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 
Jan 24  An introduction to Fourier series  1.1  1.1: 1abc, 2ad, 4, 7b, 8  Due Jan 31 
Jan 26  Determining Fourier coefficients; Examples  1.2  1.2: 1, 7c  
Jan 31  Even & odd extensions Convergence of Fourier series 
1.2, 1.3  1.2:10b, 11b  Due Feb 7 
Feb 2  Uniform convergence of Fourier series  1.3, 1.4  1.3:1abd, 2ad, 6  
Feb 7  Fourier sine & cosine series Basic operations on Fourier series 
1.4, 1.5  1.4: 1ae, 2, 3ab, 5bc page 120: 19, 20 [use a=3] 
Due Feb 14 
Feb 9  no class (snow storm)  
Feb 14  Differentiation of Fourier series The heat equation 
1.5, 2.1  1.5: 2, 5, 9 2.1: 2, 9 
Due Feb 23 
Feb 16  The heat equation Steadystate & transient solutions 
2.1, 2.2  2.2: 2, 6  
Feb 21  Fixedend temperatures  2.3  2.3: 8 [use a=pi]  
Feb 23  Insulated bar; Examples Review 
2.4  2.3: 6 2.4: 4 [use a=pi], 5, 8 
Due Mar 9 
Feb 28  Midterm 1 (2:303:50pm)
Covers 1.11.5, 2.12.3  Solutions Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) 

Mar 2  Different boundary conditions  2.5  2.5: 4, 5 [use a=pi], 6  
Mar 7  Eigenvalues and eigenfunctions Convection 
2.6, 2.7 Notes 
2.6: 7, 9, 10  Due Mar 23 Problem 3c 
Mar 9  SturmLiouville problems  2.7  2.7: 1, 3abc, 7  
Mar 14  no class (Spring break)  
Mar 16  no class (Spring break)  
Mar 21  Series of eigenfunctions & examples Fourier integral & applications to PDEs 
2.8, 1.9  2.8: 1 [use b=2] 1.9: 1ab, 3a 
Due Mar 30 
Mar 23  Semiinfinite rod The wave equation 
2.10, 3.1  2.10: 3, 4  
Mar 28  The wave equation  3.2  3.2: 3, 4, 5, 7  Due Apr 6 Comments 
Mar 30  D'Alembert's solution; Examples  3.3, 3.4  3.3: 1, 2, 5  
Apr 4  The wave equation: generalizations Laplace's equation 
3.4, 4.1  page 255: 18 page 257: 31 
Due Apr 20 Comments 
Apr 6  Dirichlet's problem in a rectangle Examples & Review 
4.2, 4.3  4.1: 2 4.2: 5 [use a=1, f(x)=sin(3pix)] 4.2: 6 

Apr 11  Midterm 2 (2:303:50pm)
Covers 2.42.8, 2.10, 1.9, 3.13.4  Solutions
Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) Extra practice problems 

Apr 13  Potential in a rectangle; Examples Potential in unbounded regions 
4.3, 4.4  4.3: 2b 4.4: 4a, 5ab 
Due Apr 27 
Apr 18  Polar coordinates Potential in a disk 
4.1, 4.5 Notes 
4.1: 6 4.5: 1 

Apr 20  Dirichlet problem in a disk; Examples  4.5  4.5: 4  
Apr 25  Twodimensional heat equation  5.3, 5.4 Notes 
5.3: 1, 7c [use a=b=pi]  Due May 4 
Apr 27  Problems in polar coordinates Bessel's equation 
5.5, 5.6  5.4: 5  
May 2  Temperature in a cylinder Applications: symmetric vibrations 
5.6, 5.7  5.6: 3 [use a=1] page 371: 1 

May 4  Examples & Review  5.7  
May 15  Final Exam (11:15am1:45pm)  in class, Melville Library E4315 The final is cumulative and covers: 1.11.5, 1.9, 2.12.8, 2.10, 3.13.4, 4.14.5, 5.35.6 Practice exams: Fall 2015 and Spring 2015. 