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Mathematical Methods and Models for Economists. Angel de la Fuente. This book is intended as a textbook for a first-year Ph.
It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization.
The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems. Algebraic Structures.
The Real Number System. Metric and Normed Spaces. Static Optimization. Comparative Statics and Value Functions. Problems and Applications Consumer Preferences and Utility. Consumer Theory. Games in Normal Form and Nash Equilibrium. Equivalent Metrics and Norms. Linear Transformations. Linear Mappings between Normed Spaces.
Change of Basis and Similarity. Polynomial Equations. Partial and Directional Derivatives Continuous Differentiability.
Homogeneous Functions. Existence of Equilibrium. Concave Functions. Quasiconcave Functions. Quadratic Forms. Basic Concepts and Scalar Systems. Autonomous Systems. Autonomous Differential Equations. Solution of Nonautonomous Linear Equations.
Higher Dimensions Neoclassical Growth Models An Introduction to Dynamic Optimization Bibliography Optimal Growth in Discrete Time Convergence of Sequences in Metric Spaces. Linear Models. Problems
Mathematical Methods and Models for Economists