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Math 308 Assignment for Unit 6

Due: Friday October 25, 2013

For each problem here, after you have done it, stop and think for a minute.
What is the point of this problem?  How does it fit with the chapter?
Did I really understand, or was I just barely getting through it?  
Solve other nearby exercises as needed so that you feel comfortable.  
You don't have to hand in any of those, but do them until you are 
comfortable with the method.

Exercises from Section 4.1 page 224-226: 
  Do these problems:  Enough from each group in 1-16 to be comfortable and #25.
      Comment: # 25(added part: show that f'(0) exists and is 0).
  To turn in: 3, 7, 8, 16, 17(don't use the normal way--see comment).
    Comment:  # 7,8: Don't use the Wronskian. (For independence you may have
    to take derivatives to show the coefficients are zero.)
    Comment:  #17:  Use the trig. identity sin^2(t)=1/2 - 1/2*cos(2t)

Exercises from Section 4.2 page 231-234: 
  Do these problems:  4, 9, Enough from 11-36.
  To turn in: 14, 22, 29, 37.
    Comment:    # 37:  Show that sin, cos, sinh, cosh are each 
          solutions and that they are linearly independent.  You 
          might want to look up what derivatives of sinh and cosh 
          are and what their values are at zero.  Use the Wronskian
          but evaluate the terms at a point before taking the determinant.

Exercises from Section 4.3 page 237-238: 
  Do these problems:  Enough of 1-18.
  To turn in: 6.

Exercises from Section 4.4 page 242: 
  Do these problems:  Enough of 1-12.(can you do 8?)
  To turn in: 14.
    Comment:  You may need to do polynomial division to find the roots.