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Exam 3

    Show all of your work: do not just give an answer.  If you use a theorem in the book, state which one(s) you are using.  If you use a Maple worksheet or Matlab function, be sure to attach a printed version (as noted during the previous class) with your exam.  Only dead sources are allowed.  Turn in this sheet with your work.  Good luck.

1. (20 points) Problem 13 in section 4.3.  Be sure to explain why the answer has the form in the back of the book.  Just quoting the answer in the back is worth exactly 0 points.

2. (20 points) Find the general solution to the differential equation

y''' + y' = 0, y(0) = 0, y'(0) = 1, y''(0) = 2.

3. (60 points) For the differential equation

y' = et + t, y(0) = 1,

find the exact solution and then approximate the solution using the following numerical methods:

(a) The exact solution
(b) Heun's method
(c) Runge-Kutta
(d) The fourth order Adams-Moulton method using the predictor-corrector methodology described in class and the text.

For (a)-(d), make a table of values for t = 0, .1, .2, .3, .4, and .5.

(e) Which is the more accurate method and why?

 

Cheers,
Craig C. Douglas

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