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Mathematical Modeling

M(x)

Mathematical Modeling

Build models to understand real-world phenomena

144Modules

8Units

Being rebuilt

This course is still in our original format. All the content is here and free to use, but it has not yet been through the rebuild that gives our newer courses their interactive animations and cleaner visuals — so you may hit some rough edges. Spot an error? Send us a note and we will fix it.

Recommended preparation

Calculus and Differential Equations give you the tools most models are built from.

Calculus 2 Differential Equations

What is Mathematical Modeling?INTRO

The Modeling ProcessINTRO

Abstraction and SimplificationLESSON

Making AssumptionsLESSON

Making Assumptions PracticePRACTICE

Dimensional AnalysisLESSON

Dimensional Analysis ExamplesEXAMPLE

Dimensional Analysis PracticePRACTICE

Scaling and Non-dimensionalizationLESSON

Scaling ExamplesEXAMPLE

Model Building WorkshopACTIVITY

Model ValidationLESSON

Sensitivity AnalysisLESSON

Model RefinementLESSON

Models Are EverywhereINTRO

Weather Prediction ModelsREAL WORLD

Introduction to Modeling SummarySUMMARY

Modeling Basics ReferenceREFERENCE

Introduction to Modeling QuizQUIZ

Discrete vs ContinuousINTRO

Sequences as ModelsINTRO

Difference EquationsLESSON

Difference Equations PracticePRACTICE

Linear Difference EquationsLESSON

Solving Difference EquationsLESSON

Financial Discrete ModelsEXAMPLE

Discrete Logistic ModelLESSON

Discrete Population ModelsEXAMPLE

Cobweb DiagramsLESSON

Cobweb Diagram PlotterACTIVITY

Stability of Fixed PointsLESSON

Discrete Stability PracticePRACTICE

BifurcationsLESSON

Introduction to ChaosLESSON

Bifurcation ExplorerACTIVITY

Markov ChainsLESSON

Stock Market ModelsREAL WORLD

Discrete Models SummarySUMMARY

Discrete Models ReferenceREFERENCE

Discrete Models QuizQUIZ

Continuous ModelsINTRO

Modeling Rates of ChangeINTRO

Exponential Growth and DecayLESSON

Logistic GrowthLESSON

Exponential and Logistic PracticePRACTICE

Compartmental ModelsLESSON

SIR Epidemic ModelLESSON

Epidemiological ModelsEXAMPLE

Epidemic SimulatorACTIVITY

Predator-Prey ModelsLESSON

Lotka-Volterra EquationsLESSON

Continuous Population ExamplesEXAMPLE

Phase Plane AnalysisLESSON

Phase Portrait ToolACTIVITY

LinearizationLESSON

Stability of EquilibriaLESSON

Limit CyclesLESSON

Systems PracticePRACTICE

COVID-19 ModelingREAL WORLD

Continuous Models SummarySUMMARY

Continuous Models ReferenceREFERENCE

Continuous Models QuizQUIZ

Stochastic ModelsINTRO

Randomness in ModelsINTRO

Random Variables in ModelingLESSON

Monte Carlo MethodsLESSON

Monte Carlo ExamplesEXAMPLE

Monte Carlo SimulatorACTIVITY

Monte Carlo PracticePRACTICE

Stochastic ProcessesLESSON

Random WalksLESSON

Random Walk VisualizerACTIVITY

Brownian MotionLESSON

Birth-Death ProcessesLESSON

Queuing ModelsLESSON

Queuing Model ExamplesEXAMPLE

Stochastic Epidemic ModelsLESSON

Stochastic Models PracticePRACTICE

Finance and Stochastic ModelsREAL WORLD

Probabilistic Models SummarySUMMARY

Probabilistic Models ReferenceREFERENCE

Probabilistic Models QuizQUIZ

Optimization in ModelsINTRO

Finding the BestINTRO

Formulating Optimization ProblemsLESSON

Problem Formulation PracticePRACTICE

Calculus-Based OptimizationLESSON

Constrained OptimizationLESSON

Lagrange MultipliersLESSON

Optimal Design ExamplesEXAMPLE

Linear ProgrammingLESSON

Resource Allocation ExamplesEXAMPLE

Optimization SolverACTIVITY

Optimization Solving PracticePRACTICE

Sensitivity in OptimizationLESSON

Introduction to Optimal ControlLESSON

Logistics OptimizationREAL WORLD

Optimization SummarySUMMARY

Optimization ReferenceREFERENCE

Optimization in Modeling QuizQUIZ

Spatial ModelsINTRO

Why Space MattersINTRO

DiffusionLESSON

Diffusion SimulatorACTIVITY

Diffusion PracticePRACTICE

The Heat EquationLESSON

Boundary ConditionsLESSON

Heat Conduction ExamplesEXAMPLE

AdvectionLESSON

Reaction-Diffusion EquationsLESSON

Turing PatternsLESSON

Pattern Formation ExamplesEXAMPLE

Pattern GeneratorACTIVITY

Wave EquationLESSON

Traveling WavesLESSON

Spatial Models PracticePRACTICE

Climate ModelingREAL WORLD

Spatial Models SummarySUMMARY

Spatial Models ReferenceREFERENCE

Spatial Models QuizQUIZ

Data-Driven ModelingINTRO

Building Models from DataINTRO

Least Squares FittingLESSON

Linear RegressionLESSON

Nonlinear Curve FittingLESSON

Curve Fitting ExamplesEXAMPLE

Curve Fitting ToolACTIVITY

Curve Fitting PracticePRACTICE

Parameter EstimationLESSON

Overfitting and UnderfittingLESSON

Model SelectionLESSON

Model Comparison ExamplesEXAMPLE

Model Selection PracticePRACTICE

Cross-ValidationLESSON

Uncertainty QuantificationLESSON

Machine Learning PreviewREAL WORLD

Data-Driven Modeling SummarySUMMARY

Data-Driven Modeling ReferenceREFERENCE

Data-Driven Modeling QuizQUIZ

Problem Solving GuideSUMMARY

Mathematical Modeling Master ReferenceREFERENCE

Complete Formula SheetFORMULA SHEET

Model CatalogFORMULA SHEET

Comprehensive Modeling TestQUIZ