Differential Equations
Math 244, Spring 2014

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 10th 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
  
• 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 for first day
• Homework schedule to the first exam
• Homework schedule to the second exam.
• Homework to Exam 3.

Links by Chapter

1. Review Material
• Defining the Hyperbolic Trig Functions
• Solutions to the Hyperbolic handout
• Integration by Parts using a Table
• Partial Fraction Decomposition
2. Chapter 1
• Laplace's Demon
• Introduction to the Mathematics Computer Lab (For people who want to use the Lab. Also has some good setup instructions for Maple.)
• A Sample Direction Field (using Maple)
• Maple file: Direction fields for 1.1, p 10.
• PDF file: Direction fields for 1.1, p. 10
• Slides for discussion on Thursday
• Selected solutions, Chapter 1
3. Chapter 2
• Several examples in detail, Section 2.1
• Selected Solutions, 2.1
• Maple file for 2.1
• PDF version of the Maple file
• Maple file for 2.2
• Selected Solutions, 2.2
• Selected Solutions, 2.3 (updated to correct the decimal approx to ln(2)/7).
• Maple file for Parachute problem in 2.3
• Selected Solutions, 2.4 (updated to include 2.4, 13).
• Maple file for class, Example in 2.4
• Selected Solutions, 2.5
• Section 2.5, Extra Practice Solutions
• Section 2.6
4. Chapter 3
• Linear Operators and Cramer's Rule
• Solution to "Linear Operators and Cramer's Rule"
• Selected Solutions, 3.1 *Updated to include full solution to 23.
• Complex Numbers
• Solutions to the Complex Numbers handout
• Selected solutions, 3.2 *Updated to include full solution to 19.
• Selected solutions, 3.3 (Updated the section on Euler Equations, March 4th)
• Helpful Trigonometry (very useful in Sections 3.7/3.8
• Selected solutions, 3.4
• Selected solutions, 3.5
• Selected solutions, 3.6 (Exercise 12 updated)
• HOMEWORK CHANGE: 3.7- 5, 7, 9, 11, 24. For 7 and 9, see how far you can go without a computer. For 24, solve for k, then see if you can solve for v. ALSO: The trig handout (linked abouve after 3.3).
• Solutions to 3.7
• HOMEWORK CHANGE, 3.8: 1-3, 6, 11, 13.
• LINKS for Section 3.8:
  • Nice video from MIT- Beating and Resonance
  • (Youtube clip) The Tacoma Narrows Bridge Collapse
  • Selected Solutions, 3.8
5. Chapter 6 (Laplace Transforms)
   • Using Complex Arithmetic for the Laplace Transform. This is an addition to Section 6.1.
   • Solutions to the previous handout
   • Table of Laplace Transforms
   • Selected solutions, 6.1
   • Selected solutions, 6.2
   • Selected solutions, 6.3
   • Notes/Solutions for 6.4
   • Selected solutions, 6.5
   • Selected solutions, 6.6
6. Chapter 5 (Series Solutions)
   • Selected solutions, 5.1
   • Slides for Sections 5.1/5.2
   • Selected solutions, 5.2
7. Chapter 7 (Setting up Systems)
   • Figure for Tanks
   • Maple example (Exercise 10, 7.1)
   • Homework: Sect 7.1
   • Solutions, 7.1-7.2 HW
   • 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 and 7.8, Day 4)
   • Selected solutions to HW set 3 (for Day 4)
   • Summary: Elements of Chapter 7
   • Here is a nice direction field calculator for linear and nonlinear systems.
8. Chapter 9 (Nonlinear Analysis)
• The Poincaré Diagram
• Intro to Nonlinear Systems (has homework as well).
• Solutions to previous HW (UPDATED May 15)
• More notes on linearization (with some extra examples

Exam Materials

1. Exam 1 Materials:
   • Summary page for Exam 1
   • Review Questions for Exam 1
   • Solutions to Review Questions
2. Exam 2 Materials:
   • Summary of topics for Exam 2
   • Sample questions for Exam 2
   • Solutions to the Sample Questions
3. Exam 3 Materials:
   • Summary of Topics. NOTE: The exam will cover Chapter 6 and 5.1-5.2 (not 5.3 or 5.4).
   • Review questions
   • Solutions to Review questions
4. Final Exam Materials:
   • Summary of Chapter 7/9 material (newest stuff)
   • Overview of the course
   • Review questions
   • Solutions to the review (Updated to correct typos in 25, 26 and finish the solution in 31)