Ordinary Differential Equations Homework Solutions
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%
- Midterm quiz 1 -- Wednesday, April 25
- Midterm quiz 2 -- Wednesday, May 16
- Final exam -- Tuesday June 12, 1-3 PM
Homework
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
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