Introduction to Difference Equations

Description

Title page Preface 0 Introduction 1 The Calculus of Finite Differences 1.1 The First Difference Function 1.2 Second and Higher Differences 1.3 The Operator E 1.4 Some Properties of Δ and E 1.5 Equivalence of Operators 1.6 Indefinite Summation: The Operator Δ^(-1) *1.7 Analogies between the Difference and Differential Calculus 2 Difference Equations 2.1 Basic Definitions 2.2 Solutions of a Difference Equation 2.3 An Existence and Uniqueness Theorem 2.4 The Equation Y_(k+l) = AY_k + B 2.5 Sequences 2.6 Solutions as Sequences 2.7 Simple and Compound Interest 2.8 Economic Dynamics 2.9 Inventory Analysis 2.10 A Probability Model for Learning 2.11 Geometric Growth *2.12 Approximating a Differential Equation by a Difference Equation 3 Linear Difference Equations with Constant Coefficients 3.1 Some Basic Theorems 3.2 Fundamental Sets of Solutions 3.3 General Solution of the Homogeneous Equation 3.4 Particular Solutions of the Complete Equation 3.5 Limiting Behavior of Solutions 3.6 Illustrative Examples from the Social Sciences 3.7 The General Case of Order n * 3.8 Linear Differential Equations with Constant Coefficients 4 Selected Topics 4.1 Equilibrium and Stability 4.2 First-Order Equations and Cobweb Cycles 4.3 A Characteristic-Value Problem *4.4 Generating Functions 4.5 Matrix Methods Selected References Answers to Problems Index