Description
Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.
Table of Contents
Preface to second edition; Preface to first edition; 1. Mathematical models in economics; 2. Mathematical terms and notations; 3. Sequences, recurrences, limits; 4. The 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; 29. Coupled systems and diagonalisation; 30. Applications of diagonalisation; Appendix A. Solutions to exercises; Appendix B. Answers to problems; Index.
