Department of Mathematics
Stony Brook University
office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu
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 |
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 | Due Sept 12 |
| Sep 12 | Uniform convergence of Fourier series | 1.4 | 1.4: 1ae, 2,3ab, 4, 5bc | 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 | 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 |
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 | 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 | Due Oct 17 |
| Oct 12 | Series of eigenfunctions & examples. Fourier integral | 2.8, 1.9 | 2.8: 1; 1.9: 1ab, 3a | |
| Oct 17 | Fourier integral & applications to PDEs. Semi-infinite rod |
2.10 | 2.10: 3, 4 | 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 | 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 | Due Nov 7 |
| Nov 2 | Midterm 2 in class, 10:00-11:20am. Covers 2.5-2.8, 1.9, 2.10, 3.1-3.3 | |||
| Nov 7 | Dirichlet's problem in a rectangle; Examples | 4.2, 4.3 | 4.2: 5, 6 | 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 |
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 | 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 | 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 | |||