Topics: Two-point Boundary value problems, Fourier series for Partial Differential Equations. PREREQS: MTH 256
LECTURE: MWF 900 - 950 Bat 250 CRN 31966, 31878 Instructor: R.E. Showalter Kidder 286 show@math.oregonstate.edu Office Hours: Monday 1500 - 1545 Wednesday 1000 - 1045
Textbook: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th ed., Wiley.
Homework will be assigned to indicate the topics for study, but it will not be collected. Two fifty-minute Tests will be given in the Lecture period. Test problems come directly from the assigned Homework. Final Exam counts the equivalent of two Tests. The Grade for the course is determined by the best three of these four scores. Absence from a Test gives a score of 0 for that Test. The Final Exam will be comprehensive and will serve as a make up for one Test.
Test#1: Friday February 1
Test#2: Friday March 1
Thursday, March 21, 930 - 1130.
NOTES:
Discrete Models of Diffusion and Vibration.
Separation of Variables
Solution with initial value u(x,0) = sin(pi x) and boundary conditions u(0,t) = u(1,t) = 0: Solution 1.
Solution with initial value u(x,0) = 1 and boundary conditions u(0,t) = u(1,t) = 0: Solution 2.
Porous Media.
SCHEDULE
1. Heat conduction in an interval `Discrete Models' pp. 1-3. (1/07)
2. examples `Discrete Models' pp. 4-6.
3. No Class today. Read remainder of `Discrete Models'.
Chapter 10: Partial Differential Equations and Fourier Series.
4. Separation of Variables pp. 1-6, Appendix A & 10.5: 7, 8. (1/14)
5. Fourier series 10.1: 1, 3; 10.2: 13, 19, 16; 10.5: 9.
6. Fourier theorem 10.3: 1, 3, 5, & Read 10.2 again.
7. MLK Holiday (1/21)
8. even and odd functions 10.4: 7, 9, 11, 15, 17, 20- 22.
9. 10.5: 9, 10, and u(x,0) = x; insulated ends 10.6: 12ab and u(x,0) = x.
10. more boundary conditions 10.4: 39; 10.6: 15, 16a, 20. (1/28)
11. Review
12. Test#1
13. nonhomogeneous boundary conditions 10.6: 1, 2, 8, 9a, 11a. (2/04)
14. nonhomogeneous pde 10.6: 17, 21-23.
15. WaveEquation Chap 10 Appendix B, and 10.7: 1a, 3a.
16. linearity, more boundary conditions 10.7: 5a, 9, 5a with free ends. (2/11)
17. Laplace's equation on a rectangle 10.8: 1-4.
18. Laplace's equation on a circle 10.8: 5-7, 11.
19. Heat conduction in a plane region homework (2/18)
20. Two-point BVPs Read 10 App A, 11.1: 25.
21. more BVPs, 1st order derivatives 11.1: 8, 11, 16.
22. Sturm-Liouville BVPs 11.2: 1-7, 10, 11. (2/25)
23. Review 10.6, 10.7, 10.8.
24. Test#2
25. Non-homogeneous BVPs 11.3: 1-7, 10, 11. (3/04)
26. Non-homogeneous Initial-BVPs Notes: Separation of Variables pp. 7-8 and 11.3: odd 15 - 25.
27. Examples
28. advection: first-order derivatives Read Porous Media notes. 11.2: 27. (3/11)
29. Divergence Theorem and Porous Medium Equation
30. Review 10.7, 10.8, 11.3.