COURSE INFORMATION |
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| Course |
Math 130B, Ordinary Differential Equations, MWF 1:00 – 1:50 PM in Center 205. You should also be enrolled in the discussion section which meets Tuesdays at 3 PM in |
| Instructor | Jeffrey M. Rabin, APM 6220, 534-2904, jrabin@ucsd.edu. My tentative office hours will be Mondays 10 – noon and by appointment. Since my regular office hours are often crowded, or may not fit your schedule, I encourage you to make an appointment if you want to see me individually. You can do this after class, or by phone or email. I am usually willing to answer short questions by email as well (but I rarely check it on weekends). |
| TA | Steve Butler, APM 6436, sbutler@math.ucsd.edu. Office hours are Monday 11 - 1 and Tuesday 1 - 2, other times are available by appointment. |
| Textbook | Nonlinear Dynamics and Chaos, by Same as last quarter. Steven Strogatz, Nonlinear Dynamics and Chaos. We will cover chapters 6 through 8, and possibly 9, this quarter. There is also a recommended book, R. C. Robinson, Introduction to Dynamical Systems, which contains more proofs. This quarter’s material is in chapters 4 through 7 here. |
| Homework |
Homework will be assigned in class, usually on Mondays, and will be due at the Tuesday discussion section the following week. Assignments and (eventually) solutions will also be posted on the course website. Homework counts for 20% of your grade. Working on homework collaboratively can be very beneficial, so I encourage it within limits. Attempt the problems on your own first. You may share ideas with your classmates where you are stuck or would like constructive criticism, but each student must write up her solutions independently to turn in. Solutions should be legible, with all calculations shown and all reasoning fully explained.
A homework dropbox is located on the 6th floor of AP&M (after exiting the elavators turn right and find the last drop box, which is also the one made out of dark wood; the slot for our class is in the lower right). Homework may be turned in EARLY to the dropbox. Any homework turned into the dropbox after 2:45pm on the Tuesday it is due will be considered late and not graded. |
| Exams |
There will be two midterm exams, each worth 20% of your grade and tentatively scheduled for |
| Holidays | No class on Monday, January 21 (Martin Luther King Day) or February 18 (Presidents’ Day). |
| Course Outline | We will mainly be studying systems of two nonlinear differential equations, developing techniques to understand and sketch their phase portraits. We will discuss the types of stable fixed points and periodic solutions they have, and the variety of bifurcations which can occur. We will prove two big theorems whose proofs are not given in the textbook: the Poincare-Bendixson theorem on periodic solutions, and the existence and uniqueness theorem. If there is time we will introduce the idea of chaotic dynamics, which first occurs for three-dimensional nonlinear systems, through the example of the Lorenz equations. |
| Academic Dishonesty | The work you are graded on must be your own, with no unauthorized assistance of any kind. You should familiarize yourself with the UCSD Policy on Integrity of Scholarship. If you are caught cheating on any assignment, you will receive a score of 0 on that assignment, and the Dean of your college may impose additional penalties such as probation or suspension. I may randomly photocopy exams to ensure that they are not altered and submitted for regrading. |
| Helpful Advice | The textbook is (mostly) very readable, so please read it! Specifically, read each section before we cover it in class, and bring your questions to class with you. I am still not assuming that you have had an analysis course (Math 140 or 142), but we will introduce terminology and quote facts from analysis when needed. I hope some of the topics we cover will serve as motivation for an analysis class by showing why one needs to be careful with things like the definitions of terms and the behavior of limits. The technique of linearization for classifying the equilibria of nonlinear systems, introduced last quarter, will be used constantly this quarter. There will also be more emphasis on proof rather than calculation this quarter. That’s because it is usually impossible to compute an explicit solution to a nonlinear differential equation. Instead we use reasoning to establish key properties of the phase portrait. Don’t wait until the last minute to tackle the homework problems: they are nontrivial, which is why you have a week to solve them. Don’t fall behind in the class: if there is a concept you aren’t grasping, ask questions in class, section, or office hours and clear it up sooner rather than later. |
HOMEWORK |
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Homework 1: 6.4.1, 6.4.2, 6.5.3, 6.5.6, 6.5.12, 6.5.13, 6.5.15, 6.5.16, 6.5.19. (Hint for 6.5.16: linearize the system around the equilibrium points.)
(All problems from Strogatz' book. Due January 15.)...Solutions... Homework 2: 6.6.1, 6.6.6, 6.6.7, 6.7.2, 6.7.4. (All problems from Strogatz' book. Due January 22.)...Solutions... Homework 3: 6.3.15, 6.8.2, 6.8.7, 6.8.8, 7.1.2, 7.1.3, 7.2.6, 7.2.7. (All problems from Strogatz' book. Due January 29.)...Solutions... Homework 4: (Due February 5.)...Solutions... Homework 5: (Due February 12.)...Solutions... Homework 6: (Due February 19.)...Solutions... Homework 7: 7.5.3, 7.5.4, 7.5.5, 7.5.6, 7.6.2 (Note that the second term in the equation is just x, not x-dot), 7.6.13. (All problems from Strogatz' book. Due February 26.)...Solutions... Homework 8: 7.6.19, 7.6.22 [Find the solution x(t) up through terms of O(epsilon), find the frequency up through terms of O(epsilon^2),as in the back of the book], 8.1.1, 8.1.8, 8.1.11, 8.2.1, 8.2.12. (All problems from Strogatz' book. Due March 4.)...Solutions... Homework 9: 8.1.12, 8.3.1, 8.3.3, 9.2.3, 9.2.6. (All problems from Strogatz' book. Although Problem 9.2.3 doesn't say so, it obviously refers to the Lorenz equations, Eqs. (1) in section 9.2. Due March 11.)...Partial solutions... | |