,2551],{},[2132,3635,2161],{},[2124,3637,2578],{"stretchy":1841},[2132,3639,3460],{},[2124,3641,2589],{"stretchy":1841},[2124,3643,2589],{"stretchy":1841},[2132,3645,2614],{"mathvariant":2134},[2124,3647,2578],{"stretchy":1841},[2132,3649,1793],{},[2132,3651,2546],{},[2132,3653,2543],{},[2132,3655,2535],{},[2132,3657,2529],{},[2132,3659,2546],{},[2132,3661,2551],{},[2132,3663,2535],{},[2124,3665,2589],{"stretchy":1841},[2179,3667,3668],{"encoding":2181},"gradient times bold(E) = -(partial bold(B))\u002F(partial t)",[1903,3670,3672,3741],{"className":3671,"ariaHidden":1850},[2186],[1903,3673,3675,3678,3681,3684,3687,3690,3693,3696,3699,3703,3707,3711,3714,3717,3720,3723,3726,3729,3732,3735,3738],{"className":3674},[2190],[1903,3676],{"className":3677,"style":2824},[2194],[1903,3679,2540],{"className":3680,"style":2453},[2242,2280],[1903,3682,2543],{"className":3683,"style":2646},[2242,2280],[1903,3685,2546],{"className":3686},[2242,2280],[1903,3688,2161],{"className":3689},[2242,2280],[1903,3691,2529],{"className":3692},[2242,2280],[1903,3694,2141],{"className":3695},[2242,2280],[1903,3697,2532],{"className":3698},[2242,2280],[1903,3700,3702],{"className":3701},[2242,2280],"tt",[1903,3704,3706],{"className":3705},[2242,2280],"im",[1903,3708,3710],{"className":3709},[2242,2280],"es",[1903,3712,3216],{"className":3713},[2242,2280],[1903,3715,2895],{"className":3716},[2242,2280],[1903,3718,2551],{"className":3719,"style":2656},[2242,2280],[1903,3721,2161],{"className":3722},[2242,2280],[1903,3724,2578],{"className":3725},[2376],[1903,3727,3227],{"className":3728,"style":2993},[2242,2280],[1903,3730,2589],{"className":3731},[2504],[1903,3733],{"className":3734,"style":2355},[2272],[1903,3736,2166],{"className":3737},[2359],[1903,3739],{"className":3740,"style":2355},[2272],[1903,3742,3744,3747,3750,3753,3756,3759,3762,3765,3769,3772,3775,3778,3781,3784,3787,3790,3794,3797,3800,3803,3806,3809,3812,3815,3818,3821],{"className":3743},[2190],[1903,3745],{"className":3746,"style":2824},[2194],[1903,3748,2146],{"className":3749},[2242],[1903,3751,2578],{"className":3752},[2376],[1903,3754,1793],{"className":3755},[2242,2280],[1903,3757,2546],{"className":3758},[2242,2280],[1903,3760,2543],{"className":3761,"style":2646},[2242,2280],[1903,3763,2535],{"className":3764},[2242,2280],[1903,3766,3768],{"className":3767},[2242,2280],"ia",[1903,3770,2551],{"className":3771,"style":2656},[2242,2280],[1903,3773,3216],{"className":3774},[2242,2280],[1903,3776,2895],{"className":3777},[2242,2280],[1903,3779,2551],{"className":3780,"style":2656},[2242,2280],[1903,3782,2161],{"className":3783},[2242,2280],[1903,3785,2578],{"className":3786},[2376],[1903,3788,3460],{"className":3789,"style":3530},[2242,2280],[1903,3791,3793],{"className":3792},[2504],"))",[1903,3795,2614],{"className":3796},[2242],[1903,3798,2578],{"className":3799},[2376],[1903,3801,1793],{"className":3802},[2242,2280],[1903,3804,2546],{"className":3805},[2242,2280],[1903,3807,2543],{"className":3808,"style":2646},[2242,2280],[1903,3810,2535],{"className":3811},[2242,2280],[1903,3813,3768],{"className":3814},[2242,2280],[1903,3816,2551],{"className":3817,"style":2656},[2242,2280],[1903,3819,2535],{"className":3820},[2242,2280],[1903,3822,2589],{"className":3823},[2504],[1903,3825,3827],{"className":3826},[2100],[1903,3828,3830,3990],{"className":3829},[2104],[1903,3831,3833],{"className":3832},[2108],[2110,3834,3835],{"xmlns":2112,"display":2113},[2115,3836,3837,3987],{},[2118,3838,3839,3841,3843,3845,3847,3849,3851,3853,3855,3857,3859,3861,3863,3865,3867,3869,3871,3873,3875,3877,3879,3881,3883,3890,3892,3894,3896,3898,3900,3903,3905,3907,3909,3915,3917,3919,3921,3923,3925,3927,3933,3935,3937,3939,3941,3943,3945,3947,3949,3951,3953,3955,3957,3959,3961,3963,3965,3967,3969,3971,3973,3975,3977,3979,3981,3983,3985],{},[2132,3840,2540],{},[2132,3842,2543],{},[2132,3844,2546],{},[2132,3846,2161],{},[2132,3848,2529],{},[2132,3850,2141],{},[2132,3852,2532],{},[2132,3854,2535],{},[2132,3856,2535],{},[2132,3858,2529],{},[2132,3860,3589],{},[2132,3862,2141],{},[2132,3864,2598],{},[2132,3866,3216],{},[2132,3868,2895],{},[2132,3870,2551],{},[2132,3872,2161],{},[2124,3874,2578],{"stretchy":1841},[2132,3876,3460],{},[2124,3878,2589],{"stretchy":1841},[2124,3880,2166],{},[2132,3882,3589],{},[2907,3884,3885,3888],{},[2132,3886,3887],{},"u",[2128,3889,2130],{},[2132,3891,3216],{},[2132,3893,2895],{},[2132,3895,2551],{},[2132,3897,2161],{},[2124,3899,2578],{"stretchy":1841},[2132,3901,3902],{},"J",[2124,3904,2589],{"stretchy":1841},[2124,3906,3070],{},[2132,3908,3589],{},[2907,3910,3911,3913],{},[2132,3912,3887],{},[2128,3914,2130],{},[2132,3916,2141],{},[2132,3918,1793],{},[2132,3920,2598],{},[2132,3922,2529],{},[2132,3924,2551],{},[2132,3926,2895],{},[2907,3928,3929,3931],{},[2132,3930,2532],{},[2128,3932,2130],{},[2124,3934,2578],{"stretchy":1841},[2132,3936,1793],{},[2132,3938,2546],{},[2132,3940,2543],{},[2132,3942,2535],{},[2132,3944,2529],{},[2132,3946,2546],{},[2132,3948,2551],{},[2132,3950,3216],{},[2132,3952,2895],{},[2132,3954,2551],{},[2132,3956,2161],{},[2124,3958,2578],{"stretchy":1841},[2132,3960,3227],{},[2124,3962,2589],{"stretchy":1841},[2124,3964,2589],{"stretchy":1841},[2132,3966,2614],{"mathvariant":2134},[2124,3968,2578],{"stretchy":1841},[2132,3970,1793],{},[2132,3972,2546],{},[2132,3974,2543],{},[2132,3976,2535],{},[2132,3978,2529],{},[2132,3980,2546],{},[2132,3982,2551],{},[2132,3984,2535],{},[2124,3986,2589],{"stretchy":1841},[2179,3988,3989],{"encoding":2181},"\ngradient times bold(B) = mu_0 bold(J) + mu_0 epsilon_0 (partial bold(E))\u002F(partial