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 2017
Schedule & Homework

Schedule

The PDF version of the schedule is available for print here.

Date Topic Section Assignments Due date
Aug 29 Introduction to Fourier series 1.1, 1.10 1.1: 1abc, 2ad, 4, 7b, 8;
1.10: 1, 2
HW1
Due Sept 7
Aug 31 Determining Fourier coefficients. Examples. 1.2 1.2: 1, 7
Sep 5 no class (Labor day)
Sep 7 Fourier sine & cosine series
Convergence of Fourier series
1.3 1.2: 10ab, 11ab
1.3: 1abd, 2ad, 5 6
HW2
Due Sept 12
Sep 12 Uniform convergence of Fourier series 1.4 1.4: 1ae, 2,3ab, 4, 5bc
HW3
Due Sept 19
Sep 14 Basic operations on Fourier series 1.5 1.5: 2, 5, 9
Sep 19 The heat equation. Steady-state solutions 2.1, 2.2 2.1: 2, 9; 2.2: 2, 6
HW4
Due Sept 26
Sep 21 Fixed-end temperatures. Transient solutions
2.3 2.3: 2, 6, 8
Sep 26
Insulated bar. Examples
2.4
2.4: 4, 5, 8
HW5
Due Oct 3
Sep 28 Different boundary conditions
Midterm 1 review
2.5 2.5: 4, 5, 6
Oct 3 Eigenvalues and eigenfunctions
Convection
2.6, 2.7 2.6: 7, 9, 10
HW6
Due Oct 10
Oct 5 Midterm 1 in class, 10:00-11:20am. Covers 1.1-1.5, 1.10, 2.1-2.4
Oct 10 Sturm-Liouville problems.
Relation to Fourier series
2.7, 2.8 2.7: 1, 3bc, 7
HW7
Due Oct 17
Oct 12 Series of eigenfunctions & examples.
Fourier integral
2.8, 1.9 2.8: 1; 1.9: 1ab, 3a
Oct 17Fourier integral & applications to PDEs.
Semi-infinite rod
2.10 2.10: 3, 4
HW8
Due Oct 24
Oct 19 The wave equation 3.1, 3.2 3.2: 3, 4, 5, 7
Oct 24 The wave equation; Examples
Solution to the vibrating-string problem
3.2 page 255: 18
page 257: 31
HW9
Due Oct 31
Oct 26 D'Alembert's solution; Examples 3.3, 3.4 3.3: 1, 2, 5
Oct 31 Laplace's equation
Midterm 2 review
4.1, 4.2 4.1: 1-6
HW10
Due Nov 10
Nov 2 Midterm 2 in class, 10:00-11:20am. Covers 2.5-2.8, 1.9, 3.1-3.4
Nov 7 Dirichlet's problem in a rectangle; Examples 4.2, 4.3 4.2: 5, 6
HW11
Due Nov 14
Nov 9 Potential in a rectangle; Examples.
Potential in unbounded regions
4.3, 4.4 4.3: 2b
4.4: 4a, 5ab
Nov 14 Polar coordinates. Potential in a disk 4.1, 4.5 4.1: 6
4.5: 1
HW12
Due Nov 21
Nov 16 Dirichlet problem in a disk; Examples 4.5 4.5: 4
Nov 21 Two-dimensional heat equation.
Problems in polar coordinates
5.3, 5.4 5.3: 1, 7; 5.4: 5
HW13
Due Dec 5
Nov 23 no class (Thanksgiving)
Nov 28 Bessel's equation. Temperature in a cylinder 5.5, 5.6 5.5: 4, 6; 5.6: 3, 7
Nov 30 Vibrations of a circular membrane 5.7 5.7: 2
Dec 5 Spherical coordinates; Legendre polynomials 5.9 5.9: 6, 8
Practice
problems
Dec 7 Review page 371: 1, 2, 6
Dec 15 Final Exam in class, 11:15am-1:45pm. The final is cumulative and covers 1.1-1.5, 1.9-1.10, 2.1-2.8, 2.10, 3.1-3.4, 4.1-4.5, 5.3-5.7, 5.9