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 30  Periodic functions and Fourier series  1.1  1.1: 1abc, 2ad, 4, 7b, 8 
Due Sept 8 
Sep 1  Even & odd extensions, Fourier sine & cosine series.  1.2  1.2: 1, 7, 10b, 11bc  
Sep 6  no class (Labor day)  
Sep 8  Convergence of Fourier series  1.3  1.3: 1abd, 2ad, 5 6, 8  Due Sept 13 
Sep 13  Uniform convergence of Fourier series  1.4  1.4: 1ae, 2,4,5  Due Sept 20 
Sep 15  Basic operations on Fourier series  1.5  1.5: 2, 5, 9  
Sep 20  The heat equation. Steadystate solutions  2.1, 2.2  2.1: 2, 8; 2.2: 2, 6  Due Sept 27 
Sep 22  Fixedend temperatures. Transient solutions 
2.3  2.3: 2, 6, 8  
Sep 27  Insulated bar; Examples 
2.4  2.4: 4, 5, 8 
Due Oct 4 
Sep 29  Different boundary conditions. Review 
2.5  2.5: 4, 5, 6  
Oct 4  Convection. Eigenvalues and eigenfunctions  2.6, 2.7  2.6: 7, 9, 10  Due Oct 11 
Oct 6  Midterm 1 in class, 10:0011:20am. Covers 1.11.5, 2.12.4  
Oct 11  SturmLiouville problems. Relation to Fourier series 
2.7, 2.8  2.7: 1, 3bc, 7  Due Oct 18 
Oct 13  Series of eigenfunctions & examples. Fourier integral  2.8, 1.9  2.8: 1; 1.9: 1ab, 3a  
Oct 18  Fourier integral & applications to PDEs. Semiinfinite rod 
2.10  2.10: 3, 4  Due Oct 25 
Oct 20  The wave equation  3.1, 3.2  3.2: 3, 4, 5, 7  
Oct 25  The wave equation; Examples Solution to the vibratingstring problem 
3.2  page 255: 18 page 257: 31  Due Nov 1 
Oct 27  D'Alembert's solution; Examples  3.3, 3.4  3.3: 1, 2, 5  
Nov 1  Laplace's equation. Review  4.1, 4.2  4.1: 16  Due Nov 10 
Nov 3  Midterm 2 in class, 10:0011:20am. Covers 2.52.8, 2.10, 1.9, 3.13.2  
Nov 8  Dirichlet's problem in a rectangle; Examples  4.2, 4.3  4.2: 5, 6  Due Nov 15 
Nov 10  Potential in a rectangle; Examples. Potential in unbounded regions 
4.3, 4.4  4.3: 2b 4.4: 4a, 5ab 

Nov 15  Polar coordinates. Potential in a disk  4.1, 4.5  4.1: 6 4.5: 1 
Due Nov 22 
Nov 17  Dirichlet problem in a disk; Examples  4.5  4.5: 4  
Nov 22  Twodimensional heat equation. Problems in polar coordinates 
5.3, 5.4  5.3: 1, 7; 5.4: 5  Due Dec 6 
Nov 24  no class (Thanksgiving)  
Nov 29  Bessel's equation. Temperature in a cylinder  5.5, 5.6  5.5: 4, 6; 5.6: 3, 7  
Dec 1  Vibrations of a circular membrane  5.7  5.7: 2  
Dec 6  Spherical coordinates; Legendre polynomials  5.9  5.9: 6, 8  problems 
Dec 8  Review  page 371: 1, 2, 6  
Dec 16  Final Exam in class, 11:15am1:45pm. The final is cumulative and it covers: 1.11.5, 1.9, 2.12.8, 2.10, 3.13.4, 4.14.5, 5.35.7, 5.9 