Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: MW 1:30-2:30pm
MLC hours: M 4-5pm (online)
Grader: Yulun Xu, e-mail: Yulun.Xu@stonybrook.edu
Grader's office: Math Tower S-240A
Grader's office hours:
on the web card
The Instructor may be reached by e-mail at
kamenova@math.stonybrook.edu.
Description: Partial differential equations of mathematical physics: the heat, wave, and Laplace equations. Solutions by techniques such as separation of variables using orthogonal functions (e.g., Fourier series, Bessel functions, Legendre polynomials). D'Alambert solution of the wave equation.
Prerequisites: C or higher in the following: MAT 203 or 205 or 307 or AMS 261; MAT 303 or 305 or AMS 361
Advisory Prerequisite: MAT 200 or MAT 250
Syllabus: Course Syllabus
Midterm 1 -- Monday, September 27, in class
Midterm 2 -- Wednesday, November 3, in class
Final -- Wednesday, December 8, 5:30pm-8:00pm in Earth&Space 131
| Week | Date | Sections | Assignment |
| 1 | Aug. 23 Aug. 25 |
1.1 Periodic functions and Fourier series 1.2 Arbitrary period and half-range expansions |
HW 1 (due Aug. 30) 1.1: 1abc, 2ad, 4, 7b, 8 1.2: 1, 7, 10b |
| 2 | Aug. 30 Sept. 1 |
1.3 Convergence of Fourier series 1.4 Uniform convergence |
HW 2 (due Sept. 8) 1.3: 1abd, 2ad, 5, 6 1.4: 1ae, 2, 3ab, 5bc |
| 3 | Sept. 6 Sept. 8 |
LABOR DAY 1.5 Operations on Fourier series, 2.1 Heat equation: derivation and boundary conditions |
HW 3 (due Sept. 13) 1.5: 2, 5, 8, 9 Ch. 1 Misc.: 19, 20 2.1: 2, 8 |
| 4 | Sept. 13 Sept. 15 |
2.2 Steady state temperatures 2.3 Example: fixed end temperatures |
HW 4 (due Sept. 20) 2.2: 3, 6, 7 2.3: 6, 8 |
| 5 | Sept. 20 Sept. 22 |
2.4 Example: insulated bar 2.5 Example: different boundary conditions |
HW 5 (due Sept. 27) 2.4: 4, 5, 8 2.5: 4, 5, 6 |
| 6 | Sept. 27 Sept. 29 |
MIDTERM 1 (1.1-1.5, 2.1-2.3) 2.6 Example: convection |
HW 6 (due Oct. 4) 2.6: 7, 9, 10 |
| 7 | Oct. 4 Oct. 6 |
2.7 Sturm--Liouville problems 2.8, 2.9 Expansion in series of eigenfunctions, generalities |
HW 7 (due Oct. 13) 2.7: 1, 3abc, 7 2.8: 1,3 |
| 8 | Oct. 11 Oct. 13 |
FALL BREAK 1.9 Fourier transform, 2.10 Semi-infinite rod |
HW 8 (due Oct. 18) 1.9: 1abc, 3a, 5a 2.10: 3, 4 |
| 9 | Oct. 18 Oct. 20 |
3.1 The vibrating string 3.2 Solution of the vibrating string problem |
HW 9 (due Oct. 25) 3.1: 3 3.2: 3, 4, 5, 7 |
| 10 | Oct. 25 Oct. 27 |
3.3, 3.4 d'Alembert's solutions, generalities 4.1 Potential equation (Laplace's equation) |
HW 10 (due Nov. 1) 3.3: 1, 2, 5 Ch. 3 Misc.: 4, 5, 31, 32 |
| 11 | Nov. 1 Nov. 3 |
4.2 Potential in a rectangle MIDTERM 2 (2.4-2.9, 1.9, 2.10, 3.1-3.3) |
HW 11 (due Nov. 8) 4.1: 1, 2, 6 4.2: 5, 6 |
| 12 | Nov. 8 Nov. 10 |
4.3 Further examples for a rectangle
4.4 Potential in unbounded regions |
HW 12 (due Nov. 15) 4.3: 1a, 2b 4.4: 4a, 5ab |
| 13 | Nov. 15 Nov. 17 |
4.5 Potential in a disk 5.3 Two-dimensional heat equation |
HW 13 (due Nov. 22) 4.5: 1, 4 5.3: 5, 7abc, 10 |
| Nov. 22 Nov. 24 |
In-class office hours THANKSGIVING BREAK |
||
| 14 | Nov. 29 Dec. 1 |
4.6 Classification and limitations Final exam review, part 1 |
Practice problems 4.6: 5, 7, 8 |
| 15 | Dec. 6 |
Final exam review, part 2 |
|
| Dec. 8 | Final Exam
5:30-8:00pm |
Cumulative All sections included in Midterms 1, 2 plus 4.1-4.5, 5.3 |
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