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 |
| Aug 25 | Periodic functions and Fourier series | 1.1 | 1.1: 1abc, 2ad, 4, 7b, 8 |
Due Sept 3 |
| Aug 27 | Determining Fourier coefficients; Examples | 1.2 | 1.2: 1, 7c | |
| Sept 1 | Even & odd extensions; Examples Convergence of Fourier series |
1.2, 1.3 | 1.2:10b, 11b | Due Sept 10 |
| Sept 3 | Uniform convergence of Fourier series Gibbs phenomenon |
1.3, 1.4 | 1.3:1abd, 2ad, 5 | |
| Sept 8 | no class (Labor day) | |||
| Sept 10 | Fourier sine & cosine series Basic operations on Fourier series |
1.4, 1.5 | 1.4: 1ae, 2, 3bc, 5ab page 120: 19, 20 |
Due Sept 17 |
| Sept 15 | Differentiation of Fourier series The heat equation |
1.5, 2.1 | 1.5: 2, 5, 9 2.1: 2, 9 |
Due Sept 24 |
| Sept 17 | Steady-state solutions Transient solutions |
2.2, 2.3 | 2.2: 2, 6 2.3: 6 |
|
| Sept 22 | Fixed-end temperatures |
2.3, 2.4 | 2.3: 2, 8 [use a=pi] | Due Oct 8 |
| Sept 24 | Insulated bar; Examples | 2.4, 2.5 | 2.4: 4 [use a=pi], 5, 8 | |
| Sept 29 | Different boundary conditions Review |
2.5, 2.6 | 2.5: 4, 5, 6 | |
| Oct 1 | Midterm 1 (10:00-11:20am)
Covers 1.1-1.5, 2.1-2.3 --
Solutions
Practice Midterms: Midterm SP2015 with Solutions SP2015 Midterm & Solutions FA2008 |
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| Oct 6 | Convection Eigenvalues and eigenfunctions |
2.6, 2.7 | 2.6: 7, 9, 10 | Due Oct 15 Graphs |
| Oct 8 | Sturm-Liouville problems Relation to Fourier series |
2.7, 2.8 | 2.7: 1, 3bc, 7 | |
| Oct 13 | Series of eigenfunctions & examples Fourier integral |
2.8, 1.9 | 2.8: 1 [use b=2] 1.9: 1ab, 3a |
Due Oct 22 |
| Oct 15 | Fourier integral & applications to PDEs Semi-infinite rod |
2.10 | 2.10: 3, 4 | |
| Oct 20 | The wave equation | 3.1, 3.2 | 3.2: 3, 4, 5, 7 | Due Oct 29 |
| Oct 22 | The wave equation; Examples Solution to the vibrating-string problem |
3.2 | page 255: 18 page 257: 31 |
|
| Oct 27 | D'Alembert's solution; Examples | 3.3, 3.4 | 3.3: 1, 2, 5 | Due Nov 12 Comments |
| Oct 29 | Laplace's equation Dirichlet's problem in a rectangle |
4.1, 4.2 | 4.1: 2 | |
| Nov 3 | Dirichlet's problem in a rectangle Examples & Review |
4.2, 4.3 | 4.2: 5 [use a=1, f(x)=sin(3pix)] 4.2: 6 |
|
| Nov 5 | Midterm 2 (10:00-11:20am) Covers 2.4-2.8, 2.10, 1.9, 3.1-3.2 --
Solutions
Practice Midterms: Midterm SP2015 with Solutions SP2015 Extra practice problems |
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| Nov 10 | Potential in a rectangle; Examples Potential in unbounded regions |
4.3, 4.4 | 4.3: 2b 4.4: 4a, 5ab |
Due Nov 19 |
| Nov 12 | Polar coordinates Potential in a disk Lecture notes |
4.1, 4.5 | 4.1: 6 4.5: 1 |
|
| Nov 17 | Dirichlet problem in a disk; Examples | 4.5 | 4.5: 4 | Due Dec 3 |
| Nov 19 | Two-dimensional heat equation | 5.3, 5.4 | 5.3: 1, 7c [use a=b=pi] | |
| Nov 24 | Problems in polar coordinates Bessel's equation |
5.5, 5.6 | 5.4: 5 | |
| Nov 26 | no class (Thanksgiving) | |||
| Dec 1 | Temperature in a cylinder Applications: vibrations |
5.6, 5.7 | 5.6: 3 [use a=1] | |
| Dec 3 | Symmetric vibrations Examples & Review |
5.7 | 5.6: 7 5.7: 2 page 371: 1, 2, 6 |
problems |
| Dec 11 | Final Exam (11:15am-1:45pm) -- in class, Melville Library W4525 The final is cumulative and it covers: 1.1-1.5, 1.9, 2.1-2.8, 2.10, 3.1-3.4, 4.1-4.5, 5.3-5.7 Practice Final FA2009 (do only problems 2, 5, 6, 8, 10) with Solutions Practice Final SP2015 |
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