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Modeling and Simulation Book - Table of ContentsFront MatterAcknowledgmentsIntroductionWho Is This Book For?How Much Math and Science Do I Need?How Much Programming Do I Need?Book OverviewTeaching ModelingGetting StartedInstalling PythonRunning JupyterSuggestions and CorrectionsPART I: DISCRETE SYSTEMSChapter 1: Introduction to ModelingThe Modeling FrameworkTesting the Falling Penny MythComputation in PythonFalse PrecisionComputation with UnitsSummaryExercisesChapter 2: Modeling a Bike Share SystemOur Bike Share ModelDefining FunctionsPrint Statementsif StatementsParametersfor LoopsTimeSeriesPlottingSummaryExercisesUnder the HoodChapter 3: Iterative ModelingIterating on Our Bike Share ModelUsing More Than One State ObjectDocumentationDealing with Negative BikesComparison OperatorsIntroducing MetricsSummaryExercisesChapter 4: Parameters and MetricsFunctions That Return ValuesLoops and ArraysSweeping ParametersIncremental DevelopmentSummaryExercisesChallenge ExercisesUnder the HoodChapter 5: Building a Population ModelExploring the DataAbsolute and Relative ErrorsModeling Population GrowthSimulating Population GrowthSummaryExerciseChapter 6: Iterating the Population ModelSystem ObjectsA Proportional Growth ModelFactoring Out the Update FunctionCombining Birth and DeathSummaryExerciseUnder the HoodChapter 7: Limits to GrowthQuadratic GrowthNet GrowthFinding EquilibriumDysfunctionsSummaryExercisesChapter 8: Projecting into the FutureGenerating ProjectionsComparing ProjectionsSummaryExerciseChapter 9: Analysis and Symbolic ComputationDifference EquationsDifferential EquationsAnalysis and SimulationAnalysis with WolframAlphaAnalysis with SymPyDifferential Equations in SymPySolving the Quadratic Growth ModelSummaryExercisesChapter 10: Case Studies Part IHistorical World PopulationOne Queue or Two?Predicting Salmon PopulationsTree GrowthPART II: FIRST-ORDER SYSTEMSChapter 11: Epidemiology and SIR ModelsThe Freshman PlagueThe Kermack-McKendrick ModelThe KM EquationsImplementing the KM ModelThe Update FunctionRunning the SimulationCollecting the ResultsNow with a TimeFrameSummaryExerciseChapter 12: Quantifying InterventionsThe Effects of ImmunizationChoosing MetricsSweeping ImmunizationSummaryExerciseChapter 13: Sweeping ParametersSweeping BetaSweeping GammaUsing a SweepFrameSummaryExerciseChapter 14: NondimensionalizationBeta and GammaExploring the ResultsContact NumberComparing Analysis and SimulationEstimating the Contact NumberSummaryExercisesUnder the HoodChapter 15: Thermal SystemsThe Coffee Cooling ProblemTemperature and HeatHeat TransferNewton's Law of CoolingImplementing Newtonian CoolingFinding RootsEstimating rSummaryExercisesChapter 16: Solving the Coffee ProblemMixing LiquidsMix First or Last?Optimal TimingThe Analytic SolutionSummaryExercisesChapter 17: Modeling Blood SugarThe Minimal ModelThe Glucose Minimal ModelGetting the DataInterpolationSummaryExercisesChapter 18: Implementing the Minimal ModelImplementing the ModelThe Update FunctionRunning the SimulationSolving Differential EquationsSummaryExerciseChapter 19: Case Studies Part IIRevisiting the Minimal ModelThe Insulin Minimal ModelLow-Pass FilterThermal Behavior of a WallHIVPART III: SECOND-ORDER SYSTEMSChapter 20: The Falling Penny RevisitedNewton's Second Law of MotionDropping PenniesEvent FunctionsSummaryExerciseChapter 21: DragCalculating Drag ForceThe Params ObjectSimulating the Penny DropSummaryExercisesChapter 22: Two-Dimensional MotionAssumptions and DecisionsVectorsSimulating Baseball FlightDrag ForceAdding an Event FunctionVisualizing TrajectoriesAnimating the BaseballSummaryExercisesChapter 23: OptimizationThe Manny Ramirez ProblemFinding the RangeSummaryExerciseUnder the HoodChapter 24: RotationThe Physics of Toilet PaperSetting ParametersSimulating the SystemPlotting the ResultsThe Analytic SolutionSummaryExerciseChapter 25: TorqueAngular AccelerationMoment of InertiaTeapots and TurntablesTwo-Phase SimulationPhase 1Phase 2Combining the ResultsEstimating FrictionAnimating the TurntableSummaryExerciseChapter 26: Case Studies Part IIIBungee JumpingBungee Dunk RevisitedOrbiting the SunSpider-ManKittensSimulating a Yo-YoCongratulationsBack MatterAppendix: Under the HoodHow run_solve_ivp WorksHow root_scalar WorksHow maximize_scalar WorksIndex