Math 1120 (Spring 2012)
"Partial Differential Equations"
Teaching Calendar



January 2012
Sun Mon Tue Wed Thu Fri Sat
22 23 24 25 Differentiation as operator 26 27 First-Order linear homogeneous PDEs 28
29 30 Second Order PDEs; bringiing to canonical form 31


February 2012
Sun Mon Tue Wed Thu Fri Sat
    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
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


April 2012
Sun Mon Tue Wed Thu Fri Sat
1 2 Homework discussion 3   4 Review/Midterm 2 5  6 Derivation of Green's Identity 7
8 9 Consequences of Green's identities, Energy principle 10 11 Reperesentation formula. Green's functions. 12 13 NO CLASS 14
15 16 Green's function for half-plane 17 18 Green's function for circle 19 20 Perron's method 21
22 23 Discussion of Final projects 24 25 Review/Midterm 3 26 27 Discussion of Final projects 2