 
Summary: 124a Exam I, Dr D. Labutin
Rules of the exam:
1. This is a workalone 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 11.
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 3 problems with a total of 16 points.
Notes:
1. (4 pts) Solve the initial value problem on R for the transport equation:
ut  4ux = t2
for t > 0, x (, +)
u = cos x for t = 0, x (, +).
2. (8 pts) For the wave equation
utt  uxx = 0, t > 0, x (, +),
with the initial conditions u(0, x) = (x),
=
1, x 1
0, x > 1,
