Solution Manual for

Ordinary Differential Equations

An Introduction to the Fundamentals

  Published by CRC Press

 

Prepared by Dr. Kenneth Howell,

Department of Mathematical Sciences, University of Alabama in Huntsville

   

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Below are the chapters of the solution manual for Ordinary Differential Equations: An Introduction to the Fundamentals, published by CRC Press.  (More precisely, below are the links to pdf files for the chapters.)

 

 

Some General Comments and Warnings:

 

1)  These solutions should be used only as a last resort!  Try doing the work yourself, first, using what is in the text as a guide.  If you need help, then see your instructor or go to any math tutoring service available to you.  Only if all else fails should you peek at the solutions here.

 

2)  Keep in mind that there may be several ways to answer a single problem.  What is given here is only one possible way to derive each correct answer.

 

3)  Beware of tpyos and dumb mistookes!  Much of what's below was written hastily and at odd hours, and was not adequately proofread.   If you find what you believe to be an error in any of these solutions, please let the author know (see below).  It would be appreciated if you included "DE Text Solutions" in the subject line of your email.

 

4)  Also feel free to send the author any other comments about this webpage or this text.

 

5)  This material is not in the public domain, and is protected by the copyright laws of the United States.  Viewers of this site have permission to download and use the material being made available here for their personal study.  You, the viewer, may download files, print a few chapters for your personal use, and have links to this website, but please, do not otherwise republish this material without the author's permission.

 

6)  By the way, "the author" is Dr. Kenneth Howell at the University of Alabama in Huntsville, and can be contacted at  howellkb@uah.edu .

 

 

 

Solutions to Selected Exercises

Chapter Published /

Modified

Notes

Part 1 - The Basics   

Chpt 1 - The Starting Point

1/30/2017

typos in 1.3c fixed

Chpt 2 - Integration

 

 

Part 2 - First-Order Equations 

Chpt 3 - Basics

 

 

Chpt 4 - Separable Eqns

 

 

Chpt 5 - Linear Eqns

 

 

Chpt 6 - Substitution

   

Chpt 7 - Exact Eqns & Gen Integrating Factors

 

 

Chpt 8 - Slope Fields

 

 

Chpt 9 - Euler's Num Method

   

Chpt 10 - Modeling

   

Part 3 - Higher Order Equations 

Chpt 11 - Extending FIrst-Order Concepts

 

 

 

Chpt 12 - Linear DEs & Reduction of Order

   

Chpt 13 - Homog DE Soln (General Results) 

 

 

Chpt 14 - Homog DE Soln (Verifying & Intro to Lin Operators) 

 

 

 

Chpt 15 - 2nd-Order Const Coeff Eqns

 

 

Chpt 16 - Springs: Part I

 

 

Chpt 17 - Arb Const Coeff Eqns

 

 

Chpt 18 - Euler Eqns

 

 

Chpt 19 - Gen Nonhomg Eqns

 

  

Chpt 20 - Method of Undet Coeffs

 

 

Chpt 21 - Springs: Part II

   

Chpt 22 - Variation of Parameters

 

 

Part 4 - Laplace Transforms         

Chpt 23 - Intro to Laplace Transforms

 

 

Chpt 24 - Differentiation & Laplace Transforms

 

 

Chpt 25 - Inverse Laplace Transforms

 

 

Chpt 26 - Convolution

 

 

Chpt 27 - Piecewise-Defined & Periodic Fcts

 

 

 

Chpt 28 - Delta Fcts

 

 

Part 5 - Power Series & Modified Power Series Solutions        

Chpt 29 - Review of Series

Chpt 30 - Power Series Solns I (Computational Methods)

Chpt 31 - Power Series Solns II (Generalizations & Theory)

Chpt 32 - Modified Power Series Solns & Frobenius Method

Chpt 33 - Theorems on Frobenius Method w/ Applics

Chpt 34 - Verifying the Theorems on Frobenius Method

There are no exercises in this chapter

Part 6 - Systems of Differential Equations (Brief Intro)        

Chpt 35 - A Starting Point

Chpt 36 - Critical Points, Direction Fields & Trajectories

 

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LEGAL STUFF:

Required Official Disclaimer: "The views, opinions, and conclusions expressed in this page are those of the author or organization and not necessarily those of The University of Alabama in Huntsville or its officers and trustees. The content of this page has not been reviewed or approved by UAHuntsville and the author or organization is solely responsible for its content."

Addendum:  According the official policy of the University of Alabama in Huntsville, this website is officially an unofficial UAHuntsville website and is not connected with UAHuntsville.

 

Copyright Notice:  The material at this site and all the material linked to from this site is protected under the copyright laws of the United States of America (see www.copyright.gov for more information on these laws).  The author grants the viewers of this site the permission to download and use this material for their personal study, but does not grant permission for any other use of this material.

 

Who to Contact If There Is a Reason to Contact the Guy Maintaining This Site:  Prof. Kenneth Howell, howellkb@uah.edu 

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