Fabian Waleffe -- Math 320 Homework-- U. of Wisconsin

Math 320 Homework for Lecture 6 (Waleffe) Fall 2002

Note: Homework will usually be due on Wednesdays. Policy: homework is optional so do it well or don't hand it in. That means write-up your solutions cleanly, completely yet briefly. You want the grader to see quickly that you know what you're doing and got the answer right for the right reasons. It's NOT up to the grader to dig into your mess. It's up to you to lay it out well. The grader will be instructed not to waste time on messy write-ups. No late homeworks.

Week one (Sept 4-6):
- READ 1.1-1.4;
- Strongly Suggested Exercises:
  1.1. 2, 3, 4, 7, 8, 13, 16, 18, 21, 24, 27, 29, 32, 36, 40;
  1.2. 3, 4, 7, 9, 10, 20-24, 29, 30, 36
  1.3. 1, 3, 4, 7, 8, 10, [Sketch direction field and some solution curves for] 13, 15, 16 without graphing calculator!
Week two (Sept 9-13):
- 1.4. 1, 2, 9, 12, 17, 22, 30, 32, 42, 45, 51, 55, 56, 60
- 1.5. 1-3, 6, 16, 17, 20, 21, 26, 29, 30, 33, 36-39, 43
- DUE Fri Sept 13 :
  - 1.1. 24; I did 27-29 in class so show that you understood by turning in 30 and 31;
  - 1.2. 4 (write answer as a definite integral then evaluate), 22, 36.
  - 1.3. Hand sketch direction field and solution curves for 16 (no computer plot!). Find two distinct solutions to y'=y^3/4 with y(0)=0, why would this initial value problem have two solutions? Aren't solution curves supposed not to cross?
  - 1.4. 22, 45
Week three (Sept 16-20):
- 2.1. 2, 3, 6, 7, 8, 9, 13, 20, 21, 22, 25, 26
- DUE Fri Sept 20 :
  - 1.5. 2, 6, 30, 36, 38
  - 2.1. 2, 6, 8, 20, 22
- 2.2. 2, 5, 9, 12, 13, 14, 15, 21
- 2.3. 1, 3, 5, 11, 15, 19, 20, 28
Week four (Sept 23-27):
- 3.1. 1, 9, 19, 31, 32, 33, 34
- 3.2. 1, 11, 12, 25, 28, Gaussian Elimination (because Windows is built for dummies, you may be forced to save this to a file, then start Matlab, then open the file with the Matlab editor to read it!).
- No hwk due because of Take-Home Exam Due 1:10pm Monday Sept 30, 2002
Week five (Sept 30-Oct 4):
- Write a Matlab code to do Backsubstitution.
- 3.3. 3, 9 , 34
- 3.4. 3, 7, 8, 13, 17, 18, 23, 24, 27--32.
- 3.5. 1, 5, 6, 9, 11, 23, 32, 33. Solve AX=I where A = [0 b ; c d] by transforming A into RREF as we did in class. What is X? under what conditions does it exist?
- DUE Wed Oct 9:
  - 3.1. 10; 3.2. 2, 4, 6
  - Write a Matlab code for Backsubstitution.
  - 3.3. 14; 3.4. 8, 32; 3.5. 2, 12
Week Six (Oct 7-Oct 11): Sections 3.5 and 3.6
- 3.6.3, 4, 7, 11, 12, 17, 18, 43--46
Week Seven (Oct 14-Oct 18): Section 3.6: Cramer's rule, inverse
- 3.6. 29, 30, 33, 34, 41, 42, 50, 52 , 61, 62
- DUE Fri Oct 18: #1 p 197, #7 p 198, 3.6.12, 14, 28, 34, 48, 52
Week Eight: Chapter 4 (with Prof. Ionel)
do the PRACTICE problems posted on Prof. Ionel's assignments
Week Nine (Oct 28-Nov 1):
- DUE Wed Nov 6: 4.1.32, 34; 4.2.6, 18; 4.3.10, 20, 24; 4.4.8, 12, 14, 24; 5.1.14, 24, 38.
Week Ten (Nov 4-8):
- 5.1. 1, 3, 9, 11, 18, 19, 21, 25, 27, 28, 33, 34, 39, 40, 43, 45, 47
- 5.2. 1, 3, 6, 7, 9, 11, 13, 14, 17, 21, 22, 26, 27, 30, 33; 35 (advanced, to satisfy your thirst for knowledge and deep understanding only).
- 5.3. 1, 2, 9, 10, 19, 21, 23, 25, 27, 28, 35, 36, 37, 39, 40, 43, 44, 49
- 5.4. 1, 3, 4, 5, 6, 9, 10, 13, 14, 15-21, 22
- DUE Wed Nov 13 : 5.1.16, 18, 24, 40; 5.2.8, 18, 24, 33; 5.3.14, 24, 30, 43, 46; 5.4.4, 10, 22.
Week Eleven (Nov 11-15):
- 5.5. 3, 4, 5, 7, 9, 21, 23, 29, 30, 31, 32, 35, 41, 43, 47, 51, 55, 59, 63, 64.
- 5.6. 1, 3, 5, 6, 7, 8, 11, 12, 20
Week Twelve (Nov 18-22):
- 6.1. 1, 2, 13, 21, 22, 31, 32, 33, 34, 35, 36, 37
- 6.2. 1, 2, 3, 13, 14, 27; Advanced: 37, 38, 39
- DUE Mon Nov 25: 5.5.2, 12, 28, 32, 40, 50, 52, 56; 5.6.6, 8, 20; 6.1.20, 34
Week Thirteen (Nov 25-27): Exam 2, Happy Thanksgiving.
- For the pendulum and phase plane: see 9.4. p. 561, this is important basic material, after all it's one of the first dynamical system you got to experience.
- 7.1. 1, 3, 7, 16, 17, 24, 26, 27, 29
Week Fourteen (Dec 2-6):
- 7.2. 1, 2, 3, 8, 9, 12, 13, 14, 19,
- 7.3. Solve and sketch phase plane: 3, 6, 7, 9, 14, 18, 25, 29, 30, 39
Week Fifteen (Dec 9-13):
- 7.5. 1, 3, 5, 7, 12, 17, 23, 25, 27.
- 8.1. 1, 2, 9, 10, 31, 33, 34, 35
- 8.2. 1, 2, 17, 18, 23, 27 (try to deduce the matrix exponential on your own).