INSTRUCTOR'S POLICY:  TRY HARD TO HAND IN ASSIGNMENTS IN CLASS ON THE INDICATED DUE DATE AND, IF YOU'RE UNABLE TO ATTEND, GIVE YOUR COMPLETED ASSIGNMENT TO A FRIEND TO HAND IN.  PAPERS SLIPPED UNDER MY OFFICE DOOR BY MID-AFTERNOON  ON THE DUE DATE HAVE  GOOD ODDS  OF GETTING INTO THE GRADER'S HANDS AND BEING GRADED WITHOUT A LATE PENALTY.      IN THE EVENT OF A SPECIAL PROBLEM (ILLNESS, ETC.) CONTACT ME BY E-MAIL. UNLESS I'VE MADE A SPECIAL ALLOWANCE FOR SOME REASON, PAPERS RECEIVED AFTER THE DUE DATE WILL BE SUBJECT TO A DEDUCTION FOR BEING LATE. DON'T PUT ANY PAPERS IN MY MAILSLOT SINCE I CHECK IT ONLY SPORADICALLY.
                IT'S PERFECTLY O.K. TO ASK FOR A HINT DURING OFFICE HOURS.  I'LL USUALLY BE QUITE "GENEROUS" WITH HINTS, MAY COME VERY CLOSE TO COMPLETING THE PROBLEM.  REMEMBER THAT IT'S ALSO PERFECTLY O.K. TO DISCUSS PROBLEMS WITH OTHERS AS LONG AS YOU INDIVIDUALLY WRITE OUT YOUR OWN SOLUTIONS AND PENCIL IN A NOTE IDENTIFYING THE OTHERS ON THE TOP OF YOUR PAPER (SEE ACADEMIC INTEGRITY SECTION).   THERE'S NO DEDUCTION AT ALL FOR SUCH IDENTIFYING NOTES BUT THERE MIGHT BE A SUBSTANTIAL DEDUCTION WHEN IT'S CLEAR THERE'S BEEN COLLABORATION BUT NO NOTES  APPEAR.
 

ASSIGNMENT #1.  DUE   WEDNESDAY, SEPTEMBER 13

    (i)    Read Chapter 1 in do Carmo's book.
    (ii)  Do the following problems from Chapter 1: #2, 4, 7, 13, 14, 15, 17, 18
You may find the notes helpful as a background for problems 13-15 on the Hodge operator and its links to gradients, divergences, curls (called rot by do Carmo), and Laplacians.

ASSIGNMENT #2.   DUE WEDNESDAY, SEPEMBER 20

    Do the following problems from Chapter 2:  #2, 3, 4, 5, 7, 8, 10.

Comments:  #8 seems tricky.  I don't have a good argument for it and will be curious to hear if you come up with a clever argument.  I suggest you read over the remaining problems.  For #1, observing that the form is not only closed but exact, you should be able to obtain the answer in your head.  #6 is an amusing fast tour through the elementary results in complex variable theory, #9 is covering the ground discussed in my notes and you should be able to prove the results quoted in parts a) and b).