Standard syllabus
Mathematical modeling · Undergraduate · Math
Learning objectives from the Mathematical modeling syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Mathematical Modeling — scope drawn from open modeling texts and typical US math modeling course outlines.
Modeling process and dimensional analysis
- The modeling cycle: formulation, analysis, interpretation, validation — The modeling cycle: formulation, analysis, interpretation, validation
- Dimensional analysis — Dimensional analysis
- Buckingham Pi theorem — Buckingham Pi theorem
- Scaling and nondimensionalization of equations — Scaling and nondimensionalization of equations
- Sensitivity analysis — Sensitivity analysis
- Parameter estimation (introduction) — Parameter estimation (introduction)
- Model comparison — Model comparison
- Goodness-of-fit measures — Goodness-of-fit measures
Deterministic models
- Growth models: exponential, logistic, and Gompertz — Growth models: exponential, logistic, and Gompertz
- Compartment models and conservation laws — Compartment models and conservation laws
- Optimization models in operations and design — Optimization models in operations and design
- Discrete-time models — Discrete-time models
- Recursion — Recursion
- Equilibrium — Equilibrium
- Stability analysis of models — Stability analysis of models
Probabilistic and statistical models
- Elementary probability models for uncertainty — Elementary probability models for uncertainty
- Monte Carlo simulation (introduction) — Monte Carlo simulation (introduction)
- Markov chains for simple stochastic models — Markov chains for simple stochastic models
- Regression — Regression
- Calibration of model parameters — Calibration of model parameters
- Confidence intervals — Confidence intervals
- Prediction in applied settings — Prediction in applied settings
Learning objectives
Click an objective for study materials.
Modeling process and dimensional analysis
- The modeling cycle: formulation, analysis, interpretation, validation — The modeling cycle: formulation, analysis, interpretation, validation
- Dimensional analysis — Dimensional analysis
- Buckingham Pi theorem — Buckingham Pi theorem
- Scaling and nondimensionalization of equations — Scaling and nondimensionalization of equations
- Sensitivity analysis — Sensitivity analysis
- Parameter estimation (introduction) — Parameter estimation (introduction)
- Model comparison — Model comparison
- Goodness-of-fit measures — Goodness-of-fit measures
Deterministic models
- Growth models: exponential, logistic, and Gompertz — Growth models: exponential, logistic, and Gompertz
- Compartment models and conservation laws — Compartment models and conservation laws
- Optimization models in operations and design — Optimization models in operations and design
- Discrete-time models — Discrete-time models
- Recursion — Recursion
- Equilibrium — Equilibrium
- Stability analysis of models — Stability analysis of models
Probabilistic and statistical models
- Elementary probability models for uncertainty — Elementary probability models for uncertainty
- Monte Carlo simulation (introduction) — Monte Carlo simulation (introduction)
- Markov chains for simple stochastic models — Markov chains for simple stochastic models
- Regression — Regression
- Calibration of model parameters — Calibration of model parameters
- Confidence intervals — Confidence intervals
- Prediction in applied settings — Prediction in applied settings
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Modeling process and dimensional analysis
The modeling cycle: formulation, analysis, interpretation, validation
Coming soon - Deterministic models
Growth models: exponential, logistic, and Gompertz
Coming soon - Probabilistic and statistical models
Elementary probability models for uncertainty
Coming soon
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