t)",[1903,3991,3993,4059,4139],{"className":3992,"ariaHidden":1850},[2186],[1903,3994,3996,3999,4002,4005,4008,4011,4014,4017,4020,4023,4026,4029,4032,4035,4038,4041,4044,4047,4050,4053,4056],{"className":3995},[2190],[1903,3997],{"className":3998,"style":2824},[2194],[1903,4000,2540],{"className":4001,"style":2453},[2242,2280],[1903,4003,2543],{"className":4004,"style":2646},[2242,2280],[1903,4006,2546],{"className":4007},[2242,2280],[1903,4009,2161],{"className":4010},[2242,2280],[1903,4012,2529],{"className":4013},[2242,2280],[1903,4015,2141],{"className":4016},[2242,2280],[1903,4018,2532],{"className":4019},[2242,2280],[1903,4021,3702],{"className":4022},[2242,2280],[1903,4024,3706],{"className":4025},[2242,2280],[1903,4027,3710],{"className":4028},[2242,2280],[1903,4030,3216],{"className":4031},[2242,2280],[1903,4033,2895],{"className":4034},[2242,2280],[1903,4036,2551],{"className":4037,"style":2656},[2242,2280],[1903,4039,2161],{"className":4040},[2242,2280],[1903,4042,2578],{"className":4043},[2376],[1903,4045,3460],{"className":4046,"style":3530},[2242,2280],[1903,4048,2589],{"className":4049},[2504],[1903,4051],{"className":4052,"style":2355},[2272],[1903,4054,2166],{"className":4055},[2359],[1903,4057],{"className":4058,"style":2355},[2272],[1903,4060,4062,4065,4068,4108,4111,4114,4117,4120,4123,4127,4130,4133,4136],{"className":4061},[2190],[1903,4063],{"className":4064,"style":2824},[2194],[1903,4066,3589],{"className":4067},[2242,2280],[1903,4069,4071,4074],{"className":4070},[2242],[1903,4072,3887],{"className":4073},[2242,2280],[1903,4075,4077],{"className":4076},[2209],[1903,4078,4080,4100],{"className":4079},[2213,2214],[1903,4081,4083,4097],{"className":4082},[2218],[1903,4084,4086],{"className":4085,"style":3387},[2222],[1903,4087,4088,4091],{"style":3390},[1903,4089],{"className":4090,"style":2231},[2230],[1903,4092,4094],{"className":4093},[2235,2236,2237,2238],[1903,4095,2130],{"className":4096},[2242,2238],[1903,4098,2259],{"className":4099},[2258],[1903,4101,4103],{"className":4102},[2218],[1903,4104,4106],{"className":4105,"style":3035},[2222],[1903,4107],{},[1903,4109,3216],{"className":4110},[2242,2280],[1903,4112,2895],{"className":4113},[2242,2280],[1903,4115,2551],{"className":4116,"style":2656},[2242,2280],[1903,4118,2161],{"className":4119},[2242,2280],[1903,4121,2578],{"className":4122},[2376],[1903,4124,3902],{"className":4125,"style":4126},[2242,2280],"margin-right:0.0962em;",[1903,4128,2589],{"className":4129},[2504],[1903,4131],{"className":4132,"style":2755},[2272],[1903,4134,3070],{"className":4135},[2759],[1903,4137],{"className":4138,"style":2755},[2272],[1903,4140,4142,4145,4148,4188,4191,4194,4197,4200,4203,4206,4246,4249,4252,4255,4258,4261,4264,4267,4270,4273,4276,4279,4282,4285,4288,4291,4294,4297,4300,4303,4306,4309,4312,4315],{"className":4141},[2190],[1903,4143],{"className":4144,"style":2824},[2194],[1903,4146,3589],{"className":4147},[2242,2280],[1903,4149,4151,4154],{"className":4150},[2242],[1903,4152,3887],{"className":4153},[2242,2280],[1903,4155,4157],{"className":4156},[2209],[1903,4158,4160,4180],{"className":4159},[2213,2214],[1903,4161,4163,4177],{"className":4162},[2218],[1903,4164,4166],{"className":4165,"style":3387},[2222],[1903,4167,4168,4171],{"style":3390},[1903,4169],{"className":4170,"style":2231},[2230],[1903,4172,4174],{"className":4173},[2235,2236,2237,2238],[1903,4175,2130],{"className":4176},[2242,2238],[1903,4178,2259],{"className":4179},[2258],[1903,4181,4183],{"className":4182},[2218],[1903,4184,4186],{"className":4185,"style":3035},[2222],[1903,4187],{},[1903,4189,2141],{"className":4190},[2242,2280],[1903,4192,1793],{"className":4193},[2242,2280],[1903,4195,2598],{"className":4196},[2242,2280],[1903,4198,2529],{"className":4199},[2242,2280],[1903,4201,2551],{"className":4202,"style":2656},[2242,2280],[1903,4204,2895],{"className":4205},[2242,2280],[1903,4207,4209,4212],{"className":4208},[2242],[1903,4210,2532],{"className":4211},[2242,2280],[1903,4213,4215],{"className":4214},[2209],[1903,4216,4218,4238],{"className":4217},[2213,2214],[1903,4219,4221,4235],{"className":4220},[2218],[1903,4222,4224],{"className":4223,"style":3387},[2222],[1903,4225,4226,4229],{"style":3390},[1903,4227],{"className":4228,"style":2231},[2230],[1903,4230,4232],{"className":4231},[2235,2236,2237,2238],[1903,4233,2130],{"className":4234},[2242,2238],[1903,4236,2259],{"className":4237},[2258],[1903,4239,4241],{"className":4240},[2218],[1903,4242,4244],{"className":4243,"style":3035},[2222],[1903,4245],{},[1903,4247,2578],{"className":4248},[2376],[1903,4250,1793],{"className":4251},[2242,2280],[1903,4253,2546],{"className":4254},[2242,2280],[1903,4256,2543],{"className":4257,"style":2646},[2242,2280],[1903,4259,2535],{"className":4260},[2242,2280],[1903,4262,3768],{"className":4263},[2242,2280],[1903,4265,2551],{"className":4266,"style":2656},[2242,2280],[1903,4268,3216],{"className":4269},[2242,2280],[1903,4271,2895],{"className":4272},[2242,2280],[1903,4274,2551],{"className":4275,"style":2656},[2242,2280],[1903,4277,2161],{"className":4278},[2242,2280],[1903,4280,2578],{"className":4281},[2376],[1903,4283,3227],{"className":4284,"style":2993},[2242,2280],[1903,4286,3793],{"className":4287},[2504],[1903,4289,2614],{"className":4290},[2242],[1903,4292,2578],{"className":4293},[2376],[1903,4295,1793],{"className":4296},[2242,2280],[1903,4298,2546],{"className":4299},[2242,2280],[1903,4301,2543],{"className":4302,"style":2646},[2242,2280],[1903,4304,2535],{"className":4305},[2242,2280],[1903,4307,3768],{"className":4308},[2242,2280],[1903,4310,2551],{"className":4311,"style":2656},[2242,2280],[1903,4313,2535],{"className":4314},[2242,2280],[1903,4316,2589],{"className":4317},[2504],[1831,4319,4321],{"id":4320},"display-math-math-code-block","Display Math (Math Code Block)",[1793,4323,4324,4325,4327],{},"You can also use fenced code blocks with ",[1805,4326,2110],{}," language:",[1903,4329,4331,4373],{"className":4330},[2104],[1903,4332,4334],{"className":4333},[2108],[2110,4335,4336],{"xmlns":2112},[2115,4337,4338,4370],{},[2118,4339,4340,4342,4344,4346,4348,4350,4352,4354,4356,4362,4364],{},[2132,4341,2878],{},[2124,4343,2166],{},[2128,4345,2883],{},[2132,4347,2614],{"mathvariant":2134},[2128,4349,2154],{},[2132,4351,2543],{},[2132,4353,2892],{},[2132,4355,2895],{},[2137,4357,4358,4360],{},[2132,4359,2900],{},[2128,4361,2154],{},[2132,4363,2905],{},[2907,4365,4366,4368],{},[2132,4367,2911],{},[2132,4369,2878],{},[2179,4371,4372],{"encoding":2181},"L = 1\u002F2 rho v^2 S