# Ordinary Differential Equations

DOI link for Ordinary Differential Equations

Ordinary Differential Equations book

# Ordinary Differential Equations

DOI link for Ordinary Differential Equations

Ordinary Differential Equations book

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The Second Edition of ** Ordinary Differential Equations: An Introduction to the Fundamentals** builds on the successful First Edition. It is unique in its approach to motivation, precision, explanation and method. Its layered approach offers the instructor opportunity for greater flexibility in coverage and depth.

Students will appreciate the author’s approach and engaging style. Reasoning behind concepts and computations motivates readers. New topics are introduced in an easily accessible manner before being further developed later. The author emphasizes a basic understanding of the principles as well as modeling, computation procedures and the use of technology. The students will further appreciate the guides for carrying out the lengthier computational procedures with illustrative examples integrated into the discussion.

Features of the Second Edition:

- Emphasizes motivation, a basic understanding of the mathematics, modeling and use of technology
- A layered approach that allows for a flexible presentation based on instructor's preferences and students’ abilities
- An instructor’s guide suggesting how the text can be applied to different courses
- New chapters on more advanced numerical methods and systems (including the Runge-Kutta method and the numerical solution of second- and higher-order equations)
- Many additional exercises, including two "chapters" of review exercises for first- and higher-order differential equations
- An extensive on-line solution manual

About the author:

**Kenneth B. Howell** earned bachelor’s degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master’s and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville. Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of *Principles of Fourier Analysis, Second Edition* (Chapman & Hall/CRC, 2016).

## TABLE OF CONTENTS

part Part I|34 pages

The Basics

part Part II|208 pages

First-Order Equations

part Part III|206 pages

Second- and Higher-Order Equations

chapter 14|16 pages

#### Higher-Order Linear Equations and the Reduction of Order Method

chapter 15|20 pages

#### General Solutions to Homogeneous Linear Differential Equations

chapter 16|17 pages

#### Verifying the Big Theorems and an Introduction to Differential Operators

chapter 17|20 pages

#### Second-Order Homogeneous Linear Equations with Constant Coefficients

chapter 19|18 pages

#### Arbitrary Homogeneous Linear Equations with Constant Coefficients

chapter 22|20 pages

#### Method of Undetermined Coefficients (aka: Method of Educated Guess)

part Part IV|125 pages

The Laplace Transform

part Part V|188 pages

Power Series and Modified Power Series Solutions

chapter 32|26 pages

#### Series Solutions: Preliminaries (A Brief Review of Infinite Series, Power Series and a Little Complex Variables)

chapter 35|38 pages

#### Modified Power Series Solutions and the Basic Method of Frobenius

part Part VI|76 pages

Systems of Differential Equations