Elementary Differential Equations

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

• ISBN13: 9780321290441
• ISBN10: 0321290445
• Edition: 2nd
• Format: Hardcover
• Copyright: 2011-03-23
• Publisher: Pearson

Summary

Elementary Differential Equations with Boundary Value Problemsintegrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way that provides students with the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it.With an emphasis on linear equations, linear and nonlinear equations (first order and higher order) are treated in separate chapters. In developing mathematical models, this text guides the student carefully through the underlying physical principles leading to the relevant mathematics. Asking students to use common sense, intuition, and ls"back-of-the-envelopers" checks as well as challenging them to anticipate and interpret the physical content of the solution encourage critical thinking.MARKET: Intended for use in introductory course in differential equations.

Table of Contents

Introduction to Differential Equations

Examples of Differential Equations

Direction Fields

First Order Differential Equations

Introduction

First Order Linear Differential Equations

Introduction to Mathematical Models

Population Dynamics and Radioactive Decay

First Order Nonlinear Differential Equations

Separable First Order Equations

Exact Differential Equations

The Logistic Population Model

Applications to Mechanics

Euler's Method

Review Exercises

Second and Higher Order Linear Differential Equations

Introduction

The General Solution of Homogeneous Equations

Constant Coefficient Homogeneous Equations

Real Repeated Roots; Reduction of Order

Complex Roots

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