Math 119B: Ordinary Differential Equations
UC Davis, Spring 2012

News and announcements

• (6/12) Have a great summer vacation!
• (6/12) The final grades have been submitted to the registrar and should be visible through your SIS account. I have also set up a Gradebook on the course SmartSite where you can see your final exam score and the final numerical score computed as a weighted average of the different course components.
• (6/12) Click here for the solutions to the final exam.
• (6/6) Click here for an information sheet with details about the final exam and some tips for studying.
• (5/16) Click here for solutions to the second midterm quiz.
• (5/15) Click here for solutions to the review problems from HW #5.
• (4/25) Click here for solutions to the first midterm quiz.
• (4/10) Starting tomorrow, all lectures will take place in Wellman 107.

General course information

• Instructor: Dan Romik
• Lecture times and place: MWF 1:10-2:00 at Wellman 107
• Office hours: W 2:30-3:30 in my office, MSB 2218
• Prerequisites: MAT 21-22 lower division math series; 119A
• Course description: Click here for a detailed syllabus.
• Textbook and lecture notes:
  • The course will use these lecture notes (last updated on 5/29/12).
  • Part of the course will cover topics from Chapters 9 and 10 in the book Nonlinear Dynamics and Chaos, by Steven H. Strogatz.
• Grading: The final grade will be determined from the following components:
  • Homework (the highest 4 scores from 8 weekly assignments) -- 20%
  • Two in-class midterm quizzes (25 minutes each) -- 30%
  • Final exam -- 50%
  Final and midterm dates:
  • Midterm quiz 1 -- Wednesday, April 25
  • Midterm quiz 2 -- Wednesday, May 16
  • Final exam -- Tuesday June 12, 1-3 PM

Homework

• Assignment #1   (solutions)
• Assignment #2   (solutions)
• Assignment #3   (solutions)
• Assignment #4   (solutions)
• Assignment #5   (solutions; solutions to review problems)
• Assignment #6   (solutions)
• Assignment #7   (solutions)
• Assignment #8   (solutions)

Some useful resources for the class:

• Recommended reading:
  • Course lecture notes
  • Mathematical Methods of Classical Mechanics, by V. I. Arnold.
  • Nonlinear Ordinary Differential Equations, by R. Grimshaw.
  • Introduction to Control Theory, by O. L. R. Jacobs.
  • Feedback Systems: an Introduction for Scientists and Engineers, a free e-textbook by K. J. Astrom and R. M. Murray.
  • Chaos: Making a New Science, by J. Gleick (an extremely well-written and successful popular science book).
• Mathematica demos
  • Cobweb diagrams, fixed points and the logistic map (Mathematica notebook of the demo I showed in class; here is the same source code in a plain text file).
  • "Three views of the Logistic Map" from the Wolfram Demonstrations Project.
  • "Classic Logistic Map" from the Wolfram Demonstrations Project.
  • Stabilized Inverted Pendulum (blog with demo videos on control theory).
• Cool control theory videos: (please email me links to other relevant videos you find)
  • Electromagnetic levitation 1
  • Electromagnetic levitation 2
  • Feedback control of inverted pendulum
  • Feedback control of double inverted pendulum
  • Triple inverted pendulum
  • Inverted pendulum, open-loop control 1
  • Inverted pendulum, open-loop control 2
  • Self balancing robot
  • Self stabilizing Acrobot (control theory model of horizontal bar gymnastics)
  • Steven Strogatz demonstrates the dynamics of the double pendulum
  • Steven Strogatz talk on synchronization in nature