Mathematics for Economics and Finance

Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.

Spis treści:
1. Mathematical models in economics
2. Mathematical terms and notations
3. Sequences, recurrences and limits
4. Elements of finance
5. The cobweb model
6. Introduction to calculus
7. Some special functions
8. Introduction to optimisation
9. The derivative in economics I
10. The derivative in economics II
11. Partial derivatives
12. Applications of partial derivatives
13. Optimisation in two variables
14. Vectors, preferences and convexity
15. Matrix algebra
16. Linear equations I
17. Linear equations II
18. Inverse matrices
19. The input output model
20. Determinants
21. Constrained optimisation
22. Lagrangians and the consumer
23. Second-order recurrence equations
24. Macroeconomic applications
25. Areas and integrals
26. Techniques of integration
27. First-order differential equations
28. Second-order differential equations
Selected solutions.