Mathematics for Economics, 4th Edition
- Length: 1104 pages
- Edition: 4
- Language: English
- Publisher: The MIT Press
- Publication Date: 2022-03-29
- ISBN-10: 0262046628
- ISBN-13: 9780262046626
- Sales Rank: #1927123 (See Top 100 Books)
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.
Cover Title Page Copyright Page Dedication Table of Contents Preface Glossary of Worked Examples 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) References and Further Reading Answers Index
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