C_L\n",[1903,4374,4376,4394],{"className":4375,"ariaHidden":1850},[2186],[1903,4377,4379,4382,4385,4388,4391],{"className":4378},[2190],[1903,4380],{"className":4381,"style":2926},[2194],[1903,4383,2878],{"className":4384},[2242,2280],[1903,4386],{"className":4387,"style":2355},[2272],[1903,4389,2166],{"className":4390},[2359],[1903,4392],{"className":4393,"style":2355},[2272],[1903,4395,4397,4400,4403,4406,4409,4412,4441,4444],{"className":4396},[2190],[1903,4398],{"className":4399,"style":2945},[2194],[1903,4401,2949],{"className":4402},[2242],[1903,4404,2543],{"className":4405,"style":2646},[2242,2280],[1903,4407,2892],{"className":4408},[2242,2280],[1903,4410,2895],{"className":4411},[2242,2280],[1903,4413,4415,4418],{"className":4414},[2242],[1903,4416,2900],{"className":4417,"style":2453},[2242,2280],[1903,4419,4421],{"className":4420},[2209],[1903,4422,4424],{"className":4423},[2213],[1903,4425,4427],{"className":4426},[2218],[1903,4428,4430],{"className":4429,"style":2977},[2222],[1903,4431,4432,4435],{"style":2980},[1903,4433],{"className":4434,"style":2231},[2230],[1903,4436,4438],{"className":4437},[2235,2236,2237,2238],[1903,4439,2154],{"className":4440},[2242,2238],[1903,4442,2905],{"className":4443,"style":2993},[2242,2280],[1903,4445,4447,4450],{"className":4446},[2242],[1903,4448,2911],{"className":4449,"style":3000},[2242,2280],[1903,4451,4453],{"className":4452},[2209],[1903,4454,4456,4476],{"className":4455},[2213,2214],[1903,4457,4459,4473],{"className":4458},[2218],[1903,4460,4462],{"className":4461,"style":3013},[2222],[1903,4463,4464,4467],{"style":3016},[1903,4465],{"className":4466,"style":2231},[2230],[1903,4468,4470],{"className":4469},[2235,2236,2237,2238],[1903,4471,2878],{"className":4472},[2242,2280,2238],[1903,4474,2259],{"className":4475},[2258],[1903,4477,4479],{"className":4478},[2218],[1903,4480,4482],{"className":4481,"style":3035},[2222],[1903,4483],{},[1903,4485,4487,4531],{"className":4486},[2104],[1903,4488,4490],{"className":4489},[2108],[2110,4491,4492],{"xmlns":2112},[2115,4493,4494,4528],{},[2118,4495,4496,4499,4501,4504,4506,4512,4518,4520,4522],{},[2132,4497,4498],{},"F",[2124,4500,2166],{},[2132,4502,4503],{},"G",[2124,4505,2578],{"stretchy":1841},[2907,4507,4508,4510],{},[2132,4509,3589],{},[2128,4511,2883],{},[2907,4513,4514,4516],{},[2132,4515,3589],{},[2128,4517,2154],{},[2124,4519,2589],{"stretchy":1841},[2132,4521,2614],{"mathvariant":2134},[2137,4523,4524,4526],{},[2132,4525,2543],{},[2128,4527,2154],{},[2179,4529,4530],{"encoding":2181},"F = G (m_1 m_2)\u002Fr^2\n",[1903,4532,4534,4553],{"className":4533,"ariaHidden":1850},[2186],[1903,4535,4537,4540,4544,4547,4550],{"className":4536},[2190],[1903,4538],{"className":4539,"style":2926},[2194],[1903,4541,4498],{"className":4542,"style":4543},[2242,2280],"margin-right:0.1389em;",[1903,4545],{"className":4546,"style":2355},[2272],[1903,4548,2166],{"className":4549},[2359],[1903,4551],{"className":4552,"style":2355},[2272],[1903,4554,4556,4559,4562,4565,4605,4645,4648,4651],{"className":4555},[2190],[1903,4557],{"className":4558,"style":2945},[2194],[1903,4560,4503],{"className":4561},[2242,2280],[1903,4563,2578],{"className":4564},[2376],[1903,4566,4568,4571],{"className":4567},[2242],[1903,4569,3589],{"className":4570},[2242,2280],[1903,4572,4574],{"className":4573},[2209],[1903,4575,4577,4597],{"className":4576},[2213,2214],[1903,4578,4580,4594],{"className":4579},[2218],[1903,4581,4583],{"className":4582,"style":3387},[2222],[1903,4584,4585,4588],{"style":3390},[1903,4586],{"className":4587,"style":2231},[2230],[1903,4589,4591],{"className":4590},[2235,2236,2237,2238],[1903,4592,2883],{"className":4593},[2242,2238],[1903,4595,2259],{"className":4596},[2258],[1903,4598,4600],{"className":4599},[2218],[1903,4601,4603],{"className":4602,"style":3035},[2222],[1903,4604],{},[1903,4606,4608,4611],{"className":4607},[2242],[1903,4609,3589],{"className":4610},[2242,2280],[1903,4612,4614],{"className":4613},[2209],[1903,4615,4617,4637],{"className":4616},[2213,2214],[1903,4618,4620,4634],{"className":4619},[2218],[1903,4621,4623],{"className":4622,"style":3387},[2222],[1903,4624,4625,4628],{"style":3390},[1903,4626],{"className":4627,"style":2231},[2230],[1903,4629,4631],{"className":4630},[2235,2236,2237,2238],[1903,4632,2154],{"className":4633},[2242,2238],[1903,4635,2259],{"className":4636},[2258],[1903,4638,4640],{"className":4639},[2218],[1903,4641,4643],{"className":4642,"style":3035},[2222],[1903,4644],{},[1903,4646,2589],{"className":4647},[2504],[1903,4649,2614],{"className":4650},[2242],[1903,4652,4654,4657],{"className":4653},[2242],[1903,4655,2543],{"className":4656,"style":2646},[2242,2280],[1903,4658,4660],{"className":4659},[2209],[1903,4661,4663],{"className":4662},[2213],[1903,4664,4666],{"className":4665},[2218],[1903,4667,4669],{"className":4668,"style":2977},[2222],[1903,4670,4671,4674],{"style":2980},[1903,4672],{"className":4673,"style":2231},[2230],[1903,4675,4677],{"className":4676},[2235,2236,2237,2238],[1903,4678,2154],{"className":4679},[2242,2238],[1797,4681,4683],{"id":4682},"more-examples","More Examples",[1831,4685,4687],{"id":4686},"calculus","Calculus",[1793,4689,4690],{},"Derivative definition:",[1903,4692,4694],{"className":4693},[2100],[1903,4695,4697,4782],{"className":4696},[2104],[1903,4698,4700],{"className":4699},[2108],[2110,4701,4702],{"xmlns":2112,"display":2113},[2115,4703,4704,4779],{},[2118,4705,4706,4714,4716,4718,4720,4722,4724,4726,4732,4734,4736,4738,4740,4742,4745,4747,4749,4751,4753,4755,4757,4759,4761,4763,4765,4767,4769,4771,4773,4775,4777],{},[2137,4707,4708,4710],{},[2132,4709,2560],{},[2124,4711,4713],{"mathvariant":2134,"lspace":4712,"rspace":4712},"0em","′",[2124,4715,2578],{"stretchy":1841},[2132,4717,2151],{},[2124,4719,2589],{"stretchy":1841},[2124,4721,2166],{},[2132,4723,2551],{},[2132,4725,2529],{},[2907,4727,4728,4730],{},[2132,4729,3589],{},[2124,4731,2578],{"stretchy":1841},[2132,4733,2892],{},[2132,4735,2546],{},[2132,4737,2543],{},[2132,4739,2543],{},[2132,4741,2895],{},[2132,4743,4744],{},"w",[2128,4746,2130],{},[2124,4748,2589],{"stretchy":1841},[2124,4750,2578],{"stretchy":1841},[2132,4752,2560],{},[2124,4754,2578],{"stretchy":1841},[2132,4756,2151],{},[2124,4758,3070],{},[2132,4760,2892],{},[2124,4762,2589],{"stretchy":1841},[2124,4764,2146],{},[2132,4766,2560],{},[2124,4768,2578],{"stretchy":1841},[2132,4770,2151],{},[2124,4772,2589],{"stretchy":1841},[2124,4774,2589],{"stretchy":1841},[2132,4776,2614],{"mathvariant":2134},[2132,4778,2892],{},[2179,4780,4781],{"encoding":2181},"f'(x) = lim_(h