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Elementary Differential Equations

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Table of Contents

Table of Contents
Preface
Chapter 1 Introduction
- Section 1.1 Some Applications Leading to Differential Equations
- Section 1.2 Basic Concepts
- Section 1.3 Direction Fields for First Order Equations
Chapter 2 First Order Equations
- Section 2.1 Linear First Order Equations
- Section 2.2 Separable Equations
- Section 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations
- Section 2.4 Transformation of Nonlinear Equations into Separable Equations
- Section 2.5 Exact Equations
- Section 2.6 Exact Equations
Chapter 3 Numerical Methods
- Section 3.1 Euler's Method
- Section 3.2 The Improved Euler Method and Related Methods
- Section 3.3 The Runge-Kutta Method
Chapter 4 Applications of First Order Equations
- Section 4.1 Growth and Decay
- Section 4.2 Cooling and Mixing
- Section 4.3 Elementary Mechanics
- Section 4.4 Autonomous Second Order Equations
- Section 4.5 Applications to Curves
Chapter 5 Linear Second Order Equations
- Section 5.1 Homogeneous Linear Equations
- Section 5.2 Constant Coefficient Homogeneous Equations
- Section 5.3 Nonhomogeneous Linear Equations
- Section 5.4 The Method of Undetermined Coefficients I
- Section 5.5 The Method of Undetermined Coefficients II
- Section 5.6 Reduction of Order
- Section 5.7 Variation of Parameters
Chapter 6 Applications of Linear Second Order Equations
- Section 6.1 Spring Problems I
- Section 6.2 Spring Problems II
- Section 6.3 The RLC Circuit
- Section 6.4 Motion Under a Central Force
Chapter 7 Series Solutions of Linear Second Equations
- Section 7.1 Review of Power Series
- Section 7.2 Series Solutions Near an Ordinary Point I
- Section 7.3 Series Solutions Near an Ordinary Point II
- Section 7.4 Regular Singular Points Euler Equations
- Section 7.5 The Method of Frobenius I
- Section 7.6 The Method of Frobenius II
- Section 7.7 The Method of Frobenius III
Chapter 8 Laplace Transforms
- Section 8.1 Introduction to the Laplace Transform
- Section 8.2 The Inverse Laplace Transform
- Section 8.3 Solution of Initial Value Problems
- Section 8.4 The Unit Step Function
- Section 8.5 Constant Coeefficient Equations with Piecewise Continuous Forcing Functions
- Section 8.6 Convolution
- Section 8.7 Constant Coefficient Equations with Impulses
- 8.8 A Brief Table of Laplace Transforms
Chapter 9 Linear Higher Order Equations
- Section 9.1 Introduction to Linear Higher Order Equations
- Section 9.2 Higher Order Constant Coefficient Homogeneous Equations
- Section 9.3 Undetermined Coefficients for Higher Order Equations
- Section 9.4 Variation of Parameters for Higher Order Equations
Chapter 10 Linear Systems of Differential Equations
- Section 10.1 Introduction to Systems of Differential Equations
- Section 10.2 Linear Systems of Differential Equations
- Section 10.3 Basic Theory of Homogeneous Linear System
- Section 10.4 Constant Coefficient Homogeneous Systems I
- Section 10.5 Constant Coefficient Homogeneous Systems II
- Section 10.6 Constant Coefficient Homogeneous Systems III
- Section 10.7 Variation of Parameters for Nonhomogeneous Linear Systems
- A Brief Table of Integrals
Answers to Selected
Index