#
|
Date |
Topic/Notes |
Reading |
Homework |
1
|
Wed Sep 07 |
Some famous pde, ode from
pde,
linearity,
series solutions (power, Fourier, special fns)
|
Lecture
Notes |
assignment 1 |
2
|
Fri Sep 09 |
Taylor thm, power series,
convergence, differentiating under the sum
|
A4 |
|
3
|
Mon Sep 12 |
Solution of ode by power
series |
A4,A5 |
|
4
|
Wed Sep 14 |
Solution of ode by power series
|
A6 |
assignment 1 due
assignment 2 |
5
|
Fri Sep 16 |
Bessel Equation, series solution, Gamma fn
|
4.7 |
|
6
|
Mon Sep 19 |
Some identities.
|
4.7, 4.8
|
|
7
|
Wed Sep 21
|
Periodic funs: Fourier series versus
power series, piecewise smooth functions, orthogonality from y''=-y
|
2.1 |
assignment 2 due
assignment 3 |
8
|
Fri Sep 23 |
Euler formulas, series for sawtooth,
manipulations
|
2.2 |
|
9
|
Mon Sep 26 |
Other periods, even/odd
fns,
|
2.3 |
|
10
|
Wed Sep 28 |
Half range expansions,
extension by symmetry
|
2.4 |
assignment 3 due
assignment 4 |
11
|
Fri Sep 30
|
Mean square approximation
|
2.5 |
|
12
|
Mon Oct 03 |
Modeling, vibrating string |
3.1, 3.2
|
|
13
|
Wed Oct 05 |
separation of variables
|
3.3 |
assignment 4 due
Prepare
for midterm
|
14
|
Fri Oct 07 |
|
3.3 |
|
|
Mon Oct 10
|
Thanksgiving
|
|
|
15
|
Wed Oct 12
|
|
|
Midterm test
on assignments 1-4
assignment 5
|
16
|
Fri Oct 14 |
D'Alembert solution,
characteristics |
3.4 |
|
17
|
Mon Oct 17 |
1d heat equation |
3.5 |
|
18
|
Wed Oct 19 |
Different boundary
conditions (omit 3.6 until Sturm
Liouville) |
3.5
|
assignment 5 due
assignment 6 |
19
|
Fri Oct 21
|
2d wave, heat eqns
(Brydges is away from Oct
18 - 22) |
3.7
|
|
20
|
Mon Oct 24 |
Laplace Eqn on
rectangular domain
|
3.8 |
|
21
|
Wed Oct 26 |
|
|
assignment 6 due
assignment 7 |
22
|
Fri Oct 28 |
Poisson
eqn, eigenfn expansion, remarks on linear algebra and orthogonality
|
3.9
|
|
23
|
Mon Oct 31
|
Orthogonality in Sturm Liouville
problems
|
6.2 |
|
24
|
Wed Nov 02 |
Different boundary
conditions
|
6.2, 3.6
|
assignment 7 due
assignment 8
|
25
|
Fri Nov 04 |
Orthogonality of Bessel fns and
expansions in Bessel fns
|
4.8 |
|
26
|
Mon Nov 07 |
Laplacian in Polar and cylindrical
coordinates
|
4.1 |
|
27
|
Wed Nov 09 |
|
|
assignment 8 due
Prepare
for test
|
|
Fri Nov 11 |
Remembrance
Day
(Fields meeting Nov 12)
|
|
|
28
|
Mon Nov 14 |
Circular membrane, symmetric case
|
4.2 |
|
29
|
Wed Nov 16 |
|
4.2 |
Midterm test
[On assignments 5,6,7,8]
assignment 9 |
30
|
Fri Nov 18 |
Circular membrane, general
case |
4.3 |
|
31
|
Mon Nov 21 |
|
4.3 |
|
32
|
Wed Nov 23 |
Laplace eqn in circular region
|
4.4 |
assignment 9 due
assignment 10
|
33
|
Fri Nov 25 |
|
4.4 |
|
34
|
Mon Nov 28 |
Cylindrical regions
|
4.5 |
|
35
|
Wed Nov 30 |
|
4.5 |
assignment 10 will not be
collected
|
36
|
Fri Dec 02 |
Last day of classes
|
|
|
|
TBA
|
Final , information |
practice final |
|