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124a Exam II, Dr D. Labutin Rules of the exam

Summary: 124a Exam II, Dr D. Labutin
Rules of the exam:
1. This is a work-alone exam.
2. You may use the lecture notes, the textbook, and your homework.
3. Write your solutions in a clean (large size, please) blue book, putting the problems in order, and leaving space
between them. This makes the grading much faster.
4. The test must be turned in at the start of the class on Monday, July 25.
Your signature on the front of the blue book is your affirmation that you have followed these rules. Unsigned bluebooks
will not be accepted. The test contains 4 problems with a total of 16 points.
1. (4 pts) Find u(t, x) solving the initial value problem on the half-line for the diffusion equation:

ut - uxx = 0 for t > 0, x (0, +)
ux(t, 0) = sin t
u(0, x) = x .
You can leave the answer in the forms of the integrals.
2. (4 pts) Solve the wave equation
utt - uxx = ex


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics