Mathematics for Economists. Made Simple

As the field of economics becomes ever more specialized and complicated, so does the mathematics required of economists. With Mathematics for Economists, expert mathematician Viatcheslav V. Vinogradov offers a straightforward, practical textbook for students in economics?for whom mathematics is not a scientific or philosophical subject but a practical necessity. Focusing on the most important fields of economics, the book teaches apprentice economists to apply mathematics algorithms and methods to economic analysis, while abundant exercises and problem sets allow them to test what they?ve learned.
?For non-mathematicians who just use math in their professional activity I believe this is a very helpful source of knowledge, and also a very efficient reference.??Elena Kustova, Saint Petersburg University

Viatcheslav V. Vinogradov is a researcher at the Economics Institute of the Academy of Sciences of the Czech Republic and a consultant to the World Bank.

Introduction

Preface

0 Preliminaries
0.1 Basic Mathematical Notation
0.2 Methods of Mathematical Proof.
0.3 Powers, Exponents, Logs and Complex Numbers

1 Linear Algebra
1.1 Matrix Algebra.
1.2 Systems of Linear Equations
1.3 Quadratic Forms
1.4 Eigenvalues and Eigenvectors
1.5 Diagonalization and Spectral Theorems
1.6 Appendix: Vector Spaces

2 Calculus
2.1 The Concept of Limit.
2.2 Differentiation - the Case of One Variable.
2.3 Rules of Differentiation
2.4 Maxima and Minima of a Function of One Variable
2.5 Integration.
2.6 Functions of More than One Variable
2.7 Multivariate Unconstrained Optimization
2.8 The Implicit Function Theorem.
2.9 (Quasi)Concavity and (Quasi)Convexity
2.10 Appendix: Matrix Derivatives
2.11 Appendix: Topological Structure and Its Implications
2.12 Appendix: Correspondences and Fixed-Point Theorems

3 Constrained Optimization
3.1 Optimization with Equality Constraints
3.2 The Case of Inequality Constraints
3.2.1 Non-Linear Programming
3.2.2 Kuhn-Tucker Conditions.
3.3 Appendix: Linear Programming.

4 Dynamics
4.1 Differential Equations.
4.1.1 Differential Equations of the First Order
4.1.2 Qualitative Theory of First-Order Differential Equations
4.1.3 Linear Differential Equations of a Higher Order with Constant Coefficients
4.1.4 Systems of First-Order Linear Differential Equations
4.1.5 Simultaneous Differential Equations and Types of Equilibria.
4.2 Difference Equations.
4.2.1 First-Order Linear Difference Equations
4.2.2 Second-Order Linear Difference Equations
4.2.3 The General Case of Order n.
4.2.4 Systems of Simultaneous First-Order Difference Equations with Constant Coefficients
4.3 Introduction to Dynamic Optimization
4.3.1 First-Order Conditions
4.3.2 Present-Value and Current-Value Hamiltonians
4.3.3 Dynamic Problems with Inequality Constraints

5 Exercises
5.1 Practice Problems
5.1.1 Problems
5.1.2 Answers.
5.2 Solved Problems
5.2.1 Linear Algebra.
5.2.2 Calculus.
5.2.3 Constrained Optimization
5.2.4 Dynamics
5.3 Economics Applications
5.4 Written Assignments
5.5 Sample Problem Sets
5.6 Unsolved Problems
5.6.1 More Problems
5.6.2 Sample Tests