Schedule

Dates

Sections covered - assigned reading before and after the class

Homework

Aug 27 & Aug 29

Orthogonal functions & Fourier series. Definitions & examples.
Ch.0, §§0.3.1-0.3.3 and Ch.1, §§1.1.1-1.1.4 and §1.1.6.

HW 1; due: Sep 5

p. 33: 1,3,7,8; pp. 44-46: 1,3,4,7,9,30; pp. 33-34: 2,6,11-14; pp. 45-46: 10,13-15,18,19,33,34.

Sep 3 & Sep 5

Pointwise and uniform convergence of Fourier series
Ch.1, §1.2.1 (proofs are optional) and §§1.3.3-1.3.4

HW 2; due: Sep 12

pp. 54-57: 1,2,3,15-17 and the following extra problems; p. 55: 4-7.

Sep 10 & Sep 12

Differentiation and integration of Fourier series. Parseval's Theorem. Complex form of Fourier series.
Ch.1, §§1.3.5-1.3.6, §§1.4.1-1.4.2 and §§1.5.1-1.5.3.

HW 3; due: Sep 19

p. 70: 9,11-13; p. 75: 4,5; pp.83: 1-3; p. 69: 4-6; p. 76: 9; p. 83: 4,5.

Sep 17 & Sep 19

Sturm-Liouville eigenvalue problems.
Ch.1, §1.6.1-1.6.6.

HW 4; due: Sep 26

pp. 96-97: 1-6,7,8,13; pp. 96-97: 10,11,14,15.

Sep 24 & Sep 26

The heat equation. Steady-state and time-periodic solutions. Homogeneous boundary conditions.
Ch.2, §§2.1.3-2.1.5 and §2.2.1.

HW 5; due: Oct 3

pp. 108-109: 1,3,4,10,11; pp. 120-121: 4,10,18.

Oct 1 & Oct 3

Solution of the initial value problem in a slab, relaxation time and uniqueness of solutions.
Ch.2, §§2.2.2-2.2.4.

HW 6; due: Oct 10

pp. 120-121: 2,3,5,7,8,11-14.

Oct 10

Midterm 1, Oct 10, 2:30pm- 3:50pm, in class. Covers §§1.1.1-1.1.4, 1.1.6, 1,2.1, 1.3.3-1.3.6, 1.4.1-1.4.2, 1.5.1-1.5.3, 1.6.1-1.6.6, 2.1.3-2.1.5, 2.2.1-2.2.2.

No HW

Oct 15 & Oct 17

Basic properties of Fourier transform and solution of the heat equation on the real line.
Ch.5, §§5.1.1-5.1.3 and §§5.2.1-5.2.6.

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

One-dimensional wave equation. The vibrating string and d'Alembert solution.
Ch.2, § 2.4.3 and §§2.4.5-2.4.7.

HW 8; due: Oct 31

p. 150-151:2,11,13 and extra problems;
pp. 150-151: 4,5, 9-11,14-16.

Oct 29 & Oct 31

Applications of multiple Fourier series to Laplace's, heat and wave equations.
Ch.2, §§2.5.1-2.5.5.

HW 9; due: Nov 7

pp. 168-169: 1,2,4-6,10-13; pp. 168-169: 3,7,8,14.

Nov 5 & Nov 7

Laplace's equation in cylindrical coordinates.
Ch.3, §§3.1.1-3.1.3 and §§3.1.6-3.1.9.

HW 10; due: Nov 14

pp. 181-182: 8,9,13-16,18,19,23.

Nov 12 & Nov 14

Bessel functions.
Ch.3, §§3.2.1-3.2.3.
Midterm 2 , Nov 14, 2:30pm - 3:50pm, in class.

HW 11, due Nov 19

pp. 207-208: 1-5,14,16,18-20; p. 207: 6,7,10-13.

Nov 19

Bessel functions, continued.Notes
Ch.3, §§3.2.5-3.2.7.

HW 12; due: Nov 28

p. 208: 22-24,28-32; p. 208: 33,34.

Nov 26 & Nov 28

Wave equation in polar coordinates. Heat flow in the infinite cylinder
Ch.3, §§3.3.1-3.3.2 and §§3.4.1-3.4.2.

HW 13 due Dec 5

p. 216: 1,4-8 and p. 226: 1-3.

Dec 3 & Dec 5

Legendre functions and spherical Bessel functions. Boundary-value problems in a sphere.
Ch. 4, § §4.1.1, 4.2.1-4.2.2 and §4.3.1.

Extra HW

p. 250: 8-10, p. 266: 3-7,11,12 and p. 275: 1-3.

Dec 12

Final exam, 5:30pm-8:00pm in class.