Mathematics for Economics and Business II: Limits and Continuity. Average Rate of Change and Slope. Derivatives, Instantaneous Rate of Change, Higher Order Derivatives. Optimization, Concavity of Inflection Points. Maxima and Minima. Revenue, Cost and Profit Applications, Anti Derivatives, Rules of Integration, Differential Equations, Mathematics of Finance, Simple and Compound Interest, Present Value, Effective Interest, Future Value, Annuities.
The aim of this course is to give the basic ingredients of mathematics for business and economics. Namely, functions, derivatives and differentials. Moreover, most of the models in economics appear in the form of linear models.
| Week | Topics |
|---|---|
| 1 | Limits. Chapter 10 (Introductory Mathematical Analysis): an introduction to the basic idea of limit, rules of limits (Pages 451 - 469) |
| 2 | Differentiation. Chapter 4: an introduction to the basic idea of differentiation, derivative of power functions, exponential and natural logarithm functions, rules of differentiation. (Pages 275 - 297 and 312- 321) |
| 3 | Marginal Functions & Elasticity. Chapter 4 (continue): standard economic applications of differentiation economic applications in marginal functions and in elasticity, (Pages 298 - 311 and 322 - 336 |
| 4 | Optimization. Chapter 4 (continue): standard economic applications of differentiation in optimisation (Pages 337 - 368) |
| 5 | Partial Differentiation. Chapter 5: functions of some variables, partial elasticity and marginal functions, first and second-order partial derivatives of functions of two variables, the application of partial derivatives in economics. (Pages 400 - 429) |
| 6 | Unconstrained Optimisation. Chapter 5 (continue): application of first and second-order partial derivatives of functions of two variables in unconstrained optimisation. (Pages 443 - 456 |
| 7 | Constraint Optimisation. Chapter 5 (continue): application of first and second-order partial derivatives of functions of two variables in constrained optimisation, Lagrange multipliers (Pages 457 - 481) |
| 8 | Review. Exercises. |
| 9 | Midterm exam. |
| 10 | Indefinite integration. Techniques of integration. Chapter 6: integration of functions of one variable, methods and techniques of integration. (Pages 493 - 508) |
| 11 | Definite integration. Chapter 6 (continue): area surface under the graph of a function, producer’s and consumer’s surpluses (Pages 509 - 523) |
| 12 | Graphical solution of linear programming problems. Chapter 8: basic mathematical techniques and special cases when problems have either no solution or infinitely many solutions, economic problem as a linear programming problem (Pages 599 - 629) |
| 13 | Differential equations. Chapter 9: the complementary function of a difference equation, the particular solution of a difference equation, the complementary function of a differential equation, the particular solution of a differential equation (Pages 643 - 672) |
| 14 | Review. Exercises. |
| Method | Qty | % Each |
|---|---|---|
| Midterm Exam(s) | 1 | 35 |
| Quiz | 2 | 5 |
| Final Exam | 1 | 45 |
| Attendance | 10 |
Ian Jacques, Mathematics for Economics and Business, Pearson ninth edition 2018