arrow 0) (f(x+h) - f(x))\u002Fh",[1903,4783,4785,4843,4943,4964],{"className":4784,"ariaHidden":1850},[2186],[1903,4786,4788,4792,4825,4828,4831,4834,4837,4840],{"className":4787},[2190],[1903,4789],{"className":4790,"style":4791},[2194],"height:1.0519em;vertical-align:-0.25em;",[1903,4793,4795,4798],{"className":4794},[2242],[1903,4796,2560],{"className":4797,"style":2711},[2242,2280],[1903,4799,4801],{"className":4800},[2209],[1903,4802,4804],{"className":4803},[2213],[1903,4805,4807],{"className":4806},[2218],[1903,4808,4811],{"className":4809,"style":4810},[2222],"height:0.8019em;",[1903,4812,4813,4816],{"style":2296},[1903,4814],{"className":4815,"style":2231},[2230],[1903,4817,4819],{"className":4818},[2235,2236,2237,2238],[1903,4820,4822],{"className":4821},[2242,2238],[1903,4823,4713],{"className":4824},[2242,2238],[1903,4826,2578],{"className":4827},[2376],[1903,4829,2151],{"className":4830},[2242,2280],[1903,4832,2589],{"className":4833},[2504],[1903,4835],{"className":4836,"style":2355},[2272],[1903,4838,2166],{"className":4839},[2359],[1903,4841],{"className":4842,"style":2355},[2272],[1903,4844,4846,4850,4853,4856,4899,4903,4906,4909,4912,4916,4919,4922,4925,4928,4931,4934,4937,4940],{"className":4845},[2190],[1903,4847],{"className":4848,"style":4849},[2194],"height:1.1052em;vertical-align:-0.3552em;",[1903,4851,2551],{"className":4852,"style":2656},[2242,2280],[1903,4854,2529],{"className":4855},[2242,2280],[1903,4857,4859,4862],{"className":4858},[2242],[1903,4860,3589],{"className":4861},[2242,2280],[1903,4863,4865],{"className":4864},[2209],[1903,4866,4868,4890],{"className":4867},[2213,2214],[1903,4869,4871,4887],{"className":4870},[2218],[1903,4872,4875],{"className":4873,"style":4874},[2222],"height:0.3448em;",[1903,4876,4878,4881],{"style":4877},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[1903,4879],{"className":4880,"style":2231},[2230],[1903,4882,4884],{"className":4883},[2235,2236,2237,2238],[1903,4885,2578],{"className":4886},[2376,2238],[1903,4888,2259],{"className":4889},[2258],[1903,4891,4893],{"className":4892},[2218],[1903,4894,4897],{"className":4895,"style":4896},[2222],"height:0.3552em;",[1903,4898],{},[1903,4900,4902],{"className":4901},[2242,2280],"ha",[1903,4904,2543],{"className":4905,"style":2646},[2242,2280],[1903,4907,2543],{"className":4908,"style":2646},[2242,2280],[1903,4910,2895],{"className":4911},[2242,2280],[1903,4913,4744],{"className":4914,"style":4915},[2242,2280],"margin-right:0.0269em;",[1903,4917,2130],{"className":4918},[2242],[1903,4920,2589],{"className":4921},[2504],[1903,4923,2578],{"className":4924},[2376],[1903,4926,2560],{"className":4927,"style":2711},[2242,2280],[1903,4929,2578],{"className":4930},[2376],[1903,4932,2151],{"className":4933},[2242,2280],[1903,4935],{"className":4936,"style":2755},[2272],[1903,4938,3070],{"className":4939},[2759],[1903,4941],{"className":4942,"style":2755},[2272],[1903,4944,4946,4949,4952,4955,4958,4961],{"className":4945},[2190],[1903,4947],{"className":4948,"style":2824},[2194],[1903,4950,2892],{"className":4951},[2242,2280],[1903,4953,2589],{"className":4954},[2504],[1903,4956],{"className":4957,"style":2755},[2272],[1903,4959,2146],{"className":4960},[2759],[1903,4962],{"className":4963,"style":2755},[2272],[1903,4965,4967,4970,4973,4976,4979,4982,4985],{"className":4966},[2190],[1903,4968],{"className":4969,"style":2824},[2194],[1903,4971,2560],{"className":4972,"style":2711},[2242,2280],[1903,4974,2578],{"className":4975},[2376],[1903,4977,2151],{"className":4978},[2242,2280],[1903,4980,3793],{"className":4981},[2504],[1903,4983,2614],{"className":4984},[2242],[1903,4986,2892],{"className":4987},[2242,2280],[1793,4989,4990],{},"Taylor series:",[1903,4992,4994],{"className":4993},[2100],[1903,4995,4997,5104],{"className":4996},[2104],[1903,4998,5000],{"className":4999},[2108],[2110,5001,5002],{"xmlns":2112,"display":2113},[2115,5003,5004,5101],{},[2118,5005,5006,5008,5010,5012,5014,5016,5018,5020,5026,5028,5030,5032,5038,5040,5042,5044,5046,5048,5050,5052,5054,5060,5062,5064,5066,5068,5070,5072,5074,5076,5078,5080,5082,5085,5087,5089,5091,5093,5095],{},[2132,5007,2560],{},[2124,5009,2578],{"stretchy":1841},[2132,5011,2151],{},[2124,5013,2589],{"stretchy":1841},[2124,5015,2166],{},[2132,5017,2598],{},[2132,5019,3887],{},[2907,5021,5022,5024],{},[2132,5023,3589],{},[2124,5025,2578],{"stretchy":1841},[2132,5027,2532],{},[2124,5029,2166],{},[2128,5031,2130],{},[2137,5033,5034,5036],{},[2124,5035,2589],{"stretchy":1841},[2132,5037,2529],{},[2132,5039,2532],{},[2132,5041,2560],{},[2132,5043,2529],{},[2132,5045,2532],{},[2132,5047,2529],{},[2132,5049,2535],{},[2132,5051,2571],{},[2124,5053,2578],{"stretchy":1841},[2137,5055,5056,5058],{},[2132,5057,2560],{},[2124,5059,2578],{"stretchy":1841},[2124,5061,2578],{"stretchy":1841},[2132,5063,2532],{},[2124,5065,2589],{"stretchy":1841},[2124,5067,2589],{"stretchy":1841},[2124,5069,2578],{"stretchy":1841},[2132,5071,2546],{},[2124,5073,2589],{"stretchy":1841},[2124,5075,2589],{"stretchy":1841},[2132,5077,2614],{"mathvariant":2134},[2124,5079,2578],{"stretchy":1841},[2132,5081,2532],{},[2124,5083,5084],{"stretchy":1841},"!",[2124,5086,2589],{"stretchy":1841},[2124,5088,2578],{"stretchy":1841},[2132,5090,2151],{},[2124,5092,2146],{},[2132,5094,2546],{},[2137,5096,5097,5099],{},[2124,5098,2589],{"stretchy":1841},[2132,5100,2532],{},[2179,5102,5103],{"encoding":2181},"f(x) = sum_(n=0)^infinity (f^((n))(a))\u002F(n!) (x-a)^n",[1903,5105,5107,5134,5199,5331],{"className":5106,"ariaHidden":1850},[2186],[1903,5108,5110,5113,5116,5119,5122,5125,5128,5131],{"className":5109},[2190],[1903,5111],{"className":5112,"style":2824},[2194],[1903,5114,2560],{"className":5115,"style":2711},[2242,2280],[1903,5117,2578],{"className":5118},[2376],[1903,5120,2151],{"className":5121},[2242,2280],[1903,5123,2589],{"className":5124},[2504],[1903,5126],{"className":5127,"style":2355},[2272],[1903,5129,2166],{"className":5130},[2359],[1903,5132],{"className":5133,"style":2355},[2272],[1903,5135,5137,5141,5144,5147,5187,5190,5193,5196],{"className":5136},[2190],[1903,5138],{"className":5139,"style":5140},[2194],"height:0.7858em;vertical-align:-0.3552em;",[1903,5142,2598],{"className":5143},[2242,2280],[1903,5145,3887],{"className":5146},[2242,2280],[1903,5148,5150,5153],{"className":5149},[2242],[1903,5151,3589],{"className":5152},[2242,2280],[1903,5154,5156],{"className":5155},[2209],[1903,5157,5159,5179],{"className":5158},[2213,2214],[1903,5160,5162,5176],{"className":5161},[2218],[1903,5163,5165],{"className":5164,"style":4874},[2222],[1903,5166,5167,5170],{"style":4877},[1903,5168],{"className":5169,"style":2231},[2230],[1903,5171,5173],{"className":5172},[2235,2236,2237,2238],[1903,5174,2578],{"className":5175},[2376,2238],[1903,5177,2259],{"className":5178},[2258],[1903,5180,5182],{"className":5181},[2218],[1903,5183,5185],{"className":5184,"style":4896},[2222],[1903,5186],{},[1903,5188,2532],{"className":5189},[2242,2280],[1903,5191],{"className":5192,"style":2355},[2272],[1903,5194,2166],{"className":5195},[2359],[1903,5197],{"className":5198,"style":2355},[2272],[1903,5200,5202,5206,5209,5238,5241,5244,5247,5250,5253,5256,5285,5288,5291,5294,5297,5300,5303,5306,5309,5312,5316,5319,5322,5325,5328],{"className":5201},[2190],[1903,5203],{"className":5204,"style":5205},[2194],"height:1.188em;vertical-align:-0.25em;",[1903,5207,2130],{"className":5208},[2242],[1903,5210,5212,5215],{"className":5211},[2504],[1903,5213,2589],{"className":5214},[2504],[1903,5216,5218],{"className":5217},[2209],[1903,5219,5221],{"className":5220},[2213],[1903,5222,5224],{"className":5223},[2218],[1903,5225,5227],{"className":5226,"style":2669},[2222],[1903,5228,5229,5232],{"style":2296},[1903,5230],{"className":5231,"style":2231},[2230],[1903,5233,5235],{"className":5234},[2235,2236,2237,2238],[1903,5236,2529],{"className":5237},[2242,2280,2238],[1903,5239,2532],{"className":5240},[2242,2280],[1903,5242,2560],{"className":5243,"style":2711},[2242,2280],[1903,5245,2715],{"className":5246},[2242,2280],[1903,5248,2535],{"className":5249},[2242,2280],[1903,5251,2571],{"className":5252,"style":2453},[2242,2280],[1903,5254,2578],{"className":5255},[2376],[1903,5257,5259,5262],{"className":5258},[2242],[1903,5260,2560],{"className":5261,"style":2711},[2242,2280],[1903,5263,5265],{"className":5264},[2209],[1903,5266,5268],{"className":5267},[2213],[1903,5269,5271],{"className":5270},[2218],[1903,5272,5274],{"className":5273,"style":2740},[2222],[1903,5275,5276,5279],{"style":2296},[1903,5277],{"className":5278,"style":2231},[2230],[1903,5280,5282],{"className":5281},[2235,2236,2237,2238],[1903,5283,2578],{"className":5284},[2376,2238],[1903,5286,2578],{"className":5287},[2376],[1903,5289,2532],{"className":5290},[2242,2280],[1903,5292,3793],{"className":5293},[2504],[1903,5295,2578],{"className":5296},[2376],[1903,5298,2546],{"className":5299},[2242,2280],[1903,5301,3793],{"className":5302},[2504],[1903,5304,2614],{"className":5305},[2242],[1903,5307,2578],{"className":5308},[2376],[1903,5310,2532],{"className":5311},[2242,2280],[1903,5313,5315],{"className":5314},[2504],"!)",[1903,5317,2578],{"className":5318},[2376],[1903,5320,2151],{"className":5321},[2242,2280],[1903,5323],{"className":5324,"style":2755},[2272],[1903,5326,2146],{"className":5327},[2759],[1903,5329],{"className":5330,"style":2755},[2272],[1903,5332,5334,5337,5340],{"className":5333},[2190],[1903,5335],{"className":5336,"style":2824},[2194],[1903,5338,2546],{"className":5339},[2242,2280],[1903,5341,5343,5346],{"className":5342},[2504],[1903,5344,2589],{"className":5345},[2504],[1903,5347,5349],{"className":5348},[2209],[1903,5350,5352],{"className":5351},[2213],[1903,5353,5355],{"className":5354},[2218],[1903,5356,5359],{"className":5357,"style":5358},[2222],"height:0.7144em;",[1903,5360,5361,5364],{"style":2296},[1903,5362],{"className":5363,"style":2231},[2230],[1903,5365,5367],{"className":5366},[2235,2236,2237,2238],[1903,5368,2532],{"className":5369},[2242,2280,2238],[1831,5371,5373],{"id":5372},"linear-algebra","Linear Algebra",[1793,5375,5376],{},"Determinant:",[1903,5378,5380],{"className":5379},[2100],[1903,5381,5383,5440],{"className":5382},[2104],[1903,5384,5386],{"className":5385},[2108],[2110,5387,5388],{"xmlns":2112,"display":2113},[2115,5389,5390,5437],{},[2118,5391,5392,5394,5396,5398,5400,5402,5404,5406,5408,5411,5413,5416,5419,5421,5423,5425,5427,5429,5431,5433,5435],{},[2132,5393,2161],{},[2132,5395,2141],{},[2132,5397,2535],{},[2132,5399,3589],{},[2132,5401,2546],{},[2132,5403,2535],{},[2124,5405,2578],{"stretchy":1841},[2132,5407,2546],{},[2124,5409,5410],{"separator":1850},",",[2132,5412,3216],{},[2124,5414,5415],{"separator":1850},";",[2132,5417,5418],{},"c",[2124,5420,5410],{"separator":1850},[2132,5422,2161],{},[2124,5424,2589],{"stretchy":1841},[2124,5426,2166],{},[2132,5428,2546],{},[2132,5430,2161],{},[2124,5432,2146],{},[2132,5434,3216],{},[2132,5436,5418],{},[2179,5438,5439],{"encoding":2181},"det mat(a, b; c, d) = a d - b