MAT 341 Lec02 Course Schedule

Dates

Sections covered - assigned reading before and after the class

Homework

Aug 25 & Aug 27

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 3 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 1 & Sep 3

Sep 1- Labor Day : No class. 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 10 pp. 54-57: 1,2,3,15-17 and the following extra problems ; p. 55: 4-7.

Sep 8 & Sep 10

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 17 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 15 & Sep 17

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

HW 4; due: Sep 24 pp. 96-97: 1-6,7,8,13; pp. 96-97: 10,11,14,15.

Sep 22 & Sep 24

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

Sep 29 & Oct 1

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

Oct 6 & Oct 8

Midterm 1, Oct 8, 2:00pm- 3:20pm, 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 13 & Oct 15

Oct 13 - Fall Break : No class. 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 22 p. 292: 1,2,4,13; p.310: 15 and extra problems ; p. 292: 11,15,16; p.308: 6,7

Oct 20 & Oct 22

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

Oct 27 & Oct 29

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

HW 9; due: Nov 5 pp. 168-169: 1,2,4-6,10-13; pp. 168-169: 3,7,8,14.

Nov 3 & Nov 5

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

Nov 10 & Nov 12

Bessel functions. Ch.3, §§3.2.1-3.2.3. Midterm 2 , Nov 12, 2:00pm - 3:20pm, in class.

HW 11, due: Nov 19 pp. 207-208: 1-5,14,16,18-20; p. 207: 6,7,10-13.

Nov 17 & Nov 19

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

HW 12; due: Nov 26 p. 208: 22-24,28-32; p. 208: 33,34.

Nov 24 & Nov 26

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. Nov 26- Thanksgiving Break : No classes in session.

HW 13 due: Dec 3 p. 216: 1,4-8 and p. 226: 1-3.

Dec 1 & Dec 3

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 08

Review

Dec 15

Final exam, Mon.Dec. 15 2:15-5:00 pm