Institute for Mathematical Science
Stony Brook University
office: Math Tower 4-103
phone: (631) 632-8266
e-mail: remus.radu@stonybrook.edu
The PDF version of the schedule is available for print here.
| Date | Topic | Section | Assignments | Due date |
| Jan 24 | An introduction to Fourier series | 1.1 | 1.1: 1abc, 2ad, 4, 7b, 8 | Due Jan 31 |
| Jan 26 | Determining Fourier coefficients; Examples | 1.2 | 1.2: 1, 7c | |
| Jan 31 | Even & odd extensions Convergence of Fourier series |
1.2, 1.3 | 1.2:10b, 11b | Due Feb 7 |
| Feb 2 | Uniform convergence of Fourier series | 1.3, 1.4 | 1.3:1abd, 2ad, 6 | |
| Feb 7 | Fourier sine & cosine series Basic operations on Fourier series |
1.4, 1.5 | 1.4: 1ae, 2, 3ab, 5bc page 120: 19, 20 [use a=3] |
Due Feb 14 |
| Feb 9 | no class (snow storm) | |||
| Feb 14 | Differentiation of Fourier series The heat equation |
1.5, 2.1 | 1.5: 2, 5, 9 2.1: 2, 9 |
Due Feb 23 |
| Feb 16 | The heat equation Steady-state & transient solutions |
2.1, 2.2 | 2.2: 2, 6 | |
| Feb 21 | Fixed-end temperatures | 2.3 | 2.3: 8 [use a=pi] | |
| Feb 23 | Insulated bar; Examples Review |
2.4 | 2.3: 6 2.4: 4 [use a=pi], 5, 8 |
Due Mar 9 |
| Feb 28 | Midterm 1 (2:30-3:50pm)
Covers 1.1-1.5, 2.1-2.3 -- Solutions Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) |
|||
| Mar 2 | Different boundary conditions | 2.5 | 2.5: 4, 5 [use a=pi], 6 | |
| Mar 7 | Eigenvalues and eigenfunctions Convection |
2.6, 2.7 Notes |
2.6: 7, 9, 10 | Due Mar 23 Problem 3c |
| Mar 9 | Sturm-Liouville problems | 2.7 | 2.7: 1, 3abc, 7 | |
| Mar 14 | no class (Spring break) | |||
| Mar 16 | no class (Spring break) | |||
| Mar 21 | Series of eigenfunctions & examples Fourier integral & applications to PDEs |
2.8, 1.9 | 2.8: 1 [use b=2] 1.9: 1ab, 3a |
Due Mar 30 |
| Mar 23 | Semi-infinite rod The wave equation |
2.10, 3.1 | 2.10: 3, 4 | |
| Mar 28 | The wave equation | 3.2 | 3.2: 3, 4, 5, 7 | Due Apr 6 Comments |
| Mar 30 | D'Alembert's solution; Examples | 3.3, 3.4 | 3.3: 1, 2, 5 | |
| Apr 4 | The wave equation: generalizations Laplace's equation |
3.4, 4.1 | page 255: 18 page 257: 31 |
Due Apr 20 Comments |
| Apr 6 | Dirichlet's problem in a rectangle Examples & Review |
4.2, 4.3 | 4.1: 2 4.2: 5 [use a=1, f(x)=sin(3pix)] 4.2: 6 |
|
| Apr 11 | Midterm 2 (2:30-3:50pm)
Covers 2.4-2.8, 2.10, 1.9, 3.1-3.4 -- Solutions
Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) Extra practice problems |
|||
| Apr 13 | Potential in a rectangle; Examples Potential in unbounded regions |
4.3, 4.4 | 4.3: 2b 4.4: 4a, 5ab |
Due Apr 27 |
| Apr 18 | Polar coordinates Potential in a disk |
4.1, 4.5 Notes |
4.1: 6 4.5: 1 |
|
| Apr 20 | Dirichlet problem in a disk; Examples | 4.5 | 4.5: 4 | |
| Apr 25 | Two-dimensional heat equation | 5.3, 5.4 Notes |
5.3: 1, 7c [use a=b=pi] | Due May 4 |
| Apr 27 | Problems in polar coordinates Bessel's equation |
5.5, 5.6 | 5.4: 5 | |
| May 2 | Temperature in a cylinder Applications: symmetric vibrations |
5.6, 5.7 | 5.6: 3 [use a=1] page 371: 1 |
|
| May 4 | Examples & Review | 5.7 | ||
| May 15 | Final Exam (11:15am-1:45pm) -- in class, Melville Library E4315 The final is cumulative and covers: 1.1-1.5, 1.9, 2.1-2.8, 2.10, 3.1-3.4, 4.1-4.5, 5.3-5.6 Practice exams: Fall 2015 and Spring 2015. |
|||