Fall 2008, Math 115 (http://www.math.hmc.edu/math115) (Muddshots)
MW 2:45-4:00 pm, Jacobs B132
Prof. Darryl Yong (dyong@hmc.edu), Olin 1265, x72844
Office Hours: TBA (open door policy)
Grader: Nate Jones
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Fourier Series and Boundary Value Problems Fall 2008, Math 115 (http://www.math.hmc.edu/math115) (Muddshots) MW 2:45-4:00 pm, Jacobs B132 Prof. Darryl Yong (dyong@hmc.edu), Olin 1265, x72844 Office Hours: TBA (open door policy) Grader: Nate Jones |
Objective: By the end of this course, I hope that
Topics covered (tentative): Complex variables and residue calculus, Laplace transforms, Fourier transforms, Separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, Bessel functions, orthogonal polynomials, the heat equation, wave equation, and Laplace's equation.
Lecture notes are available to students in this class accessing this web site using a computer on the Claremont Colleges.
| Week | Mon | Wed | Fri |
| 1 |
9/1 (Labor Day) |
9/3 Complex Arithmetic, Functions |
9/5 |
| 2 |
9/8 Exp, Log, multiple-valued functions; differentiability, analyticity |
9/10 Cauchy-Riemann eqs; complex integration |
9/12 Prob Set 1 due |
| 3 |
9/15 Cauchy's Theorem; Cauchy's Integral Formula; Taylor series |
9/17 Isolated singularities; Laurent series |
9/19 Prob Set 2 due |
| 4 |
9/22 Residues; Residue Theorem |
9/24 More residue calculus examples |
9/26 Prob Set 3 due |
| 5 |
9/29 Intro to integral transforms |
10/1 Solving DEs with integral transforms |
10/3 Prob Set 4 due |
| 6 |
10/6 Free space Green's function for 1-D heat equation |
10/8 Free space Green's function using Laplace Application to Black-Scholes PDE |
10/10 Prob Set 5 due |
| 7 |
10/13 Half space Dirichlet problem for Laplace's eq |
10/15 Half space Neumann problem for heat eq Method of images |
10/17 Prob Set 6 due |
| 8 |
10/20 (Fall Break) |
10/22 Derivation of PDE with reaction, diffusion and convection |
10/24 |
| 9 |
10/27 Deriv of heat eq 1st separation of variables example |
10/29 More separation of variables Self-adjoint eigenvalue problems |
10/31 Prob Set 7 due |
| 10 |
11/3 Fourier series |
11/5 Inhomogeneous problems Eigenfunction expansions |
11/7 Prob Set 8 due |
| 11 |
11/10 Inhomog heat eq Wave equation deriv & sep |
11/12 Laplace and Poisson eq in a disc |
11/14 Prob Set 9 due |
| 12 |
11/17 Vibrations of a circular membrane |
11/19 |
11/21 (Thanksgiving) |
| 13 |
11/24 Vibrating modes of a hanging chain |
11/26 Sturm-Liouville eigenvalue problems Heat eq w/ Robin BC |
11/28 Prob Set 10 due |
| 14 |
12/1 Laplace eq in spherical coords |
12/3 Shape of the earth |
12/5 Prob Set 11 due |
| 15 |
12/8 Energy states of H atom |
12/10 Vibrational modes of a beam |
12/12 Prob Set 12 due |
There is no required textbook for this course, but you may find some of the books in the list below helpful. I personally own these and many more textbooks and am happy to recommend some to you based on your preferences.
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Exam 1 Take home due on Monday, Oct 27 |
25% |
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Exam 2 Take home due on Friday, Dec 19 |
25% |
| Homework | 50% |
Most of your learning will occur while completing your homework assignments, so take them seriously, and complete them thoroughly. Your homework should show clearly your solution processes. I encourage you to describe your solution process in words. Poor presentation may result in loss of credit.
No late homeworks will be accepted except for family or medical emergencies. Your lowest homework grade will be dropped.
You are encouraged to work cooperatively on your homework assignments with your classmates. However, every student MUST write up his/her own homework separately. In addition, you must cite any sources of help that you use. If you work with one of your classmates on a problem, be sure to acknowledge that person in your homework write-up; if you use any textbooks or websites, acknowledge that too. Harvey Mudd's honor code is in effect for all students in this course.
I encourage you to use a computer algebra system (CAS) such as
<dyong@hmc.edu>
Last modified: Tue Aug 26 14:42:29 Pacific Daylight Time 2008