| February 2012 |
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Mon |
Tue |
Wed |
Thu |
Fri |
Sat |
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1 Homework discussion |
2 |
3 Wave equation: physical meaning |
4 |
| 5 |
6 Wave equation: solution, causality |
7 |
8 Wave: boundary conditions, reflection |
9 |
10 Diffusion equation |
11 |
| 12 |
13 Diffusion equation: maximum principle, uniqueness |
14 |
15 Diffusion on the whole line; approximation kernels. |
16 |
17 NO CLASS |
18 |
| 19 |
20 NO CLASS |
21 |
22 Review/Midterm 1 |
23 |
24 Homework discussion |
25 |
| 26 |
27 Fourier method: Dirichlet conditions, Neuman condition |
28 |
29 Fourier method: Robin condition, asymptotic formulas for eigenvalues |
| March 2012 |
| Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |
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1 |
2 Properties of eigenvalues of Hermitian operators |
3 |
| 4 |
5 Orthogonality of exponents; complete spaces. |
6 |
7 Evaluating Fourier coefficients (sin,cos,exponential series); examples of Fourier expansions; introduction to Lebegue integration. |
8 |
9 Types of convergence; least squares. |
10 |
| 11 |
12 Pointwise convergence of Fourier series |
13 |
14 Uniform convergence of Fourier series |
15 |
16 Fejer kernel |
17 |
| 18 |
19 Laplace's equation: examples (Brownian motion), uniqueness of the Dirichlet problem. |
20 |
21 Dirichlet problem for harmonic functions in a square and in a circle. |
22 |
23 Poisson's formula, mean value property, maximum principle. |
24 |
| 25 |
26 NO CLASS |
27 |
28 NO CLASS |
29 |
30 NO CLASS |
31 |