Differential Equations
Math 244, Fall 2019

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 11th 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 (first day)
• Homework through the first exam
• Homework to the second exam
• Homework to the third exam

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
• Khan Academy videos on Partial Fractions
2. Chapter 1
• Laplace's Demon
• Integration Practice Problems (with hints)
• Integration Practice solutions
• Direction Fields practice
• Day 2 slides
3. Chapter 2
• Exercise 21 in Section 2.4 (Detailed solution)
4. Chapter 3
• Extra Practice Problems, 3.1
• Solutions to the extra practice
• Handout on Complex Numbers
• Solutions to Exercises in Complex Numbers Handout
• Matching for 3.7
• Using the Complex Exponential for Periodic Forcing (and Integrals!) (Solutions attached as well).
• Summary of 3.7
• Mass-Spring model practice problems for 3.7
• Mass-Spring model solutions
• Videos for Beating and Resonance
• (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)
• (Youtube) Film from 1969 with Prof. Miller (About 14 minutes total)
• (Youtube) - Just for fun.
• Notes for Section 3.8
• Solutions to homework from 3.8 notes
5. Chapter 6 (Laplace transforms)
   • Table of Laplace Transforms
6. Chapter 5 (Power Series)
   • Class notes from Wed, Nov 13 (Power series), PLUS Quiz 8!
   • Quiz 8 Solutions
7. Systems of Differential Equations (Generally Chapter 7)
   • Homework, Day 1 (Conversions)
   • Solutions to Conversions HW
   • Homework, Friday 11/22 (Generally over 7.1-7.2)
   • Previous homework solutions (from Friday).
   • Homework, Monday Dec 02
   • Previous homework solutions (from Monday)
   • LECTURE NOTES from Monday and Wednesday. Also includes homework for Wed, Dec 4.
   • Extra practice sketching solutions (added to Wednesday homework, if time). Solutions are included.
8. Nonlinear Systems of Differential Equations (topics from Ch 9)
   • Poincare Diagram.
   • Handout that includes the Poincare Diagram and linearizing systems of nonlinear differential equations.
   • Solutions to the homework included in the handout.
   • Last quiz: Take home quiz

Exam Materials

• Exam 1 materials:
  • Summary of Material for Exam 1
  • Review Questions for Exam 1
  • Review solutions
• Exam 2 materials:
  • Summary of Material for Exam 2
  • Review Questions for Exam 2
  • Review solutions.
• Exam 3 materials:
  • Summary of Material for Exam 3
  • Review Questions for Exam 1
  • Review solutions
• Final Exam materials:
  • Summary of topics from Ch 7 and 9
  • Review Questions
  • Review solutions

Maple

• Intro to Maple.
• Here's a short video with some installation help:
  
• The following video shows you how to enter a differential equation and get a direction field:
  

Demo Software

Extra Material, for fun!

• Professor Stephen Smale, Fields Medalist in Dynamical Systems theory.
  
• Professor Benoit Mandelbrot (deceased). A great TED talk about Fractal Geometry.
  
• Professor Nancy Kopell, Mathematician and Director of Cognitive Rhythms at Boston University (Part of "the Boston group")