Department of Mathematics
Stony Brook University
office: Math Tower 5111
phone: (631) 6328287
email: 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. Steadystate solutions  2.1, 2.2  2.1: 2, 9; 2.2: 2, 6  Due Sept 26 
Sep 21  Fixedend 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, 10:0011:20am. Covers 1.11.5, 1.10, 2.12.4  
Oct 10  SturmLiouville 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. Semiinfinite 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 vibratingstring 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: 16  Due Nov 10 
Nov 2  Midterm 2 in class, 10:0011:20am. Covers 2.52.8, 1.9, 3.13.4  
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  Twodimensional 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, 11:15am1:45pm. The final is cumulative and covers 1.11.5, 1.91.10, 2.12.8, 2.10, 3.13.4, 4.14.5, 5.35.7, 5.9 