c",[1903,5441,5443,5511,5533],{"className":5442,"ariaHidden":1850},[2186],[1903,5444,5446,5449,5452,5455,5458,5462,5465,5468,5471,5475,5478,5481,5484,5487,5490,5493,5496,5499,5502,5505,5508],{"className":5445},[2190],[1903,5447],{"className":5448,"style":2824},[2194],[1903,5450,2161],{"className":5451},[2242,2280],[1903,5453,2141],{"className":5454},[2242,2280],[1903,5456,2535],{"className":5457},[2242,2280],[1903,5459,5461],{"className":5460},[2242,2280],"ma",[1903,5463,2535],{"className":5464},[2242,2280],[1903,5466,2578],{"className":5467},[2376],[1903,5469,2546],{"className":5470},[2242,2280],[1903,5472,5410],{"className":5473},[5474],"mpunct",[1903,5476],{"className":5477,"style":2273},[2272],[1903,5479,3216],{"className":5480},[2242,2280],[1903,5482,5415],{"className":5483},[5474],[1903,5485],{"className":5486,"style":2273},[2272],[1903,5488,5418],{"className":5489},[2242,2280],[1903,5491,5410],{"className":5492},[5474],[1903,5494],{"className":5495,"style":2273},[2272],[1903,5497,2161],{"className":5498},[2242,2280],[1903,5500,2589],{"className":5501},[2504],[1903,5503],{"className":5504,"style":2355},[2272],[1903,5506,2166],{"className":5507},[2359],[1903,5509],{"className":5510,"style":2355},[2272],[1903,5512,5514,5518,5521,5524,5527,5530],{"className":5513},[2190],[1903,5515],{"className":5516,"style":5517},[2194],"height:0.7778em;vertical-align:-0.0833em;",[1903,5519,2546],{"className":5520},[2242,2280],[1903,5522,2161],{"className":5523},[2242,2280],[1903,5525],{"className":5526,"style":2755},[2272],[1903,5528,2146],{"className":5529},[2759],[1903,5531],{"className":5532,"style":2755},[2272],[1903,5534,5536,5540,5543],{"className":5535},[2190],[1903,5537],{"className":5538,"style":5539},[2194],"height:0.6944em;",[1903,5541,3216],{"className":5542},[2242,2280],[1903,5544,5418],{"className":5545},[2242,2280],[1793,5547,5548],{},"Eigenvalue equation:",[1903,5550,5552],{"className":5551},[2100],[1903,5553,5555,5612],{"className":5554},[2104],[1903,5556,5558],{"className":5557},[2108],[2110,5559,5560],{"xmlns":2112,"display":2113},[2115,5561,5562,5609],{},[2118,5563,5564,5567,5569,5571,5573,5575,5577,5579,5581,5583,5585,5587,5589,5591,5593,5595,5597,5599,5601,5603,5605,5607],{},[2132,5565,5566],{},"A",[2132,5568,3216],{},[2132,5570,2895],{},[2132,5572,2551],{},[2132,5574,2161],{},[2124,5576,2578],{"stretchy":1841},[2132,5578,2900],{},[2124,5580,2589],{"stretchy":1841},[2124,5582,2166],{},[2132,5584,2551],{},[2132,5586,2546],{},[2132,5588,3589],{},[2132,5590,3216],{},[2132,5592,2161],{},[2132,5594,2546],{},[2132,5596,3216],{},[2132,5598,2895],{},[2132,5600,2551],{},[2132,5602,2161],{},[2124,5604,2578],{"stretchy":1841},[2132,5606,2900],{},[2124,5608,2589],{"stretchy":1841},[2179,5610,5611],{"encoding":2181},"A bold(v) = lambda bold(v)",[1903,5613,5615,5654],{"className":5614,"ariaHidden":1850},[2186],[1903,5616,5618,5621,5624,5627,5630,5633,5636,5639,5642,5645,5648,5651],{"className":5617},[2190],[1903,5619],{"className":5620,"style":2824},[2194],[1903,5622,5566],{"className":5623},[2242,2280],[1903,5625,3216],{"className":5626},[2242,2280],[1903,5628,2895],{"className":5629},[2242,2280],[1903,5631,2551],{"className":5632,"style":2656},[2242,2280],[1903,5634,2161],{"className":5635},[2242,2280],[1903,5637,2578],{"className":5638},[2376],[1903,5640,2900],{"className":5641,"style":2453},[2242,2280],[1903,5643,2589],{"className":5644},[2504],[1903,5646],{"className":5647,"style":2355},[2272],[1903,5649,2166],{"className":5650},[2359],[1903,5652],{"className":5653,"style":2355},[2272],[1903,5655,5657,5660,5663,5667,5670,5674,5677,5680,5683,5686,5689],{"className":5656},[2190],[1903,5658],{"className":5659,"style":2824},[2194],[1903,5661,2551],{"className":5662,"style":2656},[2242,2280],[1903,5664,5666],{"className":5665},[2242,2280],"amb",[1903,5668,2161],{"className":5669},[2242,2280],[1903,5671,5673],{"className":5672},[2242,2280],"ab",[1903,5675,2895],{"className":5676},[2242,2280],[1903,5678,2551],{"className":5679,"style":2656},[2242,2280],[1903,5681,2161],{"className":5682},[2242,2280],[1903,5684,2578],{"className":5685},[2376],[1903,5687,2900],{"className":5688,"style":2453},[2242,2280],[1903,5690,2589],{"className":5691},[2504],[1831,5693,5695],{"id":5694},"statistics","Statistics",[1793,5697,5698],{},"Normal distribution:",[1903,5700,5702],{"className":5701},[2100],[1903,5703,5705,5811],{"className":5704},[2104],[1903,5706,5708],{"className":5707},[2108],[2110,5709,5710],{"xmlns":2112,"display":2113},[2115,5711,5712,5808],{},[2118,5713,5714,5716,5718,5720,5722,5724,5726,5728,5730,5732,5734,5736,5738,5740,5742,5744,5746,5748,5750,5752,5754,5756,5758,5760,5766,5768,5770,5772,5774,5776,5778,5784,5786,5788,5790,5792,5794,5796,5798,5804,5806],{},[2132,5715,2560],{},[2124,5717,2578],{"stretchy":1841},[2132,5719,2151],{},[2124,5721,2589],{"stretchy":1841},[2124,5723,2166],{},[2128,5725,2883],{},[2132,5727,2614],{"mathvariant":2134},[2124,5729,2578],{"stretchy":1841},[2132,5731,2598],{},[2132,5733,2529],{},[2132,5735,2540],{},[2132,5737,3589],{},[2132,5739,2546],{},[2132,5741,2598],{},[2132,5743,2601],{},[2132,5745,2543],{},[2132,5747,2535],{},[2124,5749,2578],{"stretchy":1841},[2128,5751,2154],{},[2132,5753,1793],{},[2132,5755,2529],{},[2124,5757,2589],{"stretchy":1841},[2124,5759,2589],{"stretchy":1841},[2137,5761,5762,5764],{},[2132,5763,2141],{},[2124,5765,2578],{"stretchy":1841},[2124,5767,2146],{},[2124,5769,2578],{"stretchy":1841},[2132,5771,2151],{},[2124,5773,2146],{},[2132,5775,3589],{},[2132,5777,3887],{},[2137,5779,5780,5782],{},[2124,5781,2589],{"stretchy":1841},[2128,5783,2154],{},[2132,5785,2614],{"mathvariant":2134},[2124,5787,2578],{"stretchy":1841},[2128,5789,2154],{},[2132,5791,2598],{},[2132,5793,2529],{},[2132,5795,2540],{},[2132,5797,3589],{},[2137,5799,5800,5802],{},[2132,5801,2546],{},[2128,5803,2154],{},[2124,5805,2589],{"stretchy":1841},[2124,5807,2589],{"stretchy":1841},[2179,5809,5810],{"encoding":2181},"f(x) = 1\u002F(sigma