Math 520
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| Instructor: | Scott Hansen |
| Office: | Carver 494 |
| Telephone: | 294-8171 |
| E-mail: | shansen@iastate.edu |
| Office Hours: | see homepage |
| Class Meetings: | MWF 2:10-3 pm, Carver 132 |
| Textbook: | Green's Functions and Boundary Value Problems by Stakgold and Holst, 3rd edition, Wiley |
| About the course: | Course Policy and Syllabus I plan to run this course similar to the way the 519 course went, with at least 75 percent of the course grade based on 6-8 homework assignments. The remainder of the grade is based on a final exam, which may be in-class and possibly individual projects that I may assign in the last half of the semester. |
I'll post the assignments here.
HW 1: Chapter 4: 5.1, 5.3, 5.5, 5.6, 6.6, 6.7 Due: 1-27
HW 2: 5.1.2, 5.1.3, 5.1.5, P4, P5, where
P4: Find a "good" estimate for the values of parameter z for which there exists a unique solution in a)C[0,1], b) L^2(0,1), c) L^1(0,1) to: Ku + zu = f, where f is in C[0,1], K is an integral operator of the type in (5.1.7) with continuous kernel k.
P5: Find the infiite matrix for the operator Au = xu in L^2(0,1) with respect to orthonormal basis in (4.6.19).
HW 3: 5.3.1, 5.3.3, 5.3.4, 5.4.3, 5.4.6
HW 4: 5.5.4b (first part only), 5.6.2, 5.6.3, 5.6.4, 5.6.5
HW5 (Due 3-30)
HW7 , tex file (Due Final Exam day).
Comment on last HW: On prob. 3 you need to decompose data as {0,theta, 0, 0} + {0,0,r,0} and each problem has its own sequence of eigenvalues. One amounts to a Fourier series problem, the other has a sequence of functions that are orthogonal on a weighted L^2 space. Use the inner product structure of H_s to find formulae for the Fourier coefs. (Its not as bad as it looks!)
On prob. 8.3.3b, just find the eigenfunctions, i.e., do not do the normalization procedure. Example 2 in Sec. 7.2 will be helpful to read. Also, you need to know that for each n=0,1,2,... the Bessel function J_n(x) has infinitely many positive zeros. Also, it is helpful to note that the negative Laplace operator is positive (why?). Then each eigenvalue is positive.
Kevin's project problem on Riesz Rep. Thm.
Kubilay's project problem on adjoint calculation.
Preechaya's project on eigenalues of nonsymetric compact operators
Jose's project on an integro-differential eq.
Feifei's project on the Fredholm Alternative
Monalisa's project. (Prob's 6.5.5, 6.5.6)
Nuwan's project. (Prob's 6.5.4)
Juan's project on Riesz Rep. Thm.
Saulo's project on eigenvalue estimation
Final exam: Here is a random AMath Qual . Each person will be assigned 2 problems among: 3, 5, 7, 8, 9. Solutions are to be turned in at the time of the Final Exam and solutions will be written on the board.