Summary Mathematics 2 for Economics Analysis and Dynamic Optimization by Josef Leydold

Mathematics 2 for Economics Analysis and Dynamic Optimization Josef Leydold Introduction 1.1 Overview 2 Sequences and Series 2.1 Limits of Sequences 2 2.2 Series 7 Exercises 11 Problems 11 3 Topology 13 3.1 Open Neighborhood 13 3.2 Convergence 15 3.3 Equivalent Norms 18 3.4 Compact Sets 20 3.5 Continuous Functions Exercises Problems 4 Derivatives 4.1 Roots of Univariate Functions 4.2 Limits of a Function 4.3 Derivatives of Univariate Functions 4.4 Higher Order Derivatives 4.5 The Mean Value Theorem 4.6 Gradient and Directional Derivatives 4.7 Higher Order Partial Derivatives 4.8 Derivatives of Multivariate Functions Exercises 36 41 Problems 42 5 Taylor Series 5.1 Taylor Polynomial 5.2 Taylor Series Landau Symbols Power Series and Analytic Functions