Schedule
Legend: Red colored homework problems
will not be graded, but make sure that you are able to do these
problems, which give you an extra practice. The PDF version of the
schedule is available for print here.
Dates

Sections
covered  assigned reading before and after the class

Homework

Aug
27 & Aug 29

Orthogonal
functions & Fourier series. Definitions & examples. Ch.0,
§§0.3.10.3.3 and Ch.1, §§1.1.11.1.4 and §1.1.6.

HW 1;
due: Sep 5
p.
33: 1,3,7,8; pp. 4446: 1,3,4,7,9,30; pp.
3334: 2,6,1114; pp. 4546: 10,1315,18,19,33,34.

Sep
3 & Sep 5

Pointwise
and uniform convergence of Fourier series Ch.1,
§1.2.1 (proofs are optional) and §§1.3.31.3.4

HW 2;
due: Sep 12
pp.
5457: 1,2,3,1517 and the following extra
problems; p.
55: 47.

Sep
10 & Sep 12

Differentiation
and integration of Fourier series. Parseval's Theorem. Complex
form of Fourier series. Ch.1,
§§1.3.51.3.6, §§1.4.11.4.2 and §§1.5.11.5.3.

HW 3;
due: Sep 19
p.
70: 9,1113; p. 75: 4,5; pp.83: 13; p.
69: 46; p. 76: 9; p. 83: 4,5.

Sep
17 & Sep 19

SturmLiouville
eigenvalue problems. Ch.1,
§1.6.11.6.6.

HW 4;
due: Sep 26
pp.
9697: 16,7,8,13; pp. 9697: 10,11,14,15.

Sep
24 & Sep 26

The
heat equation. Steadystate and timeperiodic solutions.
Homogeneous boundary conditions. Ch.2,
§§2.1.32.1.5 and §2.2.1.

HW 5;
due: Oct 3
pp.
108109: 1,3,4,10,11; pp. 120121: 4,10,18.

Oct
1 & Oct 3

Solution
of the initial value problem in a slab, relaxation time and
uniqueness of solutions. Ch.2,
§§2.2.22.2.4.

HW 6;
due: Oct 10
pp.
120121: 2,3,5,7,8,1114.

Oct
10

Midterm
1, Oct 10, 2:30pm 3:50pm, in class.
Covers
§§1.1.11.1.4, 1.1.6, 1,2.1, 1.3.31.3.6, 1.4.11.4.2,
1.5.11.5.3, 1.6.11.6.6, 2.1.32.1.5, 2.2.12.2.2.

No
HW

Oct
15 & Oct 17

Basic
properties of Fourier transform and solution of the heat equation
on the real line. Ch.5,
§§5.1.15.1.3 and §§5.2.15.2.6.

HW 7;
due: Oct 24
p.
292: 1,2,4,13; p.310: 15 and extra
problems; p.
292: 11,15,16; p.308: 6,7

Oct
22 & Oct 24

Onedimensional
wave equation. The vibrating string and d'Alembert solution. Ch.2,
§ 2.4.3 and §§2.4.52.4.7.

HW 8;
due: Oct 31
p.
150151:2,11,13 and extra
problems; pp.
150151: 4,5, 911,1416.

Oct
29 & Oct 31

Applications
of multiple Fourier series to Laplace's, heat and wave
equations. Ch.2,
§§2.5.12.5.5.

HW 9;
due: Nov 7
pp.
168169: 1,2,46,1013; pp. 168169:
3,7,8,14.

Nov
5 & Nov 7

Laplace's
equation in cylindrical coordinates. Ch.3,
§§3.1.13.1.3 and §§3.1.63.1.9.

HW 10;
due: Nov 14
pp.
181182: 8,9,1316,18,19,23.

Nov
12 & Nov 14

Bessel
functions. Ch.3,
§§3.2.13.2.3. Midterm 2
, Nov 14, 2:30pm  3:50pm, in class.

HW 11,
due Nov 19
pp.
207208: 15,14,16,1820; p. 207: 6,7,1013.

Nov
19

Bessel
functions, continued.Notes Ch.3,
§§3.2.53.2.7.

HW 12;
due: Nov 28
p.
208: 2224,2832; p. 208: 33,34.

Nov
26 & Nov 28

Wave
equation in polar coordinates. Heat flow in the infinite
cylinder Ch.3,
§§3.3.13.3.2 and §§3.4.13.4.2.

HW 13
due Dec 5
p.
216: 1,48 and p. 226: 13.

Dec
3 & Dec 5

Legendre
functions and spherical Bessel functions. Boundaryvalue problems
in a sphere. Ch.
4, § §4.1.1, 4.2.14.2.2 and §4.3.1.

Extra HW
p.
250: 810, p. 266: 37,11,12 and p. 275: 13.

Dec
12

Final
exam, 5:30pm8:00pm in class.


