Differential Equations
Math 244, Fall 2012

Textbook for next Fall

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

  TEXT NOTE: If you're getting this on your own, you may choose to get the version without Boundary Value Problems (only a few dollars difference). Links on Amazon.com:

• With Boundary Value Problems
  
• The text without Boundary Value Problems
• 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. Chapter 7 is done as time permits.

Beginning Material

• Syllabus
• Course Calendar
• Homework Set to Exam 1
• Homework Set to Exam 2
• Homework Set to Exam 3
• For the remaining homework, see the sections below.

Links by Chapter

1. Calculus Review Material
• Integration by Parts using a Table
• Partial Fraction Decomposition
• Practice with Integrals (with hints)
2. Chapter 1
• Laplace's Demon
• Introduction to the Mathematics Computer Lab
• Examples using Maple in Chapter 1, and Section 2.1 (More examples below)
• A Sample Direction Field (using Maple)
• Samples from Section 1.1, pg. 10
• Selected Solutions, Chapter 1
3. Chapter 2
   • Selected Solutions, Section 2.1 (Linear DEs)
   • Selected Solutions, Section 2.2 (Separable Equations)
   • Selected Solutions, 2.3 (Modeling)
   • Selected Solutions, 2.4 (Existence and Uniqueness)
   • Extra Practice, 2.5
   • Extra Practice solutions Correction to 1(e): Should not be autonomous (corrected now)
   • Selected Solutions, 2.6
4. Chapter 3
   • Operators and Cramer's Rule
   • Solutions (Operators and Cramer's Rule)
   • Selected solutions to Homework, Section 3.1
   • Primer on Complex Numbers (with additional HW)
   • Solutions (Complex Numbers handout)
   • Selected solutions to Homework, Section 3.2
   • Maple file for Section 3.3 Exercises
   • PDF version of the Maple file
   • Practice with Cosine Sums (to help with Section 3.3 and later sections)
   • Selected solutions to Homework, Section 3.3
   • Selected solutions to Homework, Section 3.4
   • Lecture notes, Section 3.5
   • Handouts for Section 3.5 (of the lecture notes)
   • Extra Trig Practice (for Section 3.7).
   • Solutions to the Extra Trig Practice
   • In-class exercise for Friday
   • Video Clips for Beating, Resonance and the Tacoma Narrows Bridge (For Friday)
     1. (YouTube clip) Tacoma Narrows Bridge Collapse
     2. (YouTube clip) Short clip from a Physics class (Paul Hewitt)
     3. From Wikipedia, a nice sample at the bottom of the page
     4. (YouTube clip) Breaking glass using resonance (From CalTech, about 3 minutes)
5. Chapter 6 (Laplace Transforms)
   • A note about integrating using the complex exponential (with some extra homework to add to Section 6.1)
   • The Table of Laplace Transforms
   • Selected Solutions to Homework, Section 6.1
   • Selected Solutions to Homework, Section 6.2
   • Selected Solutions to Homework, Section 6.3
   • Solutions and Discussion, Section 6.4
   • Selected Solutions to Homework, Section 6.5
   • Selected Solutions to Homework, Section 6.6
6. Chapter 5 (Series Solutions)
   • Selected Solutions to Homework, Section 5.1
   • Examples for 5.2 and 5.3
   • (Optional)Solving and IVP using a Power Series in Maple
     • Maple file containing the examples
     • A PDF containing the Maple output of the examples.
   • Solutions to Section 5.2
   • Solutions to Section 5.3
   • Solutions to Section 5.4 (Recall that the homework was modified to: 5.4, 1, 3, 5, 8, 10, 17, 19, 27, 31, 41. Also look at the next handout.
   • End of Chapter 5 (A couple of notes, questions, and solutions)
7. Chapter 7 (Systems of DEs)
• A system of coupled tanks
• Homework set for 7.1 and 7.2
• Solutions, HW for 7.1 and 7.2
• A very nice Java demonstration (with 1950's voice over!) to give you a geometric understanding of eigenvectors (for 2x2 matrices).
• Here is the Java applet without the voice over. Credit: Pavel Grinfeld. and used by Gil Strang at MIT.
• Homework set 2 (for elements of 7.3 and 7.5)
• Homework set 2 solutions
• Homework set 3 (for elements of 7.6/7.8)
• Homework set 3 solutions
• Summary of Chapter 7 material
8. Chapter 9 (Classifying Equilibria and Nonlinear Systems)
   • Examples from Handout in-class, corrected
   • Handout from class, Poincare Diagram and Nonlinear Systems (corrected)
   • SOLUTIONS, HW for elements of Chapter 9
   • The Poincare Diagram
   • A nice Java plotter for nonlinear systems
   • The last homework set (both linear and nonlinear systems)
   • Solutions, the last homework set

Exam Materials

• Exam 1:
  1. Summary of the Material (Ignore Euler's Method)
  2. Review Questions (Ignore 11, 12)
  3. Answers to Review
• Exam 2:
  1. Solutions to Quiz 5
  2. Handout on last day- Summary of Forced, Damped Systems
  3. Solutions to the exercises in the handout.
  4. Summary of Chapter 3
  5. Sample Questions, Chapter 3
  6. Solutions to the Sample Questions
• Exam 3
  1. Exam 3 topics
  2. Review questions for Exam 3
  3. Solutions to the Review
• Final Exam
  1. Overview of the course
  2. Review questions
  3. Solutions to the Review. (Updated to correct 37(a) and give more details in 37).