Differential Equations
Math 244, Fall 2018

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 Exam 2
• Homework through Exam 3
• Homework to the Final Exam! Remember, these homework assignments refer to the notes available on our CLEO website, NOT to the regular textbook, although it will be similar to the book's Chapter 7.

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
• Integration Practice Problems (with hints)
• Integration Practice solutions
• Exercises from 1.1, 15-20 (Matching)
3. Chapter 2
• From Sep 5- Maple HW 2: Solve Exercise 21 in 2.1, and Exercises 16, 28 in 2.2 using Maple. Turn in the Maple Worksheet by Tuesday (Sep 11) at 10PM. Remember that means to upload the Maple worksheet to your CLEo dropbox.
• For 2.3, Parachute Problem. Here is the Maple Worksheet.
• More sample model practice. The solutions are in a Maple file here.
• Maple HW 3: From Sep 17, please solve Section 2.3, #11 and 17, and Section 2.5, #15 using Maple. Due: Friday, Sep 21st (10PM).
• Extra Practice, Section 2.5
• Solutions to the Extra Practice
4. Chapter 3
• Extra Practice: Linear operators and Cramer's Rule
• Extra Practice solutions
• Maple HW 4 (Sep 26): Solve Exercise 25 in Maple, Section 3.1 (There's a video solving Exercise 26 below). Due: Friday evening (28th)- As usual, upload your Maple sheet to CLEO (You might call it: MapleHW4_MyName.mw)
• A primer on Complex Numbers, with some exercises.
• Solutions to the Complex Numbers Handout exercises
• Maple HW 5 (Oct 12): Solve Exercises 24, 25 in Section 3.3. NOTE: You don't need to try to get the textbook's solution to #25(c), but your answers should be consistent.
• 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
• Notes to replace Section 3.8
• Solution to homework that replaced Section 3.8 (previous link) (All solutions except for those assigned for the quiz!)
• 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.
5. Chapter 6
   • Table of Laplace Transforms
   • Some Complex Integrals
   • Solutions to the previous handout
   • Maple HW 6 (Nov 5): Solve exercises 6.4.8, 6.4.10, 6.5.2, 6.5.6, 6.5.20 using Maple. A video is given below on how to use the Heaviside and Dirac functions. DUE: Wednesday evening.
6. Chapter 5 (Series)
   • Slides for section 5.2 (An example in detail)
7. Chapter 7 (Linear Systems of ODEs)
   • This will be covered by a different set of notes (labeled as "Chapter 3") from a different text. The chapter is available on our CLEO website.
   • Practice problems and solutions (3.1-3.2)
   • Examples (in class)
   • Maple worksheet, examples of first order systems (Identical to what's linked below as well).
   • PDF output of the previous Maple file
   • Quiz 10 (Due Friday, Dec 6)

Exam 1

• Summary/Study Guide
• Review questions
• Review answers

Exam 2

• Summary/Study Guide
• Review questions
• Review answers

Exam 3

• Summary of topics
• Review questions
• Review solutions

Final Exam

• A summary of Chapter 7 (Boyce), also known as Chapter 3 on CLEO.
• Math 244 Overview of Topics
• Review questions. (Solution to 37(c) updated)
• Review solutions. (Updated for a typo on #13).
• The final exam will be on Wednesday, Dec 12, 2-4PM (usual classroom). You will be provided with the table of Laplace transforms, Poincare diagram, and the formulas for the Variation of Parameters.

Links for Maple (Video links below the regular links)

• Intro to Maple.
• Maple file, Chapter 1, Section 1 homework (Right-click, "Save Link As...")
• How to solve a couple of exercises from 2.1 and 2.2, then upload the Maple file to CLEO. (See HW 2 under Chapter 2 handouts above)
  Here is the Maple file from the video (right-click, "Save link as...")
  
• The parachutist, from Section 2.3. Here is the Maple file from the video (right-click, save link as...)
  
• Exercise 26, Section 3.1 Here is the Maple file from the video
  
• Note for fsolve (useful for 3.3 #24, for example)
  
• Maple and Laplace transform.
  
• A couple of problems from 6.4, 6.5 using Maple (Heaviside and Dirac).
  
• Maple file: Examples of plotting systems of first order.

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")