Physics 263: Problem Set #3

1. (BTM 2.1.2) This is really just quick practice in integration by parts. The key is to rewrite "1" as the derivative of some quantity and then apply the method. As always when you can (e.g., outside of quizzes!), check your answer with MATLAB or Mathematica.
2. (BTM 2.1.3) The definition of n! that we are working with is n! = n*(n-1)*(n-2)* ... *1. So you need to show that you generate this sequence AND that it terminates with the 1. (That is, showing that F(n) = n*F(n-1) takes care of the first part; you still need to show that F(1)=1.)
3. (BTM 2.2.1,2.2.2) Just basic calculus review. Again, check your answers with MATLAB or Mathematica (but be sure to put in your intermediate steps or we can't give credit!).
4. (BTM 2.2.6) Draw the sketch of this problem before proceeding, using the interpretation of the the integral as the area under a curve as your guide to the problem. When there is a symmetry in the problem, you can usually restrict the region of integration and multiply by an appropriate factor (e.g., only integrate over positive x and multiply by two if the problem is symmetry under x <--> -x).
5. (BTM 2.2.9) I3(a) will follow from I1(a) and I4(a) from I0(a) through I2(a). All of these are worked out between equations (2.2.13) and (2.2.20).