This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, optimisation and dynamics. The final two chapters are an introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study. This new fourth edition includes two chapters on probability theory, providing the essential mathematical background for upper-level courses on economic theory, econometrics and finance. Answers to all exercises and complete solutions to all problems are available online from a regularly updated website.
1. Linear equations 2. Linear inequalities 3. Sets and functions 4. Quadratics, indices and logarithms 5. Sequences, series and limits 6. Introduction to differentiation 7. Methods of differentiation 8. Maxima and minima 9. Exponential and logarithmic functions 10. Approximations 11. Matrix algebra 12. Systems of linear equations 13. Determinants and quadratic forms 14. Functions of several variables 15. Implicit relations 16. Optimisation with several variables 17. Principles of constrained optimisation 18. Further topics in constrained optimisation 19. Integration 20. Aspects of integral calculus 21. Probability 22. Expectation 23. Introduction to dynamics 24. The circular functions 25. Complex numbers 26. Further dynamics 27. Eigenvalues and eigenvectors 28. Dynamic systems 29. Dynamic optimisation in discrete time 30. Dynamic optimisation in continuous time 31. Introduction to analysis 32. Metric spaces and existence theorems Notes on further reading Index
