MAT 341:
Fall 2018

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, §§0.3.1-0.3.3 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.NotesCh.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 cylinderCh.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.