Math 133A: Ordinary Differential Equations
Fall 2005

Contents of this page

Late breaking news
Lecture time and location
Prerequisite
Office hours
Textbook
Syllabus
Exams
How to...
Grading policy
Handouts
Homework
Quizzes
Policy on calculators
Calculus review
Academic integrity
Anonymous feedback

Review for the Final Exam

To review for the final, first review the theory and go over Math 133A essentials (updated on December 11).

Then go over the homework assignments, quizzes and midterms, as well as the these problems:
Ch. 1: sec. 1.2: #2, 11, 33; sec. 1.3: #17, 20; sec. 1.5: #2, 9, 12; sec. 1.6: 7, 12, 30; sec. 1.8: #2, 9, 12; sec. 1.9: #5, 8.

Ch. 2: sec. 2.2: #7, 20; sec. 2.3: #3, 15.

Ch. 3: sec. 3.1: #18, 25; sec. 3.2: #11, 13; sec. 3.3: #14, 16, 21; sec. 3.4: #5, 7, 23; sec. 3.5: #7, 21; sec. 3.6: #5, 11.

Ch. 6: sec. 6.1: #13, 14, 19; sec. 6.2: #3, 5, 7; sec. 6.3: #18, 29, 33.

Here's sample final: (1) sec. 1.6, #2; (2) sec. 1.8, #12; (3) sec. 3.3, #5; (4) sec. 3.4, #6; (5) sec. 3.6, #19; (6) sec. 6.3, #32.

Here's another sample final.

And of course, don't forget:

The final exam is on December 15, from 9:45 to 12, in DH 351.

Late breaking news

(12/13) I just posted another sample final (see above).

(12/11) Solutions to Homework 14 have been posted. I'll post more review stuff soon.

(12/8) Note that I will have no office hours on tomorrow (Friday, Dec. 9).

(12/7) My office hours next week (12/12-12/16) will be:

Monday & Wednesday, 10-12 and 2:30-4
Thursday, 2-3

Also, you can turn in Homework 14 on Friday, December 9, at the Math Department front desk (MH 308).

(12/6) Remember:

The final exam is on December 15, from 9:45 to 12, in DH 351.

As usual, you are allowed to bring a 3 X 5 "cheat sheet" to the exam, but no calculators. I will post some review problems as well as a simple final exam as soon as I can. (Keep checking this page.) In the meantime, you should review the theory (see the handout "Math 133A essentials" below) and go over the old homework and tests.

(12/5) I posted a handout Math 133A essentials, which you can use to review for the final.

(12/2) Solution to Quiz 6 has been posted.

(12/1) Solutions to Homework 13 have been posted. Don't forget that Quiz 6 has been postponed to tomorrow, 12/2.

(11/29) Homework 14 has been posted and is due on December 7. (XC means extra credit.)

(11/28) Solutions to Homework 12 have been posted. Don't forget that there is a quiz (the last one) on Wednesday. It covers Homework 13.

(11/23) I will bring the SOTEs on Monday, December 5.

Happy Thanksgiving!

(11/21) Quiz 6 will be on November 30 and it will cover Homework 13 (section 6.1). Also, solutions to Homework 11 have been posted.

(11/20) Homework 13 has been posted and is due on November 30.

(11/16) You can turn in the extra credit problems any time before the final exam. Write your solutions on a separate piece of paper and state the problem at the top. Also: you can turn in Homework 11 on Friday, November 18.

(11/15) Homework 12 has been posted and is due on November 23. (The homework is from section 3.7, not 3.6, as was originally posted by mistake.)

(11/14) Solution to Quiz 5 has been posted.

(11/12) Solutions to Homework 10 have been posted.

(11/8) Homework 11 has been posted and is due November 16.

(11/7) Solutions to Homework 9 have been posted.

(11/6) Quiz 5 will be on Monday, November 14 and it will cover Homework 10.

(11/3) Homework 10 has been posted and is due on Wednesday, November 9.

(11/2) Midterm 2 solutions have been posted.

(10/30) Here's a summary for Midterm 2.

(10/27) Homework 9 has been posted and is due on November 2. Solutions to Homework 8 are also on-line.

Midterm 2 will cover sections 1.9, 2.1-2.3, existence and uniqueness theorem from 2.4, 3.1-3.3. Review problems are below (you don't need to turn them in).

(10/26) If you are interested in teaching math, then you may be interested in "So you want to teach math?", an event organized by the Math Club and the Math Department. It takes place in MH 523 on October 28 at 3:30.

(10/20) Solutions to Homework 7 have been posted. Have a good weekend and see you on Monday!

(10/18) Solution to Quiz 4 has been posted, as well as Homework 8, which is due Wednesday, October 26.

