Simon C.P., Blume L. Mathematics for Economists

W.W. Norton & Company, 1994. — xx, 930 p. — ISBN 0-393-95733-0.For better or worse, mathematics has become the language of modern analytical economics. It quantifies the relationships between economic variables and among economic actors. It formalizes and clarifies properties of these relationships. In the process, it allows economists to identify and analyze those general properties that are critical to the behavior of economic systems.
Elementary economics courses use reasonably simple mathematical techniques to describe and analyze the models they present: high school algebra and geometry, graphs of functions of one variable, and sometimes one-variable calculus. They focus on models with one or two goods in a world of perfect competition, complete information, and no uncertainty. Courses beyond introductory micro- and macroeconomics drop these strong simplifying assumptions. However, the mathematical demands of these more sophisticated models scale up considerably. The goal of this text is to give students of economics and other social sciences a deeper understanding and working knowledge of the mathematics they need to work with these more sophisticated, more realistic, and more interesting models.Preface.
Introduction.One-Variable Calculus: Foundations.
One-Variable Calculus: Applications.
One-Variable Calculus: Chain Rule.
Exponents and Logarithms.
Linear Algebra.
Introduction to Linear Algebra.
Systems of Linear Equations.
Matrix Algebra.
Determinants: An Overview.
Euclidean Spaces.
Linear Independence.
Calculus of Several Variables.
Limits and Open Sets.
Functions of Several Variables.
Calculus of Several Variables.
Implicit Functions and Their Derivatives.
Optimization.
Quadratic Forms and Definite Matrices.
Unconstrained Optimization.
Constrained Optimization I: First Order Conditions.
Constrained Optimization II.
Homogeneous and Homothetic Functions.
Concave and Quasiconcave Functions.
Economic Applications.
Eigenvalues and Dynamics.
Eigenvalues and Eigenvectors.
Ordinary Differential Equations: Scalar Equations.
Ordinary Differential Equations: Systems of Equations.
Advanced Linear Algebra.
Determinants: The Details.
Subspaces Attached to a Matrix.
Applications of Linear Independence.
Advanced Analysis.
Limits and Compact Sets.
Calculus of Several Variables II.
Appendices.
Sets, Numbers, and Proofs.
Trigonometric Functions.
Complex Numbers.
Integral Calculus.
Introduction to Probability.
Selected Answers.