# Math 240 (J. Wu) Homework #3 Due Fri. Feb 5 (by 3pm)

Note: The first midterm will be on Feb 8 6:30 to 8 pm ! It will cover Ch1 and Ch2. More details to be announced in class next week Wednesday.

In Kreyszig, 2.3, 2.5,2.8,2.9

To be covered next week: 2.11,7.1-7.3

CORE PROBLEMS:

Do all core problems in 2.3,2.5,2.8,2.9

• 2.3 #22,26
• 2.5 # 2,5,16,22
• 2.9 # 2,6,10,20

• PAST FINAL EXAMS:
• Spring 98 # 10,12
• Spring 97 # 4

• EXTRA CREDIT: ( to be handed in at the end of class on Friday)

(5 points) A block whose base is a rectangle and whose height is h has mass density r and is submerged in a fluid with mass density r0. Assume that r0>r so that the block will float. If the block is slightly depressed (pushed into the fluid) and then released, it will oscillate in the vertical direction. Assuming that the damping of the fluid and the air can be neglected derive a differential equation of its motion. Show it performs a simple harmonic motion and determine its frequency. How does the height and the mass change the frequency?

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:

• 2.5 # 14 : Find the solutions in Maple and draw all of them in one picture.
• 2.5 # 22 Same as above