sqrt(2pi)) e^(-(x-mu)^2\u002F(2sigma^2))",[1903,5812,5814,5841,5931,5952],{"className":5813,"ariaHidden":1850},[2186],[1903,5815,5817,5820,5823,5826,5829,5832,5835,5838],{"className":5816},[2190],[1903,5818],{"className":5819,"style":2824},[2194],[1903,5821,2560],{"className":5822,"style":2711},[2242,2280],[1903,5824,2578],{"className":5825},[2376],[1903,5827,2151],{"className":5828},[2242,2280],[1903,5830,2589],{"className":5831},[2504],[1903,5833],{"className":5834,"style":2355},[2272],[1903,5836,2166],{"className":5837},[2359],[1903,5839],{"className":5840,"style":2355},[2272],[1903,5842,5844,5847,5851,5854,5857,5860,5863,5866,5869,5872,5875,5878,5881,5884,5887,5890,5893,5922,5925,5928],{"className":5843},[2190],[1903,5845],{"className":5846,"style":5205},[2194],[1903,5848,5850],{"className":5849},[2242],"1\u002F",[1903,5852,2578],{"className":5853},[2376],[1903,5855,2598],{"className":5856},[2242,2280],[1903,5858,2529],{"className":5859},[2242,2280],[1903,5861,2540],{"className":5862,"style":2453},[2242,2280],[1903,5864,5461],{"className":5865},[2242,2280],[1903,5867,2598],{"className":5868},[2242,2280],[1903,5870,2601],{"className":5871,"style":2453},[2242,2280],[1903,5873,2543],{"className":5874,"style":2646},[2242,2280],[1903,5876,2535],{"className":5877},[2242,2280],[1903,5879,2578],{"className":5880},[2376],[1903,5882,2154],{"className":5883},[2242],[1903,5885,1793],{"className":5886},[2242,2280],[1903,5888,2529],{"className":5889},[2242,2280],[1903,5891,3793],{"className":5892},[2504],[1903,5894,5896,5899],{"className":5895},[2242],[1903,5897,2141],{"className":5898},[2242,2280],[1903,5900,5902],{"className":5901},[2209],[1903,5903,5905],{"className":5904},[2213],[1903,5906,5908],{"className":5907},[2218],[1903,5909,5911],{"className":5910,"style":2740},[2222],[1903,5912,5913,5916],{"style":2296},[1903,5914],{"className":5915,"style":2231},[2230],[1903,5917,5919],{"className":5918},[2235,2236,2237,2238],[1903,5920,2578],{"className":5921},[2376,2238],[1903,5923],{"className":5924,"style":2755},[2272],[1903,5926,2146],{"className":5927},[2759],[1903,5929],{"className":5930,"style":2755},[2272],[1903,5932,5934,5937,5940,5943,5946,5949],{"className":5933},[2190],[1903,5935],{"className":5936,"style":2824},[2194],[1903,5938,2578],{"className":5939},[2376],[1903,5941,2151],{"className":5942},[2242,2280],[1903,5944],{"className":5945,"style":2755},[2272],[1903,5947,2146],{"className":5948},[2759],[1903,5950],{"className":5951,"style":2755},[2272],[1903,5953,5955,5958,5961,5964,5993,5996,5999,6002,6005,6008,6011,6014,6043],{"className":5954},[2190],[1903,5956],{"className":5957,"style":2769},[2194],[1903,5959,3589],{"className":5960},[2242,2280],[1903,5962,3887],{"className":5963},[2242,2280],[1903,5965,5967,5970],{"className":5966},[2504],[1903,5968,2589],{"className":5969},[2504],[1903,5971,5973],{"className":5972},[2209],[1903,5974,5976],{"className":5975},[2213],[1903,5977,5979],{"className":5978},[2218],[1903,5980,5982],{"className":5981,"style":2788},[2222],[1903,5983,5984,5987],{"style":2296},[1903,5985],{"className":5986,"style":2231},[2230],[1903,5988,5990],{"className":5989},[2235,2236,2237,2238],[1903,5991,2154],{"className":5992},[2242,2238],[1903,5994,2614],{"className":5995},[2242],[1903,5997,2578],{"className":5998},[2376],[1903,6000,2154],{"className":6001},[2242],[1903,6003,2598],{"className":6004},[2242,2280],[1903,6006,2529],{"className":6007},[2242,2280],[1903,6009,2540],{"className":6010,"style":2453},[2242,2280],[1903,6012,3589],{"className":6013},[2242,2280],[1903,6015,6017,6020],{"className":6016},[2242],[1903,6018,2546],{"className":6019},[2242,2280],[1903,6021,6023],{"className":6022},[2209],[1903,6024,6026],{"className":6025},[2213],[1903,6027,6029],{"className":6028},[2218],[1903,6030,6032],{"className":6031,"style":2788},[2222],[1903,6033,6034,6037],{"style":2296},[1903,6035],{"className":6036,"style":2231},[2230],[1903,6038,6040],{"className":6039},[2235,2236,2237,2238],[1903,6041,2154],{"className":6042},[2242,2238],[1903,6044,3793],{"className":6045},[2504],[1793,6047,6048],{},"Bayes' theorem:",[1903,6050,6052],{"className":6051},[2100],[1903,6053,6055,6121],{"className":6054},[2104],[1903,6056,6058],{"className":6057},[2108],[2110,6059,6060],{"xmlns":2112,"display":2113},[2115,6061,6062,6118],{},[2118,6063,6064,6067,6069,6071,6074,6076,6078,6080,6082,6084,6086,6088,6090,6092,6094,6096,6098,6100,6102,6104,6106,6108,6110,6112,6114,6116],{},[2132,6065,6066],{},"P",[2124,6068,2578],{"stretchy":1841},[2132,6070,5566],{},[2132,6072,6073],{"mathvariant":2134},"∣",[2132,6075,3460],{},[2124,6077,2589],{"stretchy":1841},[2124,6079,2166],{},[2124,6081,2578],{"stretchy":1841},[2132,6083,6066],{},[2124,6085,2578],{"stretchy":1841},[2132,6087,3460],{},[2132,6089,6073],{"mathvariant":2134},[2132,6091,5566],{},[2124,6093,2589],{"stretchy":1841},[2132,6095,6066],{},[2124,6097,2578],{"stretchy":1841},[2132,6099,5566],{},[2124,6101,2589],{"stretchy":1841},[2124,6103,2589],{"stretchy":1841},[2132,6105,2614],{"mathvariant":2134},[2124,6107,2578],{"stretchy":1841},[2132,6109,6066],{},[2124,6111,2578],{"stretchy":1841},[2132,6113,3460],{},[2124,6115,2589],{"stretchy":1841},[2124,6117,2589],{"stretchy":1841},[2179,6119,6120],{"encoding":2181},"P(A|B) = (P(B|A) P(A))\u002F(P(B))",[1903,6122,6124,6157],{"className":6123,"ariaHidden":1850},[2186],[1903,6125,6127,6130,6133,6136,6139,6142,6145,6148,6151,6154],{"className":6126},[2190],[1903,6128],{"className":6129,"style":2824},[2194],[1903,6131,6066],{"className":6132,"style":4543},[2242,2280],[1903,6134,2578],{"className":6135},[2376],[1903,6137,5566],{"className":6138},[2242,2280],[1903,6140,6073],{"className":6141},[2242],[1903,6143,3460],{"className":6144,"style":3530},[2242,2280],[1903,6146,2589],{"className":6147},[2504],[1903,6149],{"className":6150,"style":2355},[2272],[1903,6152,2166],{"className":6153},[2359],[1903,6155],{"className":6156,"style":2355},[2272],[1903,6158,6160,6163,6166,6169,6172,6175,6178,6181,6184,6187,6190,6193,6196,6199,6202,6205,6208,6211],{"className":6159},[2190],[1903,6161],{"className":6162,"style":2824},[2194],[1903,6164,2578],{"className":6165},[2376],[1903,6167,6066],{"className":6168,"style":4543},[2242,2280],[1903,6170,2578],{"className":6171},[2376],[1903,6173,3460],{"className":6174,"style":3530},[2242,2280],[1903,6176,6073],{"className":6177},[2242],[1903,6179,5566],{"className":6180},[2242,2280],[1903,6182,2589],{"className":6183},[2504],[1903,6185,6066],{"className":6186,"style":4543},[2242,2280],[1903,6188,2578],{"className":6189},[2376],[1903,6191,5566],{"className":6192},[2242,2280],[1903,6194,3793],{"className":6195},[2504],[1903,6197,2614],{"className":6198},[2242],[1903,6200,2578],{"className":6201},[2376],[1903,6203,6066],{"className":6204,"style":4543},[2242,2280],[1903,6206,2578],{"className":6207},[2376],[1903,6209,3460],{"className":6210,"style":3530},[2242,2280],[1903,6212,3793],{"className":6213},[2504],[1831,6215,6217],{"id":6216},"physics","Physics",[1793,6219,6220],{},"Schrödinger