MAP 6506 Mathematical Methods for Physics and Engineering II
Time and Location
Spring 2014, Section 12E9, MWF – 8th period, 3:00 – 3:50 pm; LIT 223
Description and Goals
Course Content: Integral equations. Boundary value problem for basic equations of mathematical physics. Linear operators. Compact operators. Resolvent of an operator. Fredholm alternative for linear operators on a functional space. Self-adjoint operators. General Fourier method for solving boundary value problems and the Cauchy problem. Perturbation theory for linear operators. Applications to the wave scattering theory. Perturbation theory for nonlinear differential equations of mathematical physics. Solitons (time permitted). Elements of the Lie group theory (time permitted).
Recommended Texts: V.S. Vladimirov, Equations of Mathematical Physics;
F. Riesz and B. Sz.-Nagy, Functional Analysis;
I. Stakgold, Green’s Functions and Boundary Value Problems;
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol 1-4 (for advanced reading).
Homework and Exams
There will be two homework assignments in early February and late March. Practice problems will be offered in most of lectures and some of them will be later included into the graded homework assignments and exams. So, solve them as they are offered! There will be midterm and final exams. Your course notes are permitted to use on the exams. Makeups for missed exams only with written medical excuse.
Student honor code: When turning in a homework, please write “I did the assignment myself and received no help from anybody” on the front page and sign it.
Grades and Ranking
Each assignment is graded out of 100 pts (if no extra credit problem is offered). There is a small partial credit for incomplete solutions. In your course grade, the homework average counts 50% and the exam average counts 50%. Your course score (and ranking) is
G = 0.5 HWA + 0.5 EA
where HWA = (HW1+HW2)/2 is the homework average and EA = (MT+F)/2 the exam average (MT and F are scores of the midterm and final exams, respectively).
Grading Scale
The grade thresholds
A: G>85; B+: G>75; B: G>65; C+: G>55; C: G>45; D+: G>35; D: G>30; F: G<30
Attendance and Late Policy
No credit for class attendance. You may leave or come any time without asking my permission. However the class attendance is strongly recommended as the material presented does not exactly follow any of the aforementioned books. Your notes should be sufficient for all graded assignments. Also, possible homework and exam problems will be given nearly in each lecture. A brief description of each lecture will be posted in the homework page along with recommended texts useful for further reading on the topic discussed. If you miss a class meeting, make sure you have a copy of notes either from your class mates or from me.