Elementary Differential Equations

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Description

Contents

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Language

English

ISBN

Unknown

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

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