Homework should be turned in at the BEGINNING OF CLASS.
All problem numbers refer to the Strauss book,
the required text for the course. Unless otherwise indicated,
all parts of a problem (a), (b), etc. should be completed.
You should write up solutions neatly to all problems,
making sure to SHOW ALL YOUR WORK.
A nonempty subset will be graded. You are strongly encouraged to work
on these problems with other classmates, although the solutions you turn in
should be YOUR OWN WORK.
Important: Please list the names of any students or faculty who you worked with on the assignment.
Section 1.3, pp. 18 - 19
Problems: 2, 5, 9
Hint: For #2, write down F = ma as we did in class for the wave equation. You only need to consider the horizontal direction of the force. Assume that the density of the chain p is constant. Problem #9 is a good practice problem concerning the Divergence Theorem from multivariable calculus. For the volume integral on the left, change to spherical coordinates.
Section 1.4, pp. 24 - 25
Problems: 1, 5
Hint: For #5, the key is you are looking for an equilibrium solution. How does this simplify the diffusion equation?
Section 1.5, pp. 27
Problems: 1, 4