equation:",[1903,6222,6224],{"className":6223},[2100],[1903,6225,6227,6335],{"className":6226},[2104],[1903,6228,6230],{"className":6229},[2108],[2110,6231,6232],{"xmlns":2112,"display":2113},[2115,6233,6234,6332],{},[2118,6235,6236,6238,6240,6242,6244,6246,6248,6251,6253,6255,6257,6259,6261,6263,6265,6267,6269,6271,6273,6275,6277,6279,6281,6283,6285,6287,6289,6291,6293,6295,6297,6299,6301,6303,6305,6307,6309,6311,6313,6315,6317,6319,6321,6324,6326,6328,6330],{},[2132,6237,2529],{},[2132,6239,1793],{},[2132,6241,2551],{},[2132,6243,2546],{},[2132,6245,2532],{},[2132,6247,5418],{},[2132,6249,6250],{},"k",[2132,6252,3169],{"mathvariant":2134},[2132,6254,2543],{},[2132,6256,2141],{},[2132,6258,2161],{},[2132,6260,3887],{},[2132,6262,5418],{},[2132,6264,2141],{},[2124,6266,2578],{"stretchy":1841},[2132,6268,1793],{},[2132,6270,2546],{},[2132,6272,2543],{},[2132,6274,2535],{},[2132,6276,2529],{},[2132,6278,2546],{},[2132,6280,2551],{},[2124,6282,2589],{"stretchy":1841},[2132,6284,2614],{"mathvariant":2134},[2124,6286,2578],{"stretchy":1841},[2132,6288,1793],{},[2132,6290,2546],{},[2132,6292,2543],{},[2132,6294,2535],{},[2132,6296,2529],{},[2132,6298,2546],{},[2132,6300,2551],{},[2132,6302,2535],{},[2124,6304,2589],{"stretchy":1841},[2132,6306,6066],{},[2132,6308,2598],{},[2132,6310,2529],{},[2124,6312,2166],{},[2132,6314,2892],{},[2132,6316,2546],{},[2132,6318,2535],{},[2124,6320,2578],{"stretchy":1841},[2132,6322,6323],{},"H",[2124,6325,2589],{"stretchy":1841},[2132,6327,6066],{},[2132,6329,2598],{},[2132,6331,2529],{},[2179,6333,6334],{"encoding":2181},"i planck.reduce (partial)\u002F(partial t) Psi = hat(H) Psi",[1903,6336,6338,6453],{"className":6337,"ariaHidden":1850},[2186],[1903,6339,6341,6344,6347,6351,6355,6358,6362,6365,6368,6371,6374,6377,6381,6384,6387,6390,6393,6396,6399,6402,6405,6408,6411,6414,6417,6420,6423,6426,6429,6432,6435,6438,6441,6444,6447,6450],{"className":6340},[2190],[1903,6342],{"className":6343,"style":2824},[2194],[1903,6345,2529],{"className":6346},[2242,2280],[1903,6348,6350],{"className":6349,"style":2656},[2242,2280],"pl",[1903,6352,6354],{"className":6353},[2242,2280],"an",[1903,6356,5418],{"className":6357},[2242,2280],[1903,6359,6250],{"className":6360,"style":6361},[2242,2280],"margin-right:0.0315em;",[1903,6363,3169],{"className":6364},[2242],[1903,6366,2543],{"className":6367,"style":2646},[2242,2280],[1903,6369,2141],{"className":6370},[2242,2280],[1903,6372,2161],{"className":6373},[2242,2280],[1903,6375,3887],{"className":6376},[2242,2280],[1903,6378,6380],{"className":6379},[2242,2280],"ce",[1903,6382,2578],{"className":6383},[2376],[1903,6385,1793],{"className":6386},[2242,2280],[1903,6388,2546],{"className":6389},[2242,2280],[1903,6391,2543],{"className":6392,"style":2646},[2242,2280],[1903,6394,2535],{"className":6395},[2242,2280],[1903,6397,3768],{"className":6398},[2242,2280],[1903,6400,2551],{"className":6401,"style":2656},[2242,2280],[1903,6403,2589],{"className":6404},[2504],[1903,6406,2614],{"className":6407},[2242],[1903,6409,2578],{"className":6410},[2376],[1903,6412,1793],{"className":6413},[2242,2280],[1903,6415,2546],{"className":6416},[2242,2280],[1903,6418,2543],{"className":6419,"style":2646},[2242,2280],[1903,6421,2535],{"className":6422},[2242,2280],[1903,6424,3768],{"className":6425},[2242,2280],[1903,6427,2551],{"className":6428,"style":2656},[2242,2280],[1903,6430,2535],{"className":6431},[2242,2280],[1903,6433,2589],{"className":6434},[2504],[1903,6436,6066],{"className":6437,"style":4543},[2242,2280],[1903,6439,2598],{"className":6440},[2242,2280],[1903,6442,2529],{"className":6443},[2242,2280],[1903,6445],{"className":6446,"style":2355},[2272],[1903,6448,2166],{"className":6449},[2359],[1903,6451],{"className":6452,"style":2355},[2272],[1903,6454,6456,6459,6462,6465,6468,6472,6475,6478,6481],{"className":6455},[2190],[1903,6457],{"className":6458,"style":2824},[2194],[1903,6460,4902],{"className":6461},[2242,2280],[1903,6463,2535],{"className":6464},[2242,2280],[1903,6466,2578],{"className":6467},[2376],[1903,6469,6323],{"className":6470,"style":6471},[2242,2280],"margin-right:0.0813em;",[1903,6473,2589],{"className":6474},[2504],[1903,6476,6066],{"className":6477,"style":4543},[2242,2280],[1903,6479,2598],{"className":6480},[2242,2280],[1903,6482,2529],{"className":6483},[2242,2280],[1793,6485,6486],{},"Lorentz transformation:",[1903,6488,6490],{"className":6489},[2100],[1903,6491,6493,6587],{"className":6492},[2104],[1903,6494,6496],{"className":6495},[2108],[2110,6497,6498],{"xmlns":2112,"display":2113},[2115,6499,6500,6584],{},[2118,6501,6502,6508,6510,6512,6514,6516,6518,6520,6522,6524,6526,6528,6530,6532,6534,6536,6542,6544,6546,6548,6550,6552,6554,6560,6562,6564,6566,6568,6570,6572,6574,6576,6578,6580,6582],{},[2137,6503,6504,6506],{},[2132,6505,2535],{},[2124,6507,4713],{"mathvariant":2134,"lspace":4712,"rspace":4712},[2124,6509,2166],{},[2132,6511,2540],{},[2132,6513,2546],{},[2132,6515,3589],{},[2132,6517,3589],{},[2132,6519,2546],{},[2124,6521,2578],{"stretchy":1841},[2132,6523,2535],{},[2124,6525,2146],{},[2124,6527,2578],{"stretchy":1841},[2132,6529,2900],{},[2132,6531,2151],{},[2124,6533,2589],{"stretchy":1841},[2132,6535,2614],{"mathvariant":2134},[2137,6537,6538,6540],{},[2132,6539,5418],{},[2128,6541,2154],{},[2124,6543,2589],{"stretchy":1841},[2124,6545,5410],{"separator":1850},[2132,6547,2601],{},[2132,6549,3887],{},[2132,6551,2546],{},[2132,6553,2161],{},[2137,6555,6556,6558],{},[2132,6557,2151],{},[2124,6559,4713],{"mathvariant":2134,"lspace":4712,"rspace":4712},[2124,6561,2166],{},[2132,6563,2540],{},[2132,6565,2546],{},[2132,6567,3589],{},[2132,6569,3589],{},[2132,6571,2546],{},[2124,6573,2578],{"stretchy":1841},[2132,6575,2151],{},[2124,6577,2146],{},[2132,6579,2900],{},[2132,6581,2535],{},[2124,6583,2589],{"stretchy":1841},[2179,6585,6586],{"encoding":2181},"t' = gamma(t - (v x)\u002Fc^2), quad x' = gamma(x - v 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