Math 240 (J. Wu) Homework #5 Due Fri. Feb 19 (by 3pm)

READINGS:

  In Kreyszig, 7.1, 7.2, 7.3, 7.4,7.5
  To be covered next week: 7.6,7.7
CORE PROBLEMS:

  Do all core problems in 7.1,7.2,7.3,7.4,7.5
ADDITIONAL PROBLEMS: 

  7.2  # 14,20 (do 20 before you do 19)
  7.3  # 12,14,16,20
  7.4  # 6,8,16
  7.5  # 4,8,18,26,32 In #32, if the vectors are linearly dependent, write
                      one vector as a linear combination of the others.
PAST FINAL EXAMS: 

  Spring 97 # 7
  Spring 96 # 17
MAPLE ASSIGNMENT:
  1. You can again do this part of the assignment as a study group. But each person should attach a copy of the solutions to the assignment they hand in since otherwise the grading becomes too time consuming.
  2. Read about the linear algebra commands in the Maple Manual and look at the Demos on the Web.
  3. Do 7.4 #16 , first using gausselim and backsub, and then using linsolv.
  4. Do 7.5 # 26 and 32 in Maple.
EXTRA CREDIT:

(5 points) A chain of lenght L and mass density r (and hence total mass L*r) is placed on a horizontal frictionless table and initially length b of it is hanging over the edge of the table. How long does it take for the chain, under the influence of gravity, to completely slide off the table (in terms of L and b, r should not enter)? What happens if b goes to 0?

To solve this, set up a second order differential equation for the amount of length hanging over the edge as a function of t. What if one tries to take friction into account (much more difficult)?