## Math 20D: Introduction to Differential Equations, Winter 2004

Instructor: Hans Wenzl, email: hwenzl@ucsd.edu

Office: APM 5256, tel. 534-2734

Office hours: MW 1:30-2:30, F10-11

MATLAB sessions will take place in Galbraith Hall at CLICS

Teaching assistants: Aron Lum (alum@math.ucsd.edu) office hours: W2:30-4, Th 10-11:30 at APM 2250 Michael Gurvich mgurvich@math.ucsd.edu), office hours: W, Th 2-4 at APM 6402C Jake Wildstrom (dwildstr@math.ucsd.edu) office hours: M9-10 T11-1 W10-11 at APM 2250

Computation of grade: homework: 10%, matlab: 10%, 2 midterms: 20% each, final: 40%

Dates of exams:

first midterm: 2/4, second midterm: 2/27

Course material: We will use the following books:

1. J. Stewart, Calculus: Early Transcendentals, 4th ed. (Chapter 11 only)

2. W. Boyce and R. DiPrima, Elementary Differential Equations, 7th ed. (chapters 1-3,5,6)

Matlab assignments as well as homework assignments need to be turned in at the beginning of your TA-section on Thursday. It is very important that you do the homework problems. Probably more important than the 10% for the grade is the fact that most of the exam problems will be variations of homework problems. The homework problems are listed further below. You can find the matlab problems at the following link:

Homework assignments homeworks to be turned in in TA sections.

Disclaimer: I will try to get the homework assignment on the net in time. Due to time and other limitations, this may not always be possible. The fact that there is no assignment posted for a particular date does therefore NOT necessarily mean that no homework is due.

due 1/8: fourth ed.: Section 11.1: 8, 20, 27, 38, 62, Section 11.2: 1, 20, 24, 28, 44, fifth ed.: Section 11.1: 8, 20, 28, 38, 64, Section 11.2: 1, 20, 24, 28, 44,

due 1/15: (the problems from Section 11.6 which were originally listed here are only due on 1/22)

fourth edition: Section 11.3: 4, 10, 12, 16, 22, 30, Section 11.4: 1, 3, 7, 9, 19, 29, 35, Section 11.5: 1, 5, 8, 12, 23,

fifth edition: Section 11.3: 4, 10, 12, 16, 20, 30, Section 11.4: 1, 3, 7, 9, 19, 29, 35, Section 11.5: 1, 5, 8, 12, 23,

due 1/22:

fourth edition: Section 11.6: 4, 14, 22, 29, 31, Section 11.8: 3, 5, 15, 21, 29, 31, (you should also decide whether the series converges at the endpoints of the interval of convergence!) Section 11.9: 1, 5, 7, 17, 19, 29, 34,

fifth edition: Section 11.6: 5, 14, 22, 29, 31, Section 11.8: 3, 6, 15, 21, 29, 31, (you should also decide whether the series converges at the endpoints of the interval of convergence!) Section 11.9: 1, 5, 9, 15, 17, 27, 32,

due 1/29:

fourth edition: Section 11.10: 3, 9, 15, 25, 27, 36, Section 11.11: 1, 7, 14, 15, Section 11.12: 19ab

fifth edition: Section 11.10: 3, 11, 16, 27, 29, 38, Section 11.11: 1, 7, 14, 15, Section 11.12: 19ab

due 2/5: (you should get started with it already now, as there is not much time left after the midterm): Boyce/DiPrima: Section 1.1: 5, 11, 14, Section 2.1: 3, 6, 10, 13, 20,

due 2/12: Section 2.2: 5, 10, 11, Section 2.3: 3, 7, 12, Section 2.5: 6, 11, 22

due 2/19: Section 3.1: 3, 4, 9, 11, Section 3.4: 1, 7, 18, 22 Section 3.5: 7, 12

due 2/26: Section 3.5: 16, 23, Section 3.2: 2, 5, 7, 11, 14, Section 3.6: 1, 6, 7, (hint for 6: if you get 0 after plugging your Y(t) into the differential equation, replace Y(t) by tY(t) and try again (possibly more than once)) material up to here relevant for midterm

due 3/4: Section 5.2: 1, 5, 10, 21, Section 5.3: 6, 10(b), look up the solution for 10a in the back of the book, or do it as an exercise.

due 3/11: Section 6.1: 5, 9, 13, 16, Section 6.2: 5, 6, 12, 16, 21, 24, Section 6.3: 6, 7, 9, 16, 20, Section 6.4: 1

Final: The final will take place on Wednesday, March 17 from 11:30-2:30 in the usual class room. The usual rules will apply: you are allowed to use ONE hand-written cheat sheet, but NO calculators, books or other notes.

Office hours in finals week: M1-2, T1-3.

BRING AN ID !

Material: The final will be accumulative. It will strongly concentrate on differential equations, with a particular emphasis on the material of the last two weeks (power series solutions and Laplace transforms). Other areas from which problems may be taken include modeling, autonomous equations, separations of variables, undetermined coefficients and others.

To get a better idea, click below for practice finals. You need not worry about problems involving singular points, and, for the second practice final, about problem number 8. Also, problem number 7 in the first practice final is an Euler equation which we did not cover in class; problems of such type would not appear without additional hints given. Note that you can find solutions of the first practice final as well as other practice finals and their solutions at Professor Bender's webpage: see exams and solutions