Differential Equations
Math 244, Spring 2018

Textbook

The book we're using in the Fall will be "Differential Equations", by Paul Blanchard, Bob Devaney and Glen Hall (Fourth Edition). Important NOTE: The book is often sold "with DE Tools Printed Access Card". We don't require that, so if you're buying a used version without it, don't worry. Here's an Amazon link with more book details:

Amazon link for Differential Equations text
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 1-6, as well as Appendices A and B.

Beginning Material

Online Calculus Book (for review)
Class Syllabus
Course Calendar (Updated Jan 28 to reflect the HW assignment page)
Homework through Exam 1
Homework through Exam 2
Homework through the Final

Handouts by Chapter

Chapter 1
- Laplace's Demon
- Direction Fields
- Integration Practice Handout
- Direction Fields
- Figure, Exercise 13, Section 1.3 (for class discussion)
- Figure, Exercise 16, Section 1.3 (for class discussion)
- Project 1: Learning Model
Chapter 2
Chapter 3
- Cramer's Rule: Solve a System of Equations
- Some Phase Portraits (Class handout)
- A Primer on Complex Numbers (For 3.4)
- Solutions to the practice problems above
- The Poincare Diagram (3.8)
Chapter 4
- Trigonometry note: Acos(wt)+Bsin(wt)
- Question for after Section 4.2 (overhead)
- Section 4.3 (Undamped Oscillators, Beating and Resonance)
- Section 4.4 (Oscillators with period forcing)
  - How does the maximum amplitude change with damping? (plot)
  - How does the maximum amplitude change with damping (animation)
  - Clarification and Extra Practice for Section 4.4
  - Solutions to the extra practice.
  - 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.
Chapter 5: Nonlinear Systems
- Section 5.1: Local linear analysis
  - Animation for first competing species model
  - Animation for second competing species model
  - Animation for the Predator Prey model\
  - Animation for the Nonlinear, Undamped Pendulum. Also see "Pendulums" in the DEtools software
  - CometAnimations.mw. This is a Maple file showing the commands that were used to create the animations above (optional file for people who are familiar with Maple).
- Section 5.2: Nullclines
  - Graphs from class discussion (Wed and Fri)
Chapter 6: The Laplace Transform
- Table of Laplace Transforms
- Details about the examples we did in class (6.2 HW).

Take home quizzes/projects

Exam 1 Material:

Exam 2 Materials

Chapter 2 Review: 1-11, 15-16, 22-29, 31-35. Solutions are on CLEo.
Chapter 3 Review: 1-4, 6-8, 10-13, 19-20, 27-32. Solutions are on CLEo.
Familiarize yourself with the "Extra Practice" problems in the links above (Extra Practice with Mass-Spring Systems and converting between systems and nth order DEs).
Review 2 questions
Solutions to the review 2 questions

Final Exam Review Questions

Misc Links

A nice online Euler's Method calculator.
A note about using the Java software on the Math Lab Computers: Before you run it for the first time, right-click on the icon, then choose the "Permissions" tab, then click on the box that says: "Allow executing this file as program". (You might need to do something similar on your home machine as well).

Differential EquationsMath 244, Spring 2018