Sept 4:   HW1:   Ch 1:  1.5, 1.15, 1.20,
                        1.35, 1.39, 1.40
                 (Due Sep 11 in Lecture)
       
       
       
Sept 11   HW 1 Due.

          HW 2:  1.41
                 1.45 (Only the first part, show that
                       dv/dt is perp. to v if |v| = const).
  
                 2.7, 2.8, 2.14
                 (Due Sep 18 in Lecture)
       
Sept 18     HW 2 Due

            HW 3:  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).
       
       
       
Sept 25    HW 3 Due
       
           HW 4:  2.46,  
                  3.1, 3.5, 3.8, 3.13
       
       
       
       
Oct 2     HW4 Due
          HW 5: 3.19(part b only) 
                3.27, 3.29, 3.32, 3.34
       
       
       
       
       
Oct 9      In class exam 1
       
Oct 11     HW 5 Due
           HW 6: 4.2, 4.4, 4.7
       
         
Oct 16     HW 6 Due (note only 3 problems due to short time)
           HW 7: 4.20, 4.23, 4.30, 4.36, 4.41       
       
       
       
Oct 23     HW 7 due  
           HW 8: 4:46, 4.48, 5.2, 5.10, 5.12   
       
      
       
Oct 30     HW 8 due 
           HW 9:  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 6      HW 9 Due
           HW 10: 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 13    HW 10 Due(deadline extended to Nov 14 5pm in grader's box)
       
          HW 11  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.  


       
       
             
       
Nov 20    HW 11 Due 
       
       
       
       
Dec 4     HW 12:  8.12, 8.14, 8.18 

                  8.22 (for part b, you will need to rewrite the equations
                        in terms of a new variable u= 1/r)

                  8.34  (This really is rocket science!)
              
       

Dec 11    HW 12 Due 
       
       
       
Dec 13 
       
       
       
       
Dec 18 
       
Dec 20 
       
Dec 21