(10/16) I will have no office hours on Monday and Wednesday afternoon this week and no office hours on Friday. Sorry about that. I'll try to make up this lack of office hours in the coming weeks.

(10/13) Solutions to Homework 6 have been posted.

(10/11) Homework 7 has been posted and is due on Wednesday, October 19. Also, Quiz 4 will be on Monday, October 17 and will cover Homework 6. Here's the reading for the next few lectures: Sec. 2.3, then existence and uniqueness theorem (and the swaying scyscraper example) from 2.4, then 3.1. You should read 2.5 for your information and education (it's a very interesting section especially if you ever wondered about "chaos"), but we won't cover it in class. Hint for problems 2,4 and 5 from Homework 6: x corresponds to prey, y to predators.

(10/10) Solution to Quiz 3 has been posted.

(10/6) Solutions to Homework 5 have been posted. Homework 6 has also been posted and is due Wednesday, October 12.

(10/2) Quiz 3 will be on Monday, October 10, and will cover Homework 5.

(9/29) Homework 5 has been posted and is due on Wednesday, October 5.

(9/28) Midterm 1 solutions have been posted.

(9/27) Solutions to Homework 4 have been posted, along with some useful trigonometric identities. Also, remember that on the midterm you are allowed to bring a 3X5" index card with your notes written on both sides.

(9/24) Review problems for Midterm 1 (which is on Wednesday, September 28) have been posted. You should consider them as a homework assignment, but you don't have to turn in your work. You can also look at my midterms from last semester, but since the syllabus was different, only problems 1 and 3 will be useful to you.

(9/21) Solutions to Homework 3 have been posted.

(9/20) Homework 4 has been posted and is due on Monday, September 26.

(9/19) Solution to Quiz 2 has been posted.

(9/15) Solutions to Homework 2 have been posted. Homework 3 has also been posted and is due on Wednesday, September 21.

(9/12) Solutions to Quiz 1 have been posted. Also don't forget that tomorrow (Sept. 13) is the last day to add/drop this or any other class!

(9/12) Quiz 2 will be on Monday, September 19.

(9/9) Quoting your homework grader, Edris Amin: "Each problem was [worth] 10 points. I gave them 2 for writing at least the problem down and starting it. 5-6 if they went all the way through and got a wrong answer. 7-9 if their answer was off by a little. 10 if it was correct." (See also "Homework".)

(9/8) Solutions to graded Homework 1 problems have been posted.

(9/6) Three things: 1) Quiz 1 will be on Monday, September 12. 2) Homework 2 has been posted and is due Wednesday, September 14. 3) I will not have an office hour tomorrow, 9/7, 2:30-3:30, but I will have an extra office hour on Friday, 9/9, from 2:30 to 3:30.

(8/31) I left a few copies of Sections 1.1 and 1.2 from the textbook in an envelope in front of my office. Help yourself if you don't have the book yet, but please share!

(8/25) Homework 1 has been posted and is due Friday, September 2.

(8/19) This course will be different from the standard Math 133A taught at SJSU. The emphasis will be on systems of ODEs, qualitative properties of solutions, and dynamical systems. For more details, check the syllabus.

Lecture time and location

(Section 03) MWF 11:30-12:20 in DH 351

Prerequisite

Math 32 (with a grade of "C-" or better) or instructor consent.

Office hours

Monday and Wednesday, 10:30-11:30 and 2:30-3:30, Friday 10:30-11:30 (only), and by appointment

Textbook

P. Blanchard, R. L. Devaney, and G. Hall: Ordinary Differential Equations, Brooks/Cole, second edition, 2002

Syllabus

Green sheet
First-order differential equations (Chapter 1, sec. 1.1--1.6, 1.9).
First-order systems (Chapter 2, sec. 2.1--2.4).
Linear systems, including second-order linear equations (Chapter 3, sec. 3.1--3.7).
Forcing and resonance (Chapter 4, sec. 4.1--4.3).
Nonlinear systems (Chapter 5, sec. 5.1).
Laplace transforms (Chapter 6, sec. 6.1--6.6).

Exams

There will be occasional short quizzes, two midterms, and a final exam. The exam schedule:
Midterm 1: September 28
Midterm 2: November 2
Final exam: December 15, 9:45-12:00
There will be no make-up exams.
Midterm 1 solutions
Midterm 2 solutions

How to...

How to study for this and other math classes

How to take the exam

Grading policy

Homework 10%, Quizzes 10%, Midterms 40%, Final 40%

Handouts

Math 133A essentials

Summary for Midterm 2.

Some useful trigonometric identities.

