MATHEMATICS FOR ECONOMICS------PHI

Description:

This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. It is also a useful reference for graduate students. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of the one variable, linear algebra, multivariate calculus, and dynamics. To develop the student’s problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book’s website http://mitpress.mit.edu/math_econ3. The book and the Web material are cross-referenced in the text. A Student Solutions Manual is available in ebook form, and instructors are able to access online the Instructor’s Manual, which includes PowerPoint slides.

“Mathematics is the language of economics, and this book is an excellent introduction to that language.”

— George J. Mailath, 
Walter H. Annenberg Professor in the Social Sciences 
and Professor of Economics, 
University of Pennsylvania.

“While there are many mathematics texts for economics available, this one is by far the best. It covers a comprehensive range of techniques with interesting applications, and the numerous worked examples and problems are a real bonus for the instructor. Teaching a course with this book is enjoyable and easy”.

— Kevin Denny, 
University College Dublin.

Preface.


Part I: Introduction and Fundamentals—

1. Introduction.

2. Review of Fundamentals.

3. Sequences, Series, and Limits.


Part II: Univariate Calculus and Optimization—

4. Continuity of Functions.

5. The Derivative and Differential for Functions of One Variable.

6. Optimization of Functions of One Variable.


Part III: Linear Algebra—

7. Systems of Linear Equations.

8. Matrices.

9. Determinants and the Inverse Matrix.

10. Some Advanced Topics in Linear Algebra.


Part IV: Multivariate Calculus—

11. Calculus for Functions of n-Variables.

12. Optimization of Functions of n-Variables.

13. Constrained Optimization.

14. Comparative Statics.

15. Concave Programming and the Kuhn–Tucker Conditions.


Part V: Integration and Dynamic Methods—

16. Integration.

17. An Introduction to Mathematics for Economic Dynamics.

18. Linear, First-Order Difference Equations.

19. Nonlinear, First-Order Difference Equations.

20. Linear, Second-Order Difference Equations.

21. Linear, First-Order Differential Equations.

22. Nonlinear, First-Order Differential Equations.

23. Linear, Second-Order Differential Equations.

24. Simultaneous Systems of Differential and Difference Equations.

25. Optimal Control Theory.

Answers. Index.