Differential Equations
Math 244, Spring 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 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 (first day)
• Homework through the first exam
• Homework through the second exam
• Homework through 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
• Exercises from 1.1, 15-20 (Matching)
• Take home quiz (and first Maple lab). Due next Wed, Jan 23.
3. Chapter 2
• Sample using Maple for Section 2.2
• Reminder: Maple lab 2 (Exercises 2.3 #11, 28) Due Friday evening. (Assignment was updated on Jan 31). See the videos below for Maple hints and solutions to related problems. NOTE: The lab was changed to delete the problem from 2.5, only the ones from 2.3 are due.
4. Chapter 3
• Extra Practice Problems, 3.1
• Solutions to the extra practice
• Handout on Complex Numbers
• Solutions to Exercises in Complex Numbers Handout
• Maple Lab 3: Solve Exercise 17 in Section 3.4 using Maple. A sample Maple session is shown in the video section below- In it, we solve Exercise 15. DUE: Next Wednesday, Feb 27, 11:59PM.
• Matching for 3.7
• Using the Complex Exponential for Periodic Forcing (and Integrals!) (Solutions attached as well).
• 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
• Quiz 6 (Take Home) Solutions
5. Chapter 6 (Laplace Transforms)
   • Table of Laplace Transforms
   • Some Complex Integrals
   • Solutions to the previous handout
6. Chapter 7 (Systems of Differential Equations)
   • Homework to replace Section 7.1 HW
   • Solutions to HW to replace 7.1
   • Notes and Homework to replace Section 7.2 (HW passed out in class).
   • Solutions to the homework to replace 7.2
   • Notes to replace Sections 7.3-7.5
   • Homework for the previous section (7.3-7.5)
   • Solutions to the HW.
   • Notes to replace Sections 7.6-7.8
   • Homework to replace 7.6-7.8
   • HW solutions
7. Graphical Analysis/Poincare Classification
   • Poincare Classification Diagram
   • Graphical Analysis discussion
   • Homework. NOTE: Typo in 4(a), lower left element of the matrix is -1, not +1.
   • Solutions
8. Nonlinear Analysis (for Friday)
   • Linearization and Poincare Classification

Material for Exams

• Exam 1:
  • A summary of topics
  • Review questions
  • Review solutions
• Exam 2:
  • Chapter 3 Summary
  • Chapter 3 Review Questions
  • Chapter 3 Review solutions
• Exam 3:
  • Topics for Exam 3 (Ch 6, 5.1-5.2)
  • Exam 3 Review Questions
  • Exam 3 Review solutions
• Final Exam:
  • Quiz 11 (Take Home) Solutions
  • Summary of the last part of the course
  • A one-page summary of Math 244
  • 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:
  
• Solve Exercise 10 in Section 2.3
  
• Solve Exercise 28 in Section 2.3 (Just uploaded Jan 31)
  
• Solve Exercise 15, Section 3.4
  

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")