2025最新版，上千页，内容特别丰富！
该资料面向本科中高年级经济学学生，讲解经济学相关数学方法，摒弃机械套用的教学模式。通过扩充例题数量与题材，培养学生理解现代经济分析、自主构建经济模型的能力，例题覆盖金融、环境、公共、产业经济、经济思想史等领域。新增读者练习题，用于自学自测、课后作业和课堂研讨。为控制篇幅删减部分例题，删减例题可在MIT社官网获取，配套完整例题检索清单。

The aims and scope of this edition are exactly those of the last edition. In particular, we have tried to give students a good understanding of the methods of mathematics that are most relevant to the study of economics at the intermediate to senior undergraduate level, and have consciously sought to avoid a “cookbook” approach. The main innovations in this edition have been in the direction of further developing students’ ability to understand the methods of modern economic analysis, and, we hope, to develop their ability to build economic models of their own, by expanding the number and especially the range of the worked examples in the resource. Rather than focusing mainly on applications in standard microeconomics and macroeconomics, we have also presented models taken from finance theory, environmental economics, public economics, industrial economics (IO), and the history of economic thought. The aim here was to help students develop modeling skills by seeing how the same basic mathematical methods can be applied to address a wide range of interesting and important issues. We believe that this will make clear the power of mathematics to clarify important problems and help in their solution, and thus motivate students to study the mathematics itself.
A further innovation is the introduction of “Reader Assignments.” These are inserted at points at which students may want to check their understanding of what they have just read, and they may be capable of being answered in a few words, a simple diagram, or a couple of lines of math. As well as an aid to individual study, they may be used as homework assignments or for in‑class quizzes and discussion.
Of course, to avoid making the resource even heavier than it is, we have had to make space by taking out a number of examples that were in the third edition. However, we emphasize that all of these will still be available on the resource’s website at MIT Press. To facilitate search, we have provided a list of all the worked examples, with an indication of whether they can be found here in the resource or on the website.
The preparation of a new edition has given us the opportunity to take full account of the many comments, corrections, and suggestions that have been made to us in the rather lengthy period since publication of the third edition. In addition to a number of anonymous reviewers, we would like to thank Erik Balder, Philip Hanser, Daniel Rondeau and S. Seshasayee for their comments —even (or should we say especially), for their more critical ones. We also thank Jianhan Zhang for his excellent work on the new diagrams for the resource.
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)