Mathematics for Economics 4th edition by Michael Hoy, John Livernois, Chris Mckenna, Ray Rees, Thanasis Stengos ISBN 0262046628 978-0262046626

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ISBN 10: 0262046628
ISBN 13: 978-0262046626
Author: Michael Hoy, John Livernois, Chris Mckenna, Ray Rees, Thanasis Stengos

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.

Mathematics for Economics 4th Table of contents:

Part I: Introduction and Fundamentals

Chapter 1. Introduction

1.1. What Is an Economic Model?

1.2. How to Use This Book

1.3. Conclusion

Chapter 2. Review of the Fundamentals

2.1. Sets and Subsets

2.2. Numbers

2.3. Beginning Topology: Point Sets and Distance in ℝn

2.4. Functions

Chapter 3. Sequences, Series, and Limits

3.1. Definition of a Sequence

3.2. Limit of a Sequence

3.3. Present-Value Calculations

3.4. Properties of Sequences

3.5. Series

Part II: Univariate Calculus and Optimization

Chapter 4. Continuity of Functions

4.1. Continuity of a Function of One Variable

4.2. Economic Applications of Continuous and Discontinuous Functions

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

5.1. The Tangent Line and the Derivative

5.2. Definition of the Derivative and the Differential

5.3. Conditions for Differentiability

5.4. Rules of Differentiation

5.5. Higher Order Derivatives: Concavity and Convexity of a Function

5.6. Taylor Series Formula, Rolle’s Theorem, and the Mean-Value Theorem

Chapter 6. Optimization of Functions of One Variable

6.1. Necessary Conditions for Unconstrained Maxima and Minima

6.2. Second-Order Conditions for a Local Optimum

6.3. Optimization over an Interval

Part III: Linear Algebra

Chapter 7. Linear Equations and Vector Spaces

7.1. Solving Systems of Linear Equations

7.2. Linear Systems in n Variables

7.3. Vectors in ℝn

Chapter 8. Matrices

8.1. General Notation

8.2. Basic Matrix Operations

8.3. Matrix Transposition

8.4. Some Special Matrices

Chapter 9. Determinants and the Inverse Matrix

9.1. Defining the Inverse

9.2. Obtaining the Determinant and Inverse of a 3 × 3 Matrix

9.3. The Inverse of an n × n Matrix and Its Properties

9.4. Cramer’s Rule

9.5. Rank of a Matrix

Chapter 10. Further Topics in Linear Algebra

10.1. The Eigenvalue Problem

10.2. Quadratic Forms

10.3. Hyperplanes

Part IV: Multivariate Calculus

Chapter 11. Calculus for Functions of n Variables

11.1. Partial Differentiation

11.2. Second-Order Partial Derivatives

11.3. The First-Order Total Differential

11.4. Implicit Differentiation

11.5. Curvature Properties: Concavity and Convexity

11.6. Quasiconcavity and Quasiconvexity

11.7. More Properties of Functions with Economic Applications

11.8. Taylor Series Expansion

Chapter 12. Optimization of Functions of n Variables

12.1. First-Order Conditions

12.2. Second-Order Conditions

12.3. Direct Restrictions on Variables

Chapter 13. Constrained Optimization

13.1. Constrained Problems and Approaches to Solutions

13.2. Second-Order Conditions for Constrained Optimization

13.3. Existence, Uniqueness, and Characterization of Solutions

13.4. Problems, Problems

Chapter 14. Comparative Statics

14.1. Introduction to Comparative Statics

14.2. General Comparative Statics Analysis

14.3. The Envelope Theorem

Chapter 15. Nonlinear Programming and the Kuhn-Tucker Conditions

15.1. The Kuhn-Tucker Conditions

15.2. Hyperplane Theorems and Quasiconcavity

Part V: Integration and Dynamic Methods

Chapter 16. Integration

16.1. The Indefinite Integral

16.2. The Riemann (Definite) Integral

16.3. Properties of Integrals

16.4. Improper Integrals

16.5. Techniques of Integration

Chapter 17. An Introduction to Mathematics for Economic Dynamics

17.1. Modeling Time

Chapter 18. Linear, First-Order Difference Equations

18.1. Linear, First-Order, Autonomous Difference Equations

18.2. The General, Linear, First-Order Difference Equation

Chapter 19. Nonlinear, First-Order Difference Equations

19.1. The Phase Diagram and Qualitative Analysis

19.2. Cycles and Chaos

Chapter 20. Linear, Second-Order Difference Equations

20.1. The Linear, Autonomous, Second-Order Difference Equation

20.2. The Linear, Second-Order Difference Equation with a Variable Term

Chapter 21. Linear, First-Order Differential Equations

21.1. Autonomous Equations

21.2. Nonautonomous Equations

Chapter 22. Nonlinear, First-Order Differential Equations

22.1. Autonomous Equations and Qualitative Analysis

22.2. Two Special Forms of Nonlinear, First-Order Differential Equations

Chapter 23. Linear, Second-Order Differential Equations

23.1. The Linear, Autonomous, Second-Order Differential Equation

23.2. The Linear, Second-Order Differential Equation with a Variable Term

Chapter 24. Simultaneous Systems of Differential and Difference Equations

24.1. Linear Differential Equation Systems

24.2. Stability Analysis and Linear Phase Diagrams

24.3. Systems of Linear Difference Equations

Chapter 25. Optimal Control Theory

25.1. The Maximum Principle

25.2. Optimization Problems Involving Discounting

25.3. Alternative Boundary Conditions on x(T)

25.4. Infinite-Time-Horizon Problems

25.5. Constraints on the Control Variable

25.6. Free-Terminal-Time Problems (T Free)

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