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.
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.
