Institute for Mathematical Science
Stony Brook University
office: Math Tower 4103
phone: (631) 6328266
email: 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  Steadystate solutions Transient solutions 
2.2, 2.3  2.2: 2, 6 2.3: 6 

Sept 22  Fixedend 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 (10:0011:20am)
Covers 1.11.5, 2.12.3 
Solutions
Practice Midterms: Midterm SP2015 with Solutions SP2015 Midterm & Solutions FA2008 

Oct 6  Convection Eigenvalues and eigenfunctions 
2.6, 2.7  2.6: 7, 9, 10  Due Oct 15 Graphs 
Oct 8  SturmLiouville 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 Semiinfinite 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 vibratingstring 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 (10:0011:20am) Covers 2.42.8, 2.10, 1.9, 3.13.2 
Solutions
Practice Midterms: Midterm SP2015 with Solutions SP2015 Extra practice problems 

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  Twodimensional 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 (11:15am1:45pm)  in class, Melville Library W4525 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 Practice Final FA2009 (do only problems 2, 5, 6, 8, 10) with Solutions Practice Final SP2015 