Homework assignments Homework is to be turned in in class on the given date at the latest.

for 1/8: (for first edition) Section 1.1:3, 4, 12, Section 1.2: 1, 3. The material for Problems 3,4 will be explained on Wednesday - or read about it in the book.

----------------------------------------------------------------- Please ignore below line. These were assignments from a previous course which may be changed

for 1/15: Section 1.3: 1, 3, 9, Section 1.4: 1, 3 (use your physical intuition to guess what the solution should look like for large t), Section 2.1: 2, 5

for 1/25: Section 2.2: 3, Section 2.3: 4ab (hint: you can use the strong maximum principle, stated below the maximum principle on page 41), Section 2.4: 1, 7 (please do the actual calculation, using the trick indicated in problem 6 and also in class), also do the problem below.

for 2/1: Section 2.3: 8 (try to express the derivative of the energy function in terms of values at the endpoints) Section 2.4: 8, 18 (hint: consider the function w(x,t)=u(x-Vt, t) which satisfies an easier PDE). Section 4.1: 2, 3 and see problem below:

for 2/8: Section 5.1: 2, 8 (equilibrium solution means a solution only depending on x), 9, 4, Section 5.2: 2, 13 recommended (not to be turned in): Section 5.2: 10, 16

for 2/25: Section 4.3: 8, Section 5.2: 5, (8, 12, 13) Section 5.3: 2 (two functions on the interval [a,b] are called orthogonal if the integral \int f(x)g(x) dx from a to b is equal to 0), Section 5.3: 8, 12, 13, Section 5.4: 9, 12

for 3/3: Section 6.1: 6, 9, Section 6.2: 3 and see below

for 3/10: Section 6.1: 10, Section 6.3: 3, Section 6.4: 3, 5, 10

problems from old finals

sketches of solutions

Solutions of first two homework assignments

Solutions of third, fourth and (in part) fifth homework assignments

Solutions of homework assignments until including Section 6.1

(a) Is there a harmonic function (i.e. a solution of \Delta u = 0) for h = z? What about for h = z^2?

(b) Find the constant c for which \Delta u = c has a solution for the Neumann boundary condition with h = z and with h = z^2.

1. Show that there is no solution on the disk of radius 1 to the boundary problem \Delta u = 0 with u = 0 on the circle r=1 as well as u_r = 0 on the circle r=1.

2. Solve \Delta u = 0 for r < 1 with the boundary condition u(1,\theta) = 2 + 3 sin (2\theta) - 2 cos (4\theta) (please ask if any of the notation is unclear).

Please click below for review exercises for the midterm, taken from midterms last year. The solutions need not be turned in. You can also find links to the solutions of some of the homework problems on the main course page.

old exam problems

more old exam problems