Advanced Engineering Math
Math 4581

Fall 1997

Course syllabus (look here for updates throughout the quarter)

I've written up my responses to your comments provided on the questionaire. Thanks for filling them out.

What's New:

• Added solutions for assignment 5.
• Added PRELIMINARY lecture notes covering through Wed. of dead week
• Fixed a couple of graphing problems in the day 20 lecture notes, as of Nov. 15, at 5:15 p.m.
• Please see the notice regarding the on-line lecture notes
• Need help with Maple? If you can't reach me, try the Maple assistants in room 140 in the Rich Building

Partial test solutions:

• Test 2, all problems (4 works now)
• Test 1, problems 4 and 5

Lecture Notes (as Maple worksheets):

1. Sept. 24. Definition of Laplace transform, calculating Laplace transforms with Maple
2. Sept. 26. Sectionally continuous functions, and exponential order (updated Sept. 26 afternoon)
3. Sept. 29. Transforms of derivatives
4. Oct. 1. The Gamma function, transforms of integrals, example ODE, and the inverse transform
5. Oct. 3. The inverse transform, solving ODEs and partial fractions, and the substitution theorem
6. Oct. 6. ODE examples, Substitution theorem
7. Oct. 8. Translation theorem, scaling theorem, piecewise functions
8. Oct. 8. Pulse functions and the Dirac distribution
9. Oct. 13. Convolutions and their properties
10. Oct. 15. Convolutions for differential and integral equations, limits of transforms
11. Oct. 17. Derivatives of transforms
12. Oct. 20. Integrals of transforms, transforms of periodic functions
13. Oct. 22. Vibrating Springs
14. Oct. 24. Resonance, periodic forcing, and periodic extensions
15. Continued the discussion from last time
16. Oct. 29. Solving ODE's with periodic forcing, setting up systems of ODE's (Updated Oct. 29, at 6:10 p.m.)
17. Oct. 31. More on systems of ODE's: solved examples
18. Nov. 3. A first look at PDE's
19. Nov. 5. One-dimensional heat and wave equations, damped wave equation
20. Nov. 7. Damped wave equation, more on wave equations, solving a heat equation with human intervention
21. Nov. 10. Continue discussion from the previous day's lecture notes
22. Nov. 9. Solving the heat equation, more on finding inverse transforms
23. Nov. 11. Continue examples from last time
24. Nov. 14. Continue examples from last time
25. Nov. 17. A summary of methods for computing inverse Laplace transforms (includes a generalization for Method 3), updated Nov. 17, 2:40 p.m.
26. Nov. 19. Continue with lecture notes from last time
27. Nov. 21. Return of the Heat Equation: Inverse transforms involving quotients of sinh's (now finished)
28. Nov. 24. The complex inversion integral for the Laplace transform
29. Nov. 26. Non-insulated, cooling bar
30. Nov. 31. Intro to Fourier transforms
31. Dec. 2. A little more on Fourier transforms

Assignments: (by due date)

1. Oct. 1
2. Oct. 8
3. Oct. 15
4. Nov. 5
5. Nov. 12
6. Dec. 3

Solutions to Previous Assignments: (as Maple worksheets)

1. Assignment 1
2. Assignment 2
3. Assignment 3
4. Assignment 4
5. Assignment 5
6. Assignment 6