Extra Chapters for

Ordinary Differential Equations

An Introduction to the Fundamentals

  2016 Edition


Prepared by Dr. Kenneth Howell,

Department of Mathematical Sciences, UAH'ville


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Below are links to chapters of the text that did not get into the published text, either because of concerns about the length of the text, the level of the material or because the author just had not finished those chapters in time.



Some General Comments and Warnings:


1)  Much of the material in these extra chapters assume that the reader has a basic knowledge of linear algebra and multivariable calculus, such as covered in a standard introductory course in linear algebra, and the standard "calc. III" course.  (This is not assumed in the published text.)


2)  The answers to the exercises are at the end of the chapters.


3)  Material may be added, modified or removed at the author's whim.


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


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 the author's 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)  If you were not already aware, "the author" is Dr. Kenneth Howell, Associate Professor (Emeritus) of Mathematics at the University of Alabama in Huntsville, and can be contacted at  howell@math.uah.edu .



  Extra Chapters  

Part 6 - Systems of Differential Equations  (cover page)            

Table of Contents for Part 6



Addendum to Chpt 35: Higher-Order Systems


Chpt 36: Trajectories (Alt. Version) 

1/1/2016    A little more complete than the version in the published text

Chpt 37: Gen Homog Lin Systems


Chpt 38:  Homog Const Matrix Sys 1


Chpt 39:  Homog Const Matrix Sys 2


Chpt 40:  Homog Const Matrix Sys 3


Chpt 41:  Nonhomog Linear Systems


Chpt 42:  NonLinear Systems


Chpt 43:  Coord Curves & Trajectories

1/1/2016    Draft Version

Chpt 44:  Liapunov Method

1/1/2016    Draft Version

Chapters 43 -- 50 (or so) on autonomous nonlinear systems

and numerical methods

TBD   To be added 
Part 7 - Boundary-Value Problems  (cover page)  All the following should be considered as "early drafts".

Table of Contents for Part 7



Chpt 51: Boundary-Value Problems (Intro)


Chpt 52: Sturm-Liouville Problems


Chpt 53: Some Applications


Chpt 54: Choosing the Sturm-Liouville Problems

1/1/2016   (A very preliminary version)  


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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, howell@math.uah.edu