Math 135A, Lecture 1

Ordinary Differential Equations

Summer 2001@UCLA

Course description: This course is intended to introduce students basic procedures and techniques for solving ordinary differential equations; linearity, basis of solutions, variation of parameters, Green's function; system of equations; constant coefficient equations, matrix differential equations, method of eigenvalues and eigenvectors.

Textbook: G. Simmons, Differential Equations with Applications and Historical Notes, 2nd Edition

Chapters:

Prerequisites: Math 33A and Math 33B.

Lectures: MTWR 2:30PM -3:20PM, MS 6627

Discussion Section: TR 1:30P-2:20P, MS6627

Useful Links:

Class Web Page: http://www.math.ucla.edu/~hliu/135a.1.011/index.html

Instructor: Hailiang Liu

Office : MS 7620-D
Office hours: MW 3:30-4:30PM
Tel: 310 825 4201
E-mail : hliu@math.ucla.edu

Teaching Assistant: Chiu-Yen KAO

Office: MS3905
Office hours: TR 11:00AM--12:00AM
E-mail: ckao@math.ucla.edu

Homework Assignments:

There will be 7 homework assignments for this course.

The homework assignments will be assigned and partially graded weekly.

The homework is due on Tuesday at the end of the discussion.

LABEL your homework clearly, indicating your name(last and first) and

homework set.

No late homework will be accepted.

Your TA will return your graded homework in the Discussion

Section after the Homework Assignment is due. If

you do not attend the Discussion Section, your homework will

be returned during your TA's office hours.

Examinations: One midterm exam and one final exam.

Midterm: Thursday, July 19, 1:30--2:30PM in the usual classroom

Final: Thursday, August 16, 1:30--3:00PM at MS 6627!

The examinations are closed-book and closed-note.

No calculators, graphing calculators or computers are allowed during the exams.

No exams at a time other than the designated ones will be allowed.

Grading Policy: Homework assignments: 25%. Midterm: 25%. Final: 50%.

Weekly Homework Assignments: Due each Tuesday on Discussion Section

Before you solve each problem, you may want to hear my suggestions

HW SECTIONS/PROBLEMS DUE DATE&

1 Ch.1   p.9 #1: b, e, j, o; #2: b, c; #3: b; #4: a; (General remarks of solutions)
           p.16 #1: b, c; #3; (Family of curves)
           p.24 #1. (Applications) Tue. July 3

2 Ch.2   p.49, #1: (a), (g), (e); #4: (a); #5: (a); (Homogeneous Eqs.)
           p.53, #5, #22; (Exact solutions)
           p.59, #2, (b), (g), (h); (Integrating factors) Tue. July 10

3 Ch.2   p. 62, #2, (h); #3: (b) (Linear equations)
           p.65, #1, (b), (f); #2: (b); (Reduction of order)
Ch.3   p.91, #4; #6: (c); (2nd order homegeneous equation)
           p. 94, #4; #10; (Find solution based on a known one)
           p.97, #1, (b), (i), (k); #2: (c), (d); (Homogeneous eqs. with constant coefficients) Tue. July 17

4 Ch. 3 p.97, #3; (Solution behavior of Homogeneous Eqs) .
            p.103, #1, (b), (d), (e), (j);    #2, #3, (a); (The method of undetermined coefficients)
            p. 106, #3, (b), (d); #6, (a), (d); (The method of variation of parametres)
           + midterm (due July 19) Tue. July 24

5 Ch. 3   p.127, #7, #20; p.128, #21; (Higher order linear equations);
             p. 113, #1; (Vibrations in mechanical system);
           p.122, #2; (Newton's Law of Gravitation);
             p.135, #4, #8; p.136, #17, #23 (Operator methods for finding particular solutions). Tue. July 31

6 Ch. 4 p. 161, #3; (Oscillations and the Sturm seperation theorem);
            p. 164, #3; (The Sturm comparison theorem);
Ch. 5 p. 172, #5, #6, #7 (b); (Review of power series);
            p. 175, #3, #4; (Series solution of first order equations); Tue . August 7

7 Ch. 5 p. 182, #2;   p.183, #5 (b), (c); #7 (a); ( Second order linear equations);
            p. 191, #1 (d); #2 (b), (c), (d); #4 (a), (d); #5;   #6 (a).(Regular singular points);
            p. 198, #1; (Frobenius series solution). Tue. August 14

8 Review: Aug. 13-Aug.15
          Aug. 13 (Monday), general review will be given on what has been covered in the class and   what   will be covered in the final;
            Aug.14-Aug.15, review will be focused on solving various problems.
   Final: Aug. 16, 1:30--3:00PM at MS 6627.

August 16

HW	SECTIONS/PROBLEMS	DUE DATE&
1	Ch.1 p.9 #1: b, e, j, o; #2: b, c; #3: b; #4: a; (General remarks of solutions) p.16 #1: b, c; #3; (Family of curves) p.24 #1. (Applications)	Tue. July 3
2	Ch.2 p.49, #1: (a), (g), (e); #4: (a); #5: (a); (Homogeneous Eqs.) p.53, #5, #22; (Exact solutions) p.59, #2, (b), (g), (h); (Integrating factors)	Tue. July 10
3	Ch.2 p. 62, #2, (h); #3: (b) (Linear equations) p.65, #1, (b), (f); #2: (b); (Reduction of order) Ch.3 p.91, #4; #6: (c); (2nd order homegeneous equation) p. 94, #4; #10; (Find solution based on a known one) p.97, #1, (b), (i), (k); #2: (c), (d); (Homogeneous eqs. with constant coefficients)	Tue. July 17
4	Ch. 3 p.97, #3; (Solution behavior of Homogeneous Eqs) . p.103, #1, (b), (d), (e), (j); #2, #3, (a); (The method of undetermined coefficients) p. 106, #3, (b), (d); #6, (a), (d); (The method of variation of parametres) + midterm (due July 19)	Tue. July 24
5	Ch. 3 p.127, #7, #20; p.128, #21; (Higher order linear equations); p. 113, #1; (Vibrations in mechanical system); p.122, #2; (Newton's Law of Gravitation); p.135, #4, #8; p.136, #17, #23 (Operator methods for finding particular solutions).	Tue. July 31
6	Ch. 4 p. 161, #3; (Oscillations and the Sturm seperation theorem); p. 164, #3; (The Sturm comparison theorem); Ch. 5 p. 172, #5, #6, #7 (b); (Review of power series); p. 175, #3, #4; (Series solution of first order equations);	Tue . August 7
7	Ch. 5 p. 182, #2; p.183, #5 (b), (c); #7 (a); ( Second order linear equations); p. 191, #1 (d); #2 (b), (c), (d); #4 (a), (d); #5; #6 (a).(Regular singular points); p. 198, #1; (Frobenius series solution).	Tue. August 14
8	Review: Aug. 13-Aug.15 Aug. 13 (Monday), general review will be given on what has been covered in the class and what will be covered in the final; Aug.14-Aug.15, review will be focused on solving various problems. Final: Aug. 16, 1:30--3:00PM at MS 6627.	August 16