The links to the videos below constitute a course in mathematical economics that was taught over two semesters at the University of Victoria in British Columbia, Canada. The first semester covered static optimization, while the second covered dynamic optimization. This material was designed as an upper-level undergraduate sequence for a BSc (STEM-oriented) degree as opposed to the regular BA (where students were encouraged to take the static optimization component of mathematical economics. Graduate students in Economics. should be familiar with both components at the end of their first year.
The course is based on the following textbooks:
Dixit, A.K., 1990. Optimization in Economic Theory. 2nd Edition. Oxford, UK: Oxford University Press. Hoy, M., J. Livernois, C. McKenna, R. Rees & T. Stengos, 2011. Mathematics for Economics. 3rd Ed. MIT Press.
Conrad, Jon M., 2010. Resource Economics. Second Edition. Cambridge: Cambridge University Press.
| Name of Video | CONTENT |
| Calculus Review | |
| CalculusReview01 | Review and introduction to calculus |
| CalculusReview02 | |
| CalculusReview03 | |
| CalculusReview04 | |
| CalculusReview05 | |
| CalculusReview06 | Explanation of Taylor series as a math sequences |
| CalculusReview07 | Put bond formula here. Example of math sequence |
| Integration | |
| Integration01 | Integration |
| Integration02 | Integration (cont) |
| Integration03 | Application of measurement of areas under curves to international trade |
| Matrices | |
| Matrices01 | Introduction to matrix algebra |
| Matrices02 | Systems of equations in matrix form and matrix rank |
| Matrices03 | Elementary matrices |
| Matrices04 | Find determinants of a matrices |
| Matrices05 | Find eigen values of matrices |
| Matrices06 | Find eigen vectors and matrices |
| Matrices07 | Additional matrix algebra |
| Static Optimization | |
| Optimization01 | Introduction to tangency in constrained optimization |
| Optimization01 | |
| Optimization01 | The concept of a Lagrangian and lagragian multipliers |
| Optimization01 | Constrained optimization: Static optimization |
| Optimization01 | Constrained optimization (cont) |
| Optimization01 | Static optimization and the Karsh-Kuhn-Tucker conditions |
| Welfare Economics | |
| Welfare01 | These lectures include consumer demand theory, |
| Welfare02 | the envelope theorem and duality, welfare |
| Welfare03 | measurement and index number theory. |
| Welfare04 | SlutskyEquation |
| Welfare05 | |
| Welfare06 | |
| Welfare07 | |
| Production Economics | |
| Production01 | Production economics: supply side and costs |
| Production02 | |
| Production03 | |
| Dynamic Optimization: Differential/Difference Equations | |
| Dynamic01 | Introduction to dynamic optimization |
| Dynamic02 | Solving difference equations (discrete time) |
| Dynamic03 | Solving difference equations (cont.) |
| Dynamic04 | Solving systems of difference equations |
| Dynamic05 | Phase plane diagrams for solving difference equations |
| Dynamic06 | Solving differential equations (continuous time) |
| Dynamic07 | Solving differential equations (cont) |
| Dynamic08 | Solving system of difference equations |
| Dynamic09 | Solving system of differential equations |
| Dynamic10 | Second lecture solving differential equation systems |
| Dynamic11 | Third lecture solving differential equation systems |
| Optimal Control Theory | |
| OptimalControl01 | Calculus of variations |
| OptimalControl02 | Calculus of variations continued |
| OptimalControl03 | Continuous time optimal control theory |
| OptimalControl04 | Discrete time optimal control theory |
| OptimalControl05 | Example of optimal extration from a mine |
| OptimalControl06 | Optimal extraction rule for nonrewable resource |
| Dynamic Programming | |
| OptimalControl07 | Introduction to dynamic programming |
| OptimalControl08 | Dynamic programming (cont) |
| OptimalControl09 | Introduction to Stochastic Dynamic Programming |
| OptimalControl10 | Application of stochastic dynamic programming |
| Operations Research: Operations Research | |
| Program01 | Introduction to Linear Programming |
| Program02 | Introduction to the Simplex Algorithm |
| Program03 | Simplex (cont.) |
| Program04 | Discussion of shadow prices and Karsh-Kuhn-Tucker conditions |
| Program05 | Introduction to R programming |
| Program06 | Intro to R Studio, R programming and solving LP problems in R |