Topics: Power series method for Ordinary Differential Equations, Bessel's and Legendre's equations, Fourier series for Partial Differential Equations. PREREQS: MTH 256
LECTURE: MWF 900 - 950 Cordley 3121 CRN 32074 Instructor: R.E. Showalter Kidder 286 show@math.oregonstate.edu Office Hours: Wednesday 1200 - 1245 Friday 1400 - 1445
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 10.
Test#2: Monday, March 5.
Final Exam: Thursday, March 22, 1400.
SCHEDULE
Chapter 10: Partial Differential Equations and Fourier Series.
1. Introduction: Separation of Variables Read 10.5: 7, 8. (1/09)
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.
2. Introduction: Orthogonality & Convergence: 10.5: 9 & Read 10.1: 1, 3, 5, 15.
3. Fourier series 10.2: 13, 19, 16.
-- Holiday -- (1/16)
-- Snow Day --
-- Rain Day
4. Fourier theorem 10.3: 1, 3, 5. (01/23)
5. even or odd functions 10.4: odd 7 - 11, odd 15b - 21b, 22.
6. Diffusion Equation Chap 10 Appendix A , and nonhomogeneous boundary conditions 10.6: 1, 2, 9a, 11a.
7. DiffusionEquation.pdf pp 4-8; 10.6: 21-23. (01/30)
8. insulated ends 10.6: 12ab, 13ac.
9. review of boundary conditions 10.6: 15, 17.
10. WaveEquation.pdf Examples 1 & 2; Chap 10 Appendix B, and 10.7: 1a, 5a, 9. (02/06)
11. Review
12. Test#1
13. Review (02/13)
Sequences and Series Web Study Guide
14. sequences : Section 1
15. series : Section 2
16. sequences of functions : Section 3 (02/20)
Chapter 5: Series Solutions of ODE.
17. uniform convergence; Section 5.1: odd 1-15, 19-24.
18. series solutions 5.2: 1-4.
19. ordinary point 5.2: 7-10, 19, 21. (02/27)
20. ordinary point, II 5.3: odd 1-7, 10, 23.
21. Review
22. Test#2 (03/05)
23. Euler's equation 5.4: 1 - 12.
24. boundary-value problems 11.1: 7-10, 16.
25. Laplace's equation 10.8: 1-4. (03/12)
26. Laplace's equation 10.8: 6, 7.
27. Review
Extra office hours: Monday 3/19 1-3pm.
