Sept 1:   HW1:   Ch 1:  1.5, 1.15, 1.20,
                        1.35, 1.39, 1.40
                 (Due Sep 8 in Lecture)
       

Sept 13   HW 2:  2.7, 2.8, 
                 2.14,
                 2.24, 2.27, 2.36,
                 2.40 (you will get and integral of the type
                          dx/(ax - bx^2) which you will look up).

                 (Due Sep 22 in Lecture)

Sept 22   HW 2 Due.
          HW 3   2.46,  
                 3.1, 3.5, 3.8, 3.13

Sept 29   HW 3 Due.
          HW 4: 3.19(part b only)
                3.27, 3.29, 3.32, 3.34

Oct  6   HW4 Due.

OCT  8   IN CLASS EXAM 1

Oct 13   HW 5: 4.2, 4.4, 4.7, 4.20, 4.23

Oct 15  Exam 1 returned

Oct 20  HW 5 Due
Oct 21  HW 6: 4:46, 4.48, 5.2, 5.10, 5.12   

Oct 27  HW 6 Due
Oct 27  HW 7:  5.22,
             5.24  In order to show that the solution
                     given approaches t*exp(-Beta*t) as
                     Beta --> omega_0,  you will need the
                     following:

                       sin(k*t)/k --> t as k-->0.
                      (this is reasonably easy to show)

                5.30, 5.40, 5.43

Nov 3:  HW 7 Due
Nov 4:  HW 8: 6.2,
              6.6 (It will be helpful to draw the curves out.
                   Curves on a plane, cylinder, and sphere are easier
                   to visulaize that way)
              
              6.11 (of course you can use the Euler-Lagrange eqn we
                     derived in lecture, you need not rederive it)
              6.16,

              6.18 (after you solve the Euler-Lagrange eqn to get the
                    differential eqn, you will need to make a substitution
                    like const/r = cos(u) to solve the integral and get an
                    equation for a straight line.  Note: the equation for a
                    straight line in polar coordinates looks fairly strange)

Nov 10:  HW 8 Due.
Nove 10: HW 9:7.4,  
              7.14,
              7.20  for a bead travelling on a helix, the radius, R,
                    is fixed, and z is a function of phi.  The velocity
                    can be written as:
                            0 r-hat, R dphi/dt phi-hat, dz/dt z-hat
                    Since z=lambda*phi, you can express T as function
                    solely of dz/dt.

              7.22  It is best to set up the Lagrangian in an inertial
                    frame (relative to the Earth).  To do this, find the
                    T and U of the pendulum relative to the elevator ceiling,
                    and notice that the ceiling is moving up. The velocity
                    of the ceiling is at y-hat and the distance is
                    1/2 a t^2 y-hat.


              7.30  As in 7.22, find the position of the pendulum relative
                    to the train, and add the positon and velocity of the
                    the train to those of the pendulum.


                    Note that 7.22 and 7.30 will give you Lagrangians that
                    have an explicit dependence on t.   That's ok.

Nov 17: HW 9 Due