APPM 4350/5350: Fourier Series and Boundary Value Problems Homework #1 Aug. 23, 2010 Due: Friday, September 3, 2010. Usually HW are due on Mondays, but this one is due on Friday because of late Labor day holiday. 1. Solve: dy + k y = b, where y (t = 0) =

APPM 4/5350 Worksheet Week 7
Figure 1: www.xkcd.com
1. What are the requirements to differentiate a Fourier sine series on [0, L] term by term? 2. What are the requirements to differentiate a Fourier series on [L, L] term by term? 3. Draw a function that

APPM 4/5350 Worksheet Week 6
Figure 1: www.xkcd.com
1. Integration If you were to nd and Integrate the Fourier Cosine Series of the function in part (a) would you get the Fourier sine series of part (b)? Explain why or why not. (a) h(x) = x 0<x<L (b) k (

APPM 4/5350 Worksheet Week 5
Figure 1: www.xkcd.com
1. Piecewise smoothness (a) Come up with an analogy (from a realm OUTSIDE of mathematics) for piecewise smoothness. Put in haiku form if desired. BONUS! Come up with a more exciting (but nonetheless germ

APPM 4/5350 Worksheet Week 4
Figure 1: www.xkcd.com
1. Consider
2
u=0
inside a disk of radius R, with u(R, ) = 0 (i) What other boundary conditions should you enforce? (ii) Write down the steps you would use to solve the boundary value problem (you dont n

APPM 4/5350 Worksheet Week 3
Figure 1: www.xkcd.com
1. Eigenvalues/Eigenvectors (a) Solve Av = v where A= 32 23
Identify the eigenvalues and eigenvectors. What relationship do the eigenvectors have? (b) now solve Av = v where 2 2 +2 x2 y Once again, ident

APPM 4/5350 Worksheet Week 2
Figure 1: www.xkcd.com
1. Linearity Which of the following operators L are linear operators? L(x) = L(f ) = L(w) = L(w) =
w 2 x 2w x2
13x + 7
2f x2
1 2f c2 t2 3w x3 3w x3
+ q (x, t)w + + q (x, t)w +
Is a linear combination of

APPM 4/5350 Worksheet Week 1
Figure 1: www.xkcd.com
1. ODEs (a)Find a solution (t) for: m = g sin() with small angle approximation sin() , and initial conditions (0) = 0, (0) = 1
(b)Obtain a general solution y (t) (including arbitrary constants) for y + t

Course Syllabus
APPM 4350/5350
Fall 2010
Methods in Applied Mathematics Fourier Series and Boundary Value Problems (BVPs)
Instructor: M. J. Ablowitz Email: mark.ablowitz@colorado.edu Oce: ECCR 255 Phone: 2-5502 Oce Hours: MWF 23pm or by appointment Classr

POTENTIAL PROJECTS
APPM 4350/5350
FALL 2010
Below is a list of potential projects for APPM 4350/5350. You can purpose your own project, but it must be approved by MJA. If youd like more information on any of the projects below, feel free to stop by ECCR 2

APPM 4350/5350: Fourier Series and Boundary Value Problems Homework #4 Monday October 11, 2010 Due: Monday, October 25, 2010 1. Solve: T 2T 2x = 2 + et sin , T (x = 0, t) = T (x = L, t) = 0, T (x, t = 0) = f (x) t x L > 0, constant, > 0, constant, 0 < x <

APPM 4350/5350: Fourier Series and Boundary Value Problems Homework #3 Monday, September 20, 2010 Due: Friday, October 8, 2010 Note date due! 1. (a) Given the equation for y = y (x): x2 d2 y dy + (2b + 1)x + cy = 0 dx2 dx
where b, c are real constants and

APPM 4350/5350: Fourier Series and Boundary Value Problems Homework #2 Friday September 3, 2010 Due: Monday, September 20, 2010 In what follows, and in the future, all arbitrary functions are assumed to be piecewise smooth unless otherwise specied. 1. Con