M331 Lectures

• Lecture 1. General introduction to mathematical modeling.  Course outline.
• Lecture 2.  Managing a baseball franchise.  Group discussions.
• Lecture 3.  Marginal cost, revenues, modeling a profitable team.  Group discussions.
• Lecture 4.  Additional examples.
• Lecture 5.  Supply and demand.  The effect of the baseball strike.
• Lecture 6.  Modeling with discrete dynamical systems: an introduction.
• Lecture 7.  Population models, interpretation of terms and constants.
• Lecture 8.  Analytically solution of linear difference equations.
• Lecture 9.  Interpretation of solutions: equilibria and stability.
• Lecture 10. Additional examples of modeling with difference equations.
• Lecture 11. Modeling with systems of difference equations.  Stability, fixed points.
• Lecture 12. In class exam on lectures 1-9.
• Lecture 13. The rental car agency and the voting tendencies problems.
• Lecture 14. Analytic solution of homogeneous systems of difference equations.
• Lecture 15. Power outage--no class.
• Lecture 16. Examples of models using nonlinear difference equations. Group work.
• Lecture 17. Test
• Lecture 18. Modeling using proportionality.
• Lecture 19. Vehicular Stopping Distance.
• Lecture 20. Geometric Similarity, Terminal Velocity of Geometrically Similar Raindrops.
• Lecture 21. Geometric Similarity, Bass Fishing Derby, Gymnastics.
• Lecture 22.  Introduction to Model Fitting, Least Squares.  Lines of Best Fit.
• Lecture 23.  Additional Models and Least Squares.
• Lecture 24. Chebyshev Criterion for Data Fitting, Test.
• Lecture 25. Comparison of fitting errors.  Introduction to Empirical modeling.
• Lecture 26. Polynomial approximation.  Least squares vs interpolation of data.
• Lecture 27. Lagrange interpolating polynomial, linear and cubic splines.
• Lecture 28. Simulation Modeling.  The Monte Carlo Method.  Monte Hall and Marilyn von Savant.
• Lecture 29. Simulating an Inventory Model: Gasoline and Consumer Demand.
• Lecture 30. Code Discussion of Inventory Model.
• Lecture 31. Classification of Optimization Problems. Examples.
• Lecture 32. Calculus of Variations.  The Brachistochrone Problem.
• Lecture 33. Constrained Optimization via the Method of Lagrange Multipliers. Test.
• Lecture 34. Lagrange multipliers.  Geometrical interpretation and more examples.