| Week |
Date |
Chapter |
Subject |
Problem Set |
| 1 |
16 Jan |
1.1-1.2 |
Introduction to PDE's; Definitions and Vector Calculus; Where they come from;
conservation equations; Additional Pretty pictures |
1 |
| 18 Jan |
1.3-1.4 |
Steady Solutions and the importance of Boundary Conditions |
| 2 |
23 Jan |
2.1-2.3.3 |
Separation of Variables 1: Linearity, homogeneity, separability |
2 |
| 25 Jan |
2.3.4-2.3.5 |
Separation of Variables 2: Eigenvalues &
Eigenfuctions, BVP's, Importance of Boundary conditions |
| 3 |
30 Jan |
2.3.6-2.3.8 |
Separation of Variables 3: Product Solutions,
Superposition, Initial conditions and Orthogonal Functions
|
3 |
| 1 Feb |
2.3.6-2.3.8 |
Separation of Variables 4: More Orthogonal function fun |
| 4 |
6 Feb |
2.5.2-2.5.4 |
Separation of Variables 5: Review of technique and new
example: Laplace's Equation on a disk, properties of
Laplace's Eq.
|
4 |
| 8 Feb |
3.1-3.3 |
Fourier Series 1: definitions (Fourier series, Fourier
Sine Series, Fourier Cosine series), extensions,
convergence, even and odd functions. plus some
lovely figures of Fourier Series (pdf format) |
| 5 |
13 Feb |
3.4-3.5 |
Fourier Series 2: Differentiation and integration of
infinite (fourier) series (do's and dont's) PLUS! a
real application of Fourier series (FFT filtering fun).
|
5 |
| 15 Feb |
4.1-4.4 |
1-D Waves: vibrating strings |
| 6 |
20 Feb |
4.5 |
2-D Waves: vibrating membranes (deferred to after midterm)
|
6 |
| 22 Feb |
5.1-5.5 (5.4 redundant) |
Sturm-Liouville Eigenvalue Problems 1: |
| 7 |
27 Feb |
5.5-5.6 |
Sturm-Liouville Eigenvalue Problems 2: |
7 |
| 1 Mar |
5 |
Sturm-Liouville Eigenvalue Problems 3: |
| 8 |
6 Mar |
5 |
Sturm-Liouville Eigenvalue Problems 4 and or review |
review |
| 8 Mar |
5 |
Mid-term |
| Spring Break: 12-16 Mar |
| 9 |
20 Mar |
7.1-7.3 |
Initial Value problems in 2 and 3-D: 1) separation of
time and Helmholtz equation |
8 |
| 22 Mar |
7.4-7.5 |
Initial Value problems in 2 and 3-D: 2) Tom-tom Club: Vibrating
circular membranes: introducing the Bessel
Functions (and a matlab script to view
them). Also here is another matlab script to visualize
the solutions of helmoltz equation on a disk diskmodes.m |
| 10 |
27 Mar |
7.7-7.9 |
Initial Value problems in 2 and 3-D: 3) Laplace's
Equations in a cylinder |
9 |
| 29 Mar |
7.10 |
Initial Value problems in 2 and 3-D: 4) Laplace's
Eq. contd. Spherical harmonics and Legendre Polynomials |
| 11 |
3 Apr |
8.1-8.2 |
Non-homogenuous PDE's 1: |
10 |
| 5 Apr |
8.3-8.4 |
Non-homogenuous PDE's 2: |
| 12 |
10 Apr |
8.5-8.6 |
Non-homogenuous PDE's 3: |
11 |
| 12 Apr |
8 |
Non-homogenuous PDE's 4: |
| 13 |
17 Apr |
9.3.4 |
Green's Functions 1: 1-d problems |
12 |
| 19 Apr |
9.4. 9.5.1-9.5.2, 9.5.6-9.5.7 |
Green's Functions 2: Infinite space Green's functions
for Poisson's equation in 3-D |
| 14 |
24 Apr |
12.1-12.5 |
Method of Characteristics #1: linear problems |
13 |
| 26 Apr |
12.6 |
Method of Characteristics #2: Non-linear wave
equations and shock waves |
| 8 May: Final 9:00am-12:00 (see Study Guide) |
