Math 240 (J. Wu) Homework #2 Due Fri. Jan 29

READINGS:

In Kreyszig, 1.9,2.1-2.2

To be covered next week:2.3, 2.5,2.8,2.9

CORE PROBLEMS:

Do all core problems in 1.9,2.1-2.2

ADDITIONAL PROBLEMS:

1.9 # 24

2.1 # 26,34

2.2 # 12,14,18

PAST FINAL EXAMS:

Spring 95 # 12,13

EXTRA CREDIT:

A pond forms as water collects in a conical depression of radius Pi and depth 3. (I.e. the shape looks like an inverted cone of height 3. You can also do the problem for arbitrary radius and depth, these particular choices will only simplify things a little). Suppose water flows in at a constant rate k and is lost through evaporation at a rate proportional to the surface area, the proportionality factor being s.

  1. (5 points) Derive a differential equation for the volume V(t) in the pond.
  2. (10 points) Solve the differential equation and determine under what conditions on k and s the pond will overflow, dry out, or eventually reach a constant level. (If you do this part completely, I will be impressed!).

MAPLE ASSIGNMENT:

  1. You can form a study group (of no more than 4 people) to do your Maple assignment and turn in one copy per study group with all the names on the top. Make sure you all do the work and take turns writing it up.
  2. Do the follwing problems in Kreyszig:

    1.9 # 24 : produce a good picture in Maple showing 10 curves in each family all in the same picture.

  3. See if Maple can solve the following linear equations:

    x^2y"+xy'+y=0

    exp(x)y"+xy'+y=0

    4x^2y"-4xy'+3y=8x^(4/3)