COURSE INFORMATION |
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| Course | Math 130A, Ordinary Differential Equations, MWF 1:00-1:50 PM in Center Hall 222. You should be enrolled in one of the two discussion sections, which meet at 10 and 11 AM on Thursdays in HSS 1305. The first section meeting will be Thursday, October 4. This is a course on linear and nonlinear systems of ordinary (as opposed to partial) differential equations, including basic concepts of chaos, with applications. |
| Instructor | Jeffrey M. Rabin, APM 6220, 534-2904, jrabin@ucsd.edu. My tentative office hours will be Tuesdays 10 AM to noon, and by appointment. Since my scheduled office hours are often crowded, you may wish to make an appointment 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 11am-12pm, Tuesday 12pm-1pm, and Wednesday 8am-10am. |
| Textbook | Nonlinear Dynamics and Chaos, by Steven Strogatz. There is also a recommended book, An Introduction to Dynamical Systems: Continuous and Discrete by R. C. Robinson. You might also look at Hirsch, Smale, and Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd edition, which has been used as the text for this course in the past. Strogatz’s book is very readable and chock full of scientific applications, but rather short on proofs. Robinson’s book is more systematic and complete, and contains more of the proofs. My presentation in class will be somewhere in between the two. |
| Homework |
Homework will be assigned in class, usually
on Wednesdays, and will be due at the Thursday 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 9:45am on the Thursday it is due will be considered late and not graded. |
| Exams | There will be two midterm exams, each counting for 20% of your course grade and tentatively scheduled for Wednesday, October 24 and Monday, November 26. The final exam is on Monday, December 10 at 11:30 AM and counts 40%. |
| Holidays | No class on Monday, November 12 (Veterans’ Day) and Friday, November 23 (Thanksgiving). |
| Course Outline | We will try to cover (most of) chapters 1 through 7 in Strogatz this quarter. [This material is in chapters 1 through 6 of Robinson.] Our coverage of linear systems (chapter 5) will go beyond what’s in the text. Some of the more complex topics will be postponed to 130B next quarter, along with most of the proofs. Our goal is to familiarize ourselves with the general behavior of solutions to linear and nonlinear systems of differential equations, and some of their scientific applications. For linear systems we will learn complete solution methods, but it is rarely possible to explicitly write down the solution to a nonlinear system. Instead we want to understand the qualitative behavior of the solutions and how this can change as parameters in the system are varied. We will develop various graphical methods for visualizing this. |
| 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 very readable, so please read it! Specifically, read each section before we cover it in class, and bring your questions to class with you. You should review elementary methods for solving differential equations covered in 20D, such as separation of variables, integrating factors, and the theory of second-order linear equations. We will also use some linear algebra from 20F, particularly the use of eigenvalues and eigenvectors to diagonalize matrices. Math 109 is also helpful for this class, as homework assignments may include proofs. I will not assume you have taken analysis (Math 140 or 142) already, but we may need to use some facts from those courses which I will state without proof. 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 0 (Due October 4.) ...Solutions... Homework 1: 2.2.3, 2.2.7, 2.2.10, 2.3.1, 2.3.4, 2.4.2, 2.4.8, 2.5.1, 2.5.3, 2.7.1, 2.7.6 (All problems from Strogatz' book. Due October 11.)...Solutions... Homework 2: 3.1.1, 3.1.3, 3.2.3, 3.4.3, 3.4.6, 3.4.8, 3.4.10, 3.4.14, 3.5.2, 3.5.3, 3.5.6 (skip part e) (All problems from Strogatz' book. Due October 18.)...Solutions... Homework 3: 3.7.2, 3.7.3, 3.7.4, 4.1.5, 4.3.2, 4.3.3, 4.3.5 (All problems from Strogatz' book. Due November 2.)...Solutions... Homework 4 (Due November 15.)...Solutions... Homework 5 (Due November 26.)...Solutions... Homework 6 (Due December 6.)...Solutions... | |