Instructor: Ljudmila Kamenova
Office: Math Tower 3115
Office hours: MW 1:302:30pm
MLC hours: M 45pm (online)
Grader: Yulun Xu, email: Yulun.Xu@stonybrook.edu
Grader's office: Math Tower S240A
Grader's office hours:
on the web card
The Instructor may be reached by email 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, 5:30pm8:00pm 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 halfrange 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 (1.11.5, 2.12.3) 2.6 Example: convection 
HW 6 (due Oct. 4) 2.6: 7, 9, 10 
7  Oct. 4 Oct. 6 
2.7 SturmLiouville 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 Semiinfinite 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 (2.42.9, 1.9, 2.10, 3.13.3) 
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 Twodimensional heat equation 
HW 13 (due Nov. 22) 4.5: 1, 4 5.3: 5, 7abc, 10 
Nov. 22 Nov. 24 
Inclass 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
5:308:00pm 
Cumulative All sections included in Midterms 1, 2 plus 4.14.5, 5.3 
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