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MA221: Differential Equations

Unit 1: Introduction to Ordinary Differential Equations   In this unit, we will examine ODEs, their use, and their types.  We will also take a look at some classic ODE-based problems.  While this course will focus on the solution of linear initial-value problems expressed as ODEs, you should know the limits and characteristics of the various classes of ODE as well. 

Unit1 Learning Outcomes
Upon successful completion of this unit, the student should be able to:
- Define ordinary differential equations. - Distinguish ordinary differential equations from other types of differential equations. - Determine the order of an ordinary differential equation. - Classify ordinary differential equations. - Identify common errors which arise when attempting to find the solution for ordinary differential equations. - Apply the superposition principle to find the solution for ordinary differential equations. - Find the solution for initial value problems. - Find the solution for boundary value problems.

1.1 Introduction to the Study of ODEs   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” Link: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the section titled “Differential Equation” on page 2.  This reading will be used again in Unit 3.
 
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  • Reading: Jirka.org: Jiri Lebl’s Notes on Diffy Qs: “0.2 Introduction to Differential Equations” Link: Jirka.org: Jiri Lebl’s Notes on Diffy Qs: “0.2 Introduction to Differential Equations”  (PDF)
     
    Also available in:
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    EPUB
     
    Instructions: Click on the link above and then click on the link that says “Download the book as PDF.”  Please only read the content of section 0.2.1 on page 7.

    Terms of Use: The work above is released under a Creative Commons Attribution-Share-Alike License 3.0 (HTML).  It is attributed to Jiri Lebl and the original version can be found here (PDF).

1.2 Classification of ODEs   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” Link: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the sections titled “Order” and “Ordinary and Partial Differential Equations” on pages 2 and 3.
 
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1.3 Examples of ODEs and their Solutions   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts “ Link: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the section titled “Solution” on pages 3 to 5.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

  • Reading: Jirka.org: Jiri Lebl’s Notes on Diffy Qs: “0.2 Introduction to Differential Equations” Link: Jirka.org: Jiri Lebl’s Notes on Diffy Qs: “0.2 Introduction to Differential Equations” (PDF)
     
    Also available in:
    HTML

    EPUB
     
    Instructions: Click on the link above and then click on the link that says “Download the book as PDF.”  Please only read the content of section 0.2.2 and 0.2.3 on page 7 to 11.

    Terms of Use: The work above is released under a Creative Commons Attribution-Share-Alike License 3.0 (HTML).  It is attributed to Jiri Lebl and the original version can be found here (PDF).

  • Reading: MIT: Professor Haynes Miller’s 18.03 Supplementary Notes: “Chapter 1” Link: MIT: Professor Haynes Miller’s 18.03 Supplementary Notes: “Chapter 1” (PDF)
     
    Instructions: Click on the PDF linked above and read the whole chapter.
     
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  • Web Media: YouTube: Dr. Chris Tisdell’s “What is a Differential Equation?” Link: YouTube: Dr. Chris Tisdell’s “What is a Differential Equation?” (YouTube)
     
    Instructions: Watch this 23-minute video for a summary of some of the concepts that you have studied so far.
     
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1.4 Linear ODEs and the Superposition Principle   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” Link: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the section titled “Linear Differential Equations” on page 3.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

  • Reading: Efunda’s “Higher Order Linear Differential Equations” Link: Efunda’s “Higher Order Linear Differential Equations” (HTML)
     
    Instruction: Please click on the above link and read the entire section.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

  • Web Media: Khan Academy: “What is a Differential Equation” Link: Khan Academy: “What is a Differential Equation”  (YouTube)
     
    Also available in:
    iTunes U
     
    Instructions: Please watch the lecture, which is an introduction to differential equations.

    Watching this lecture should take approximately 10 minutes.

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

1.5 Initial Value Problems   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” Link: Lamar University: Paul Dawkins’ Differential Equations: “Basic Concepts” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the sections titled “Initial Condition,” “Initial Value Problem,” “Interval of Validity,”  “Actual Solution,” and “Implicit/Explicit Solution,” which can be found on pages 5 to 7.
 
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1.6 Boundary Value Problems   - Reading: Lamar University: Paul Dawkins’ Differential Equations: “Boundary Value Problems & Fourier Series” Link: Lamar University: Paul Dawkins’ Differential Equations: “Boundary Value Problems & Fourier Series” (PDF)
 
Instructions: Click on the link above and then look for the line that says “Here is the file you requested: Differential Equations (Math 3301).”  Click on the link associated with “Differential Equations (Math 3301).”  Read only the first three pages of the section titled “Boundary Value Problems” on pages 375 to 377.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.