Differential Equations
Math 244, Fall 2024

Textbook

• Elementary Differential Equations and Boundary Value Problems, by William Boyce and Richard DiPrima (9th Edition)
  

  TEXT NOTE: This is NOT the current version, which is the 12th edition. There are a couple of different versions of the text; here are the links to Amazon.com for the information:

• With Boundary Value Problems (Used copies should run under $10.00)
  
• The text without Boundary Value Problems (Link removed- couldn't find a good used copy for a reasonable price).
• There also is an optional Student Solution Manual Available (typically, these have more detailed solutions to odd numbered problems)
• We'll generally be covering topics from Chapters 1-7 except Chapter 4. Also, topics from Chapter 7, 9 as time permits.

Beginning Material

• Syllabus
• Course Calendar
• Homework to Exam 1
• Homework to Exam 2
• Homework to Exam 3

Links by Section

• Video lectures from a past semester (Optional- This is here primarily for a backup in case you want to see what we did in class again. You shouldn't rely on this however since it is from a past semester.
• Review Material - Read these at your leisure.
• Defining the Hyperbolic Trig Functions
• Solutions to the Hyperbolic handout
• Integration by Parts using a Table
  • Video summarizing the process.
  • Would you rather watch Edward James Olmos in a classic pre-Battlestar Galactica performance ("Stand and Deliver")?
  • Integration by Parts using a Table (PDF)) Summary and Examples
• Partial Fractions
  • Partial Fraction Decomposition (PDF) Summary and Examples
  • Khan Academy videos on Partial Fractions
• Chapter 1
  • Practice Problems (used in the quiz below)
  • Direction Fields example
  • Take Home Quiz 1: Turn in the solutions to the following problems from the Practice Problems handout. \#1 in Partial Fractions, \#1 in Integration by Parts, \#1(a,b), 2(a,b), 3(c,d), 4(c,d), 5 from the section on algebra. Write your solutions up NEATLY and upload them to Canvas. Due: Monday Sep 4th at 11:59PM.
• Chapter 2
  • Homework to Replace 2.3
  • Homework solutions
• Chapter 3
  • Cramer's rule
  • Solutions to Cramer's rule handout
  • Linear Operators handout
  • Solutions to Linear Operators handout
  • Intro to Complex Numbers handout
  • Solutions to the Complex Numbers handout
  • Quiz 5 - due Monday after break (corrected last question)
  • Practice with constructing the Mass-Spring equation (HW to replace 3.7)
  • Solutions to the Mass-Spring practice problems
• Section 3.8:
  • Using a Complex Ansatz (not on the exam, but nice to know if you have some time).
  • Notes to replace 3.8
  • Solutions to the practice problems, 3.8
  • (Youtube clip) Video from MIT- Beating and Resonance (About 2 minutes)
  • Watch a wine glass shatter. (Less than 1 minute)
  • (Youtube clip) The Tacoma Narrows Bridge Collapse (Or was it resonance?) (About 6 minutes)
• Chapter 6 - The Laplace Transform
  • A table of Laplace transforms
  • Two excellent videos about the convolution:
    • 3Blue1Brown: But what is a convolution?
    • MIT- Convolutions in Image Processing (the person behind 3Blue1Brown)
• Chapter 5
  • Overhead slides for 5.1/5.2
  • Slides for handout (no pauses)
  • Chapter 5.2 Homework
    Exercises 1, 3, 4, 6, 7: Just compute the recurrence relation for each.
    Exercises 15, 17, 18: Compute the first five terms of each power series by using the derivative method.
    
  • Full solutions to the 5.2 homework
• To Replace Chapter 7:
  • Fri, Nov 22: Replacement for 7.1
    • Notes (in PDF) for today
    • Video notes 1 of 2
    • Video notes 2 of 2
    • Homework Handout. (with solutions)
  • Mon, Dec 2: Replaces 7.2/7.3
    • Notes for this material (in PDF), also with homework on the last page
    • Solutions to Homework
    • Video discussion 1 of 2
    • Video discussion 2 of 2
  • Wed, Dec 4: Replaces 7.3-7.5.
    • PDF notes for Section 7.3
    • Homework problems
    • Solutions to Homework
    • Optional video: Section 7.3-7.5, Part 1
    • Optional video: Section 7.3-7.5, Part 2
    • Optional video: Section 7.3-7.5, Part 3
  • Fri, Dec 6:
    • Complex Eigenvalues/vectors
      • Complex Eigenvalues, Part 1.
      • Complex Eigenvalues, Part 2
      • Notes about Complex Eigenvalues
      • Homework for Complex Eigenvalues
      • Solutions to Homework
  • Monday, Dec 9:
    • Double Root:
      • (Video) A Single Eigenvalue (and summary) (An error was made and then repeated about 0:30- The trace is 2 for both matrices).
      • (PDF) Notes
      • (PDF) Homework
    • Poincare Diagram:
      • (Video) Poincare Diagram Part 1
      • (Video) Poincare Diagram Part 2 with Examples
      • (PDF) The Poincare Diagram
      • (PDF) Notes

Exam Links

• Exam 1
  • Summary of topics for Exam 1
  • Exam 1 review questions
  • Exam 1 review solutions
• Exam 2
  • Summary of topics for Exam 2
  • Exam 2 review questions
  • Exam 2 review solutions
• Exam 3 (Moved to Wed, Nov 20)
  • Topics for Exam 3
  • Review questions
  • Solutions to the Review
• Final Exam
• Summary of "Chapter 7", or the material since Exam 3
• General review questions (lots to choose from)
• Solutions to the review questions
• Sample Final 1
• Sample Final 1 Solutions
• Sample Final 2
• Sample Final 2 Solutions

Other Links

• An online direction field plotter. You'll need it for 1.1, and in general for plotting the direction fields for first order DEs.
• A good plotter for 2x2 systems (ch 7, 9)