HW07
Assigned:       THU 15 OCT 09
Due:                THU 22 OCT 09

Problem 1.   Boas Problem #1, Ch.11.11, page 553.

Problem 2.   Boas Problem #3, Ch.11.11, page 554.

Problem 3.   Boas Problem #8, Ch.11.11, page 554.

Problem 4.   Boas Problem #1, Ch.11.12, page 558.

Problem 5.   Boas Problem #14, Ch.11.12, page 559.

Problem 6.   Boas Problem #22, Ch.11.12, page 560. This was solved in class so don't solve it again but just assume the solution and solve for theta as a function of t and then plot theta as a function of t from t = 0 to 6*Pi, assuming g and l are both equal to one. Plot for alpha = 0.1, Pi/2, and Pi. Interpret the results. Then plot the exact solution for alpha = 0.1 on top of the small angle approximate solution theta[t]=alpha*Sin[t] and see if you can see any difference. (You may have to blow up the graphs to see any.)

Problem 7.    Prove that: Sum[n^3, {n, 0, Infinity}] – Integrate[x^3, {x, 0, Infinity}] = –1/120.
Hint: Use either the Euler-MacLaurin or the Abel-Plana summation formulas.
Note: Technically both the series and the integral are divergent.