## Mathematics for Economics

by Hoy, Livernois, McKenna, Rees, Stengos

### Instructor Requests

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 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. The book and the web material are cross-referenced in the text. A student solutions manual is available, and instructors can access online instructor’s material that includes solutions and PowerPoint slides. Visit http://mitpress.mit.edu/math_econ3 for complete details.

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
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Contents (pg. vii)
Preface (pg. xiii)
Part I: Introduction and Fundamentals (pg. 1)
Chapter 1: Introduction (pg. 3)
Chapter 2: Review of Fundamentals (pg. 11)
Chapter 3: Sequences, Series, and Limits (pg. 61)
Part II: Univariate Calculus and Optimization (pg. 101)
Chapter 4: Continuity of Fractions (pg. 103)
Chapter 5: The Derivative and Differential for Functions of One Variable (pg. 127)
Chapter 6: Optimization of Functions of One Variable (pg. 195)
Part III: Linear Algebra (pg. 233)
Chapter 7: Systems of Linear Equations (pg. 235)
Chapter 8: Matrices (pg. 267)
Chapter 9: Determinants and the Inverse Mix (pg. 301)
Chapter 10: Some Advanced Topics in Linear Algebra (pg. 347)
Part IV: Multivariate Calculus (pg. 391)
Chapter 11: Calculus for Functions of n-Variables (pg. 393)
Chapter 12: Optimization of Functions of n-Variables (pg. 473)
Chapter 13: Constrained Optimization (pg. 503)
Chapter 14: Comparative Statics (pg. 529)
Chapter 15: Concave Programming and the Kuhn-Tucker Conditions (pg. 567)
Part V: Integration and Dynamic Methods (pg. 583)
Chapter 16: Integration (pg. 585)
Chapter 17: An Introduction to Mathematics for Economic Dynamics (pg. 633)
Chapter 18: Linear, First-Order Difference Equations (pg. 643)
Chapter 19: Nonlinear, First-Order Difference Equations (pg. 665)
Chapter 20: Linear, Second-Order Difference Equations (pg. 681)
Chapter 21: Linear, First-Order Differential Equations (pg. 715)
Chapter 22: Nonlinear, First-Order Differential Equations (pg. 739)
Chapter 23: Linear, Second-Order Differential Equations (pg. 753)
Chapter 24: Simultaneous Systems of Differential and Difference Equations (pg. 781)
Chapter 25: Optimal Control Theory (pg. 845)
Index (pg. 953)

#### Michael Hoy

Michael Hoy is a faculty member in the Economics Department at the University of Guelph.

#### John Livernois

John Livernois is a faculty member in the Economics Department at the University of Guelph, Ontario.

#### Chris McKenna

Chris McKenna is a faculty member in the Economics Department at the University of Guelph, Ontario.

#### Ray Rees

Ray Rees is a faculty member at the Ludwig Maximilians University, Munich.

#### Thanasis Stengos

Thanasis Stengos is a faculty member in the Economics Department at the University of Guelph, Ontario.

Instructors
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