Mathematics for Economics, fourth edition

An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students.

This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced undergraduate levels but also a large collection of problem sets. This updated and expanded fourth edition contains numerous worked examples drawn from a range of important areas, including economic theory, environmental economics, financial economics, public economics, industrial organization, and the history of economic thought. These help students develop modeling skills by showing how the same basic mathematical methods can be applied to a variety of interesting and important issues.
 
The five parts of the text cover fundamentals, calculus, linear algebra, optimization, and dynamics. The only prerequisite is high school algebra; the book presents all the mathematics needed for undergraduate economics. New to this edition are “Reader Assignments,” short questions designed to test students’ understanding before they move on to the next concept. The book’s website offers additional material, including more worked examples (as well as examples from the previous edition). Separate solutions manuals for students and instructors are also available.

Michael Hoy is Professor in the Department of Economics and Finance at the University of Guelph. John Livernois is Professor in the Department of Economics at the University of Guelph. Chris McKenna is formerly a Professor in the Department of Economics and Finance at the University of Guelph. Ray Rees is Professor of Economics Emeritus at the Center for Economic Studies (CES) at the University of Munich. Thanasis Stengos is Professor in the Department of Economics and Finance at the University of Guelph.
 

Preface xiii
Glossary of Worked Examples xv
Part I Introduction of Fundamentals 
Chapter 1
Introduction 3
Chapter 2
Review of the Fundamentals 19
Chapter 3 
Sequences, Series, and Limits 75
Part II Univariate Calculus and Optimization
Chapter 4 
Continuity of Functions 119
Chapter 5 
The Derivative and Differential of Functions of One Variable 145
Chapter 6 
Optimization of Functions of One Variable 225
Part III Linear Algebra
Chapter 7
Linear Equations and Vector Spaces 287
Chapter 8 
Matrices 333
Chapter 9 
Determinants and the Inverse Matrix 365
Chapter 10
Further Topics in Linear Algebra 407
Part IV Multivariate Calculus 
Chapter 11
Calculus for Functions of n Variables 443
Chapter 12 
Optimization of Functions of n Variables 519
Chapter 13
Constrained Optimization 551
Chapter 14
Comparative Statics 597
Chapter 15
Nonlinear Programming and the Kuhn-Tucker Conditions 635
Part V Integration and Dynamic Methods
Chapter 16 
Integration 681
Chapter 17
An Introduction to Mathematics for Economic Dynamics 731
Chapter 18
Linear, First-Order Difference Equations 743
Chapter 19
Nonlinear, First-Order Difference Equations 767
Chapter 20
Linear, Second-Order Difference Equations 783
Chapter 21
Linear, First-Order Differential Equations 817
Chapter 22
Nonlinear, First-Order Differential Equations 843
Chapter 23
Linear, Second-Order Differential Equations 857
Chapter 23
Simultaneous Systems of Differential and Difference Equations 885
Chapter 25
Optimal Control Theory 949
References and Further Reading 1025
Answers 1027
Index 1061