Elementary Differential Equations With Boundary Value Problems

by Kohler, Werner E.; Johnson, Lee W.

• ISBN13: 9780321121646
• ISBN10: 0321121643
• Additional ISBN(s): 9780321288356
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Addison Wesley
• More Book Details
• Purchase Benefits

Table of Contents

Introduction to Differential Equations

Introduction

Direction Fields

First Order Linear Differential Equations

Existence and Uniqueness

First Order Linear Homogeneous Differential Equations

Nonhomogeneous Differential Equations

Introduction to Mathematical Models

Mixing Problems and Cooling Problems

First Order Nonlinear Differential Equations

Existence and Uniqueness

Separable First Order Equations

Exact Differential Equations

Bernoulli Equations

The Logistic Population Model

One-Dimensional Motion with Air Resistance

One-Dimensional Dynamics with Distance as the Independent Variable

Euler's Method

Second Order Linear Differential Equations

Introduction

Existence and Uniqueness

The General Solution of Homogeneous Equations

Fundamental Sets and Linear Independence

Constant Coefficient Homogeneous Equations

Real Repeated Roots

Reduction of Order

Complex Roots

Unforced Mechanical Vibrations

The General Solution of the Linear Nonhomogeneous Equation

The Method of Undetermined Coefficients

The Method of Variation of Parameters

Forced Mechanical Vibrations, Electrical Networks, and Resonance

Higher Order Linear Differential Equations

Existence and Uniqueness

The General Solution ofnth Order Linear Homogeneous Equation

Fundamental Sets and Linear Independence

Constant Coefficient Homogeneous Equations

Nonhomogeneous Linear Equations

First Order Linear Systems

The Calculus of Matrix Functions

Existence and Uniqueness

Homogeneous Linear Systems

Fundamental Sets and Linear Independence

Constant Coefficient Homogeneous Systems

Complex Eigenvalues

Repeated Eigenvalues

Nonhomogeneous Linear Systems

Euler's Method for Systems of Differential Equations

Diagonalization

Functions of a Matrix and the Exponential Matrix

Laplace Transforms

The Laplace Transform

Lapla

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