Assignments: Mat360

• read pages xiii-12, and begin Homework problem set 1, p. 11, #1-7 (note these will be due Tuesday, 1/17).
• See if you can get Mathematica installed on some machine of your own, or one you have access to. If not, you'll want to find a computer on campus where you can conveniently use Mathematica routinely.
• Once you have access to Mathematica, begin working through Appendix A: Getting Started with Mathematica. I'll assign one section to each of you to prepare from lessons one and two (due in one week). We'll put these all on-line, so that we can easily try any of them.
• Read on into Section 1.3 (and through 1.5 if you're able).
• If you get Mathematica up and working, you might give the second computer problem on p. 11 a try.

Homework problem set 2: p. 14, #3 (you may use the results of #1 and 2, which we will have done in class); p. 20, #1,2,5-7. Due Tuesday, 1/24.

• p. 35, #1 (and what would be the disadvantages?), 3, 8
• p. 42, #1, 3, 5
• p. 48, #1bcd, 2, 5, 6

• p. 54, #3, 5, 12
• p. 68, #1, 2, 3, 7, 12, 13

• p.77 #1; then use bisection to find the m=4 root. You may have to look up the definition of tanh...!
• p.80 #1
• p.88 #2,4,7,8

1. Given three initial guesses, , , and ; find the unique quadratic that passes through the three points .
2. Find the zeros of this quadratic (use a sensible choice of formula for finding the roots).
3. Make a sensible choice of root to replace "the oldest guess" .
4. Describe how to iterate (Do it again!).
5. Illustrate the method graphically, and numerically, for the function .
6. Explain how Muller's method will allow us to find complex roots with an example (e.g. ).

1. p. 178, #2, 3
2. p. 181, #6

1. p. 190, #1, 2, 8
2. p. 206, #2, 4
3. p. 221, #7, 10

Homework, due 4/13:

1. p. 264, #2, 3, 6
2. Use Richardson's Extrapolation once to obtain a higher-order estimate to the second derivative, using the centered difference formula of exercise 1, p. 264. You'll need the error term for that method that we obtained in class (or you can get it from any other source).

• p. 281, #1, but do it for all three methods -- trap, mid, simp; 2, 15
• p. 293, #1, 4a (I'm not sure about b!), 5

You can make use of my code for these problems where needed (but adapt them so that they make sense to you!)::

• Computer problem #1, p. 344 (I'm not sure why the authors suggest the step-size control that they do -- they seem to be off by a power of h, and a derivative.)
• A modification of that code to do other examples, e.g. Example 8.10, p. 340