Leon Takhtajan


Department of Mathematics
Stony Brook University

office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu

MAT 341: Applied Real Analysis
Fall 2018
Schedule & Homework

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 28 & Aug 30 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 6
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 4 & Sep 6 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 13
pp. 54-57: 1,2,3,15-17 and the following extra problems; p. 55: 4-7.
Sep 11 & Sep 13 Differentiation and integration of Fourier series. Parseval's Theorem. Complex form of Fourier series.
Ch. 0, §§ 0.3.4, 0.3.7, 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 20
p. 70: 9,11-13; p. 75: 4,5; p. 83: 1-3; p. 69: 4-6; p. 76: 9; p. 83: 4,5.
Sep 18 & Sep 20 Sturm-Liouville eigenvalue problems.
Ch.1, §1.6.1-1.6.6.
HW 4; due: Sep 27
pp. 96-97: 1-6,7,8,13; pp. 96-97: 10,11,14,15.
Sep 25 & Sep 27 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 4
pp. 108-109: 1,3,4,10,11; pp. 120-121: 4,10,18.
Oct 2 & Oct 4 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 11
pp. 120-121: 2,3,5,7,8,11-14.
Oct 11 Midterm 1, Oct 11, 10:00 - 11:20, 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 16 & Oct 18 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 25
p. 292: 1,2,4,13; p.310: 15 and extra problems;
p. 292: 11,15,16; p.308: 6,7
Oct 23 & Oct 25 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: Nov 1
p. 150-151:2,11,13 and extra problems;
pp. 150-151: 4,5, 9-11,14-16.
Oct 30 & Nov 1 Applications of multiple Fourier series to Laplace's, heat and wave equations.
Ch.2, §§2.5.1-2.5.5.
HW 9; due: Nov 8
pp. 168-169: 1,2,4-6,10-13; pp. 168-169: 3,7,8,14.
Nov 6 & Nov 8 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 15
pp. 181-182: 8,9,13-16,18,19,23.
Nov 13 & Nov 15 Bessel functions.
Ch.3, §§3.2.1-3.2.3.
Midterm 2, Nov 15, 10:00 - 11:20, in class. Covers §§2.4.3, 2.4.5.-2.4.7, 2.5.1-2.5.5, 5.1.1-5.1.3, 5.2.1-5.2.2, 5.2.4-5.2.6.
HW 11, due Nov 20
pp. 207-208: 1-5,14,16,18-20; p. 207: 6,7,10-13.
Nov 20 Bessel functions, continued.
Ch.3, §§3.2.5-3.2.7.
HW 12; due: Nov 29
p. 208: 22-24,28-32; p. 208: 33,34.
Nov 27 & Nov 29 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 6
p. 216: 1,4-8 and p. 226: 1-3.
Dec 4 & Dec 6 Legendre functions ans 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 20 Final exam, 8:00am - 10:45am in class.