Basic integrals and integration techniques you have to know well

Homework

Late homework policy. One day late: 50% penalty; two days late: no credit.

Homework grading policy. 4 problems are graded. Each one is worth 10 points which are assigned as follows: 2 for writing at least the problem down and starting it; 5-6 if you go all the way through and get a wrong answer; 7-9 if your answer is off by a little; 10 if it the answer is correct.

# Due date Assignment Sol'ns to graded problems
1 9/2 Ex. 1.1: #1, 2, 3, 7, 8, 9. Ex. 1.2: # 1, 2, 3, 6, 8, 12, 24, 31, 34 HW 1
2 9/14 Ex. 1.3: #2, 5, 6, 7, 10, 14, 16, 17, 20, 21.
Ex. 1.4: #2, 3, 4, 12		 HW 2
3 9/21 Ex. 1.5: #2, 7, 8, 10, 12, 13, 14.
Ex. 1.6: #1, 7, 12, 13, 19, 30, 34, 37		 HW 3
4 9/26 Ex. 1.8: #2, 4, 6, 8, 9, 11, 12, 14, 17, 24. HW 4
* 9/28 Midterm 1 review:
Ex. 1.1: #3, 7, 9. Ex. 1.2: #1, 2, 24, 31.
Ex. 1.3: #2, 14, 16, 17. Ex. 1.4: #3. Ex. 1.5: #7, 8, 12, 14. Ex. 1.6: 1, 12, 13, 30, 37. Ex. 1.8: #11, 12, 14, 24		 *
5 10/5 Ex. 1.9: #1-5, 8, 10, 12, 13, 21. HW 5
6 10/12 Ex. 2.1: #2, 4, 5, 7, 19, 20.
Ex. 2.2: #1, 2, 5, 7, 11, 15, 17, 20, 23. 		HW 6
7 10/19 Ex. 2.3: #2, 5, 7, 10, 15, 19.
Ex. 2.4: #14, 15. #16 is extra credit. 		HW 7
8 10/26 Ex. 3.1: #6, 9, 13, 17, 24, 25, 27.
Ex. 3.2: #1, 11, 13, 16, 20abc. 		HW 8
9 11/2 Ex. 3.3: #1, 2, 5, 14, 16, 21, 27. HW 9
* 11/2 Midterm 2 review:
Ex. 1.9: #7, 11, 19ab. Ex. 2.1: #3, 5, 6, 20.
Ex. 2.2: #4, 8, 17, 19. Ex. 2.3: #7, 10, 17.
Ex. 2.4: #7, 8, 9, 15. Ex. 3.1: #18, 26, 29, 34.
Ex. 3.2: #3, 5, 7, 15, 21. Ex. 3.3: #3, 7, 13, 17. 		*
10 11/9 Ex. 3.4: #1, 3, 5, 8, 9, 11, 16, 17, 18, 23. HW 10
11 11/16 Ex. 3.5: #3, 12, 13, 14, 16 (XC), 20 (XC), 21.
Ex. 3.6: #4, 9, 17, 24, 31, 32 (XC). XC = extra credit		 HW 11
12 11/23 Ex. 3.7 (not 3.6): #2, 5, 9, 10, 11. HW 12
13 11/30 Ex. 6.1, #1-5, 7, 8, 10, 13, 15, 18, 19, 25, 26. HW 13
14 12/7 Ex. 6.2: #2, 5, 6, 8, 11, 13, 16 (XC), 17.
Ex. 6.3: #6, 7, 8, 15, 17, 27, 28, 31, 34 (XC).		 HW 14

Quizzes

Quizzes will be based on the homework. The date of each quiz will be announced in class.

Date Quiz # Solutions
9/12 Quiz 1 Quiz 1 solution
9/19 Quiz 2 Quiz 2 solution
10/10 Quiz 3 Quiz 3 solution
10/17 Quiz 4 Quiz 4 solution
11/14 Quiz 5 Quiz 5 solution
12/2 Quiz 6 Quiz 6 solution

Policy on calculators

Feel free to use them as a study tool, but don't get too dependent on them.

Calculators will not be permitted on exams.

For numerical explorations and simulation, we will use MATLAB and ODE software that comes with the book. However, good pencil and paper skills for solving and analyzing equations will definitely still be a must!

Calculus review

You need to know the basics of calculus to understand differential equations. Follow this link for a helpful online calculus review developed by Professor Linda Valdes.

Academic integrity

By default, I regard my students as honest individuals and expect them to abide by the University policy on academic integrity.

Anonymous feedback

If you have any comments or suggestions, please fill out this anonymous feedback form.
Slobodan N. Simić

Last modified: Tue Dec 13 14:41:05 PST 2005