MTH 482/582: Applied Partial Differential Equations (Winter, 2018)

LECTURE:	MWF 900 - 950	Kidder 280	CRN 482: 31339, 582: 31288
Instructor:	R.E. Showalter	Kidder 286	show@oregonstate.edu
Office Hours:	MWF 8:30-9:00	& 10-10:30	or by appointment

Topics: Partial differential equations, Bessel's and Legendre's equations, Fourier analysis, separation of variables. PREREQS: MTH 256 or MTH 480 or MTH 481 or MTH 581
Textbook: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, 11th ed., Wiley.
The course will cover topics from Chapter 10 (Partial Differential Equations and Fourier Series) and Chapter 11 (Boundary-Value Problems). Model problems of diffusion or vibration from various areas will be described in supplementary materials.

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 can serve as a make up for one Test.

Test#1: Week 4: Wednesday, Jan 31.
Test#2: Week 7. Wednesday, Feb 21.
Final Exam: Tu 3/20/2018, 1200.

Extra Office hours: Monday 3/19, 3-5pm.

Notes(new) These contain previous Notes and Heat Equation, somewhat rearranged. Comments & questions are welcome.

SCHEDULE
Chapter 10: Partial Differential Equations and Fourier Series.
1. 10.1: 1, 3, 5, 7, 14, 18 & same ODE with y(0) = y(L), y'(0) = y'(L). Read Section 7.3, particularly, eigenvalues & eigenvectors. (01/08)
2. The Heat Equation and Chap 10 Appendix A. Read Section 7.7.
3. 10.2: 9, 11, 13, 28, 29.
4. MLK - No class. (01/15)
5. 10.2: 19; 10.3: 1, 3, 17. See additions to Heat Equation.
6. 10.4: odd 7 - 17, 16, 21, 33, 37-40. Two Examples: sgn(x), |x|, |x| < L.
7. Symmetry & BCs: Fourier cosine or sine series. (01/22)
8. Notes and 10.5: 7-9.
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.
9. 10.6: 3, 5, 15. Insulated ends, mixed BCs.
10. Review (01/29)
11. Test #1.
12. Chap 10 Appendix B and Rotating string.
13. Wave Equation. 10.7: 1a, 5a, 9. (02/05)
14. BCs from symmetry 10.7: 13, 14, 16, 17, 18.
15. 10.7: 20. Repeat with BCs u(0,t)=0, u_x(L,t)=0.
16. 10.6: 21, 22. Repeat with BCs u(0,t)=T, u_x(L,t)=F. (02/12)
17. 10.6: 17. Non-homogeneous problems (PDE & BCs).
18. Porous Medium Equation. (See Notes(new), pp. 16-18.)
19. Review (02/19)
20. Test #2.
21. Recap.
22. Robin BC and time-derivative in BC: 10.6: 12(a,b), 13(c), 20. (02/26)
23. Longitudinal vibrations. (See Notes(new), pp 25-27.)
24. Viscous Wave Equation.
25. Dynamic BCs: Try sums of exp(\lambda t)X(x); Exc 11, p. 31 in Notes. (03/05)
26. Stationary systems: Sec 1.1, pp. 3,4,12; Laplace on square, 10.8: 1(a,b),2.
27. Laplace on square: the Eigenvalue Problem.
28. Heat equation on a square ... or circle 10.8, or sector of an annulus. (03/12)
29. Heat equation review. 10.6: 1-7 & 13c, 15.
30. Wave equation review.

Extra Office hours: Monday 3/19 , 3-5pm.