Math 333: Differential Equations

Spring 1999

Daily Schedule

• 1/17:
  • 1.1 Homework p. 13: 1, 3, 4, 13, 15 (due 2/3)
  • Lab 1: "An introduction to ODE Architect" (separate sheet).
• 2/1: 1.2; Homework p. 31: 1, 7, 9, 14, 25, 27, 29 (due 2/8)
• 2/3:
  • 1.3; Homework p. 46: 2, 4 (do by hand), 8, 11 (explain your answers), 13, 14, 16 (due 2/8)
  • 1.4. Homework p. 62: 2, 5 (due 2/15).
  • Lab 2: Play golf: Open the Multimedia ODE Architect, push button 2 "Introduction to ODE's", and click on "Slope fields and golf". The educational material in the first few screens is optional; when you come to to golf game, play it! (And turn on the speakers to get the sound effects.) You don't have to hand anything in.
• 2/8: 1.5: Homework p. 68: 1, 2, 5, 6, 14, 16 (due 2/15).
• 2/10:
  • 1.6. Homework p. 88: 1, 2, 9, 10, 24, 28 (due 2/15)
  • 1.7. Homework p. 104: 1, 3 (due 2/15)
• 2/15: Homework p. 104: 2, 10 (due 2/22). Also Lab 1 is due 2/22. Be sure to explain connection between the theory (text pp 101--103) and your conclusions.
• 2/17:
  • 1.8. Homework p. 115: 1, 3, 9, 15 (due 2/22)
  • 2.1; also read pp. 11-12. Homework p. 18: 18a, 19i, and p. 151: Do problems 1 through 6 for system (i), and also 9i and 10i.
• 2/22:
  • 2.2. Homework p. 169: 3, 4, 8, 19, 20, 21, 22 (due 3/3)
  • E. Coli (Lab 3): Open the multimedia ODE Architect and turn on the speakers. Go to "Population models" (number 9). Open the "Population growth" module. Listen to the video. Go ahead to screen "Experiment 2: Fit the data". (If you can't find it, use the pull-down menu.) What values of r and K best fit the E. Coli data? Also explain how changing r changes the graph, and how changing K changes the graph. Write a paragraph with your answers and hand in (you can do this with another person and hand in one writeup for both of you; due 3/3). Extra credit: Identify the background music in the video!
• 2/24: Review for test.
• 2/26: Test 1 on Sections 1.1--1.7
• 3/1:
  • Homework p. 181: 14 (due 3/8)
  • Lab 2.2 (p. 209) (do assigned pair of equations with assigned partner; if you don't have one see me. Use ODE Architect. Due 3/10)
• 3/3: Homework p. 247: 1, 2, 22 (due 3/8)
• 3/8: p. 232: 24, 25 (due 3/24)
• 3/10: p. 277: 1, 3, 4, 9, 10 (due 3/24)
• 3/22: 3.5, p. 294: 1, 2, 5, 6, 17 (due 3/29; use ODE Architect as necessary)
• 3/26: Test 2 on material through 3.3.
• 3/29: 4.1. Homework p. 358: 1, 4, 6, 7, 17, 18 (due 4/5)
• 3/31: 2.7. Homework p. 204: 1, 2, 3 (due 4/5)
• 4/5: 4.2. Homework p. 370: 1, 3, 15a (due 4/12)
• 4/7: 4.3. Computer homework on family of linear equations due 4/12.
• 4/12: 5.1. Homework:
  • Sheet on sensitive dependence on initial conditions for Lorenz equations (due 4/19)
  • For the pair of equations you did in Lab 2.2, (a) find the Jacobian matrix at each equilibrium point, (b) find the type of the equilibrium from the Jacobian matrix, and (c) check your results with what ODE Architect says for the type of the equilibrium. Also find the separatrices for these systems. You can do this in the group which worked on this lab initially.
• 4/14: 5.3. Homework p. 448: 1, 4, 9, 10, 13, 15 (due 4/21). Also, what is wrong about the phase plane plot of the hare/lynx data in the handout?
• 4/23: Test 3
• 4/26: SIR lab (due 5/3)
• 4/28: Using linearization at equilibria to understand the Lorenz equations (3.8, 5.5). Roessler handout.
• 5/3:

Note: All assignments must be handed in by 5 PM, Tue May 4