Differential Forms Math 437 Spring 2014

Official Course Number: MATH 437, Section 0101 (3 credits, Grade Method: REG/P-F/AUD)
Sessions: Tuesday-Thursday 9:30 - 10:45, Room 0409 Math Building
Professor: Bill Goldman (wmg@math.umd.edu), 3106 Math Building, 301-405-5124
Assistant: David Reynosa Valle (vrd@math.umd.edu), 4423 Math Building
Prerequisites: MATH240/461, MATH 410, Strongly reommended: MATH 405, 403 or 436.
Text: David Bachman, A Geometric Approach to Differential Forms, Birkhauser Boston, 2nd Edition

This course develops the theory of exterior differential forms and integration on smooth manifolds. The course aims at the general version of the fundamental theorem of calculus (Green's theorem, Gauss's theorem, the Divergence Theorem and Stokes's theorem).

Tentative Course Schedule:

  • First homewok due Thursday, 6 February. (Chapter 2: Problems 6,11,18,20,35-36,41
  • Second homewok (Chapter 3, Problems 3,6-10,14,27-28,34) due Tuesday, 18 February.
  • Third homewok (Chapter 4, Problems 1,2,3,7,8) due Tuesday, 25 February.
  • Fourth homewok (Chapter 4, Problems 12,17,24,28,30,32) due Tuesday, 4 March.
  • Fifth homewok (Chapter 5, Problems 4, 6, 12, 15, 16) due Tuesday, 11 March.
  • li> First midterm, Thursday, 13 March.
  • Sixth homework (Chapter 6, Problems 2,4,7,12,14, 19), due Tuesday, 1 April
  • Seventh homework (Chapter 6, Problems 22,20, 23, 26, 29, 30), due Tuesday, 8 April
  • Eighth homework (Chapter 7, Problems 1,3,6,7,8), due Tuesday, April 22
  • Ninth homework (Chapter 7, Problems 14,15,16, Chapter 8, Problems 1,2,3 due Thursday, May 1
  • Second Midterm, Thursday, 1 May
  • Handout on Derivations and Interior Multiplication, due Whenever

Grading: The course grade will be determined by homework (40 %), two in-class midterm exams (30 %) a final problem set (20%), and class participation (10 %). Attendance of the lectures is strongly recommended, since there will be material covered in class which may not be in the textbook.

Written Absence Policy: If for some reason you are unable to attend the in-class exams, make arrangements with the instructor before the exam date.

Academic Integrity You may collaborate on homework assignments, but on neither quizzes nor exams. Please be prepared to show photo ID for midterms and final (there have been unfortunate cases of dishonesty in the past). For general information on the Honor Code, please consult http://www.shc.umd.edu/code.html.

Religious observances: If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact the instructor at the beginning of the semester to discuss alternatives.

Disabilities: If you have some disability related to testing under the usual timed, in-class conditions, you may contact the office of Disabled Students Services (DSS) in Shoemaker. If they assess you as meriting private conditions and/or extra time, then you may arrange to take your tests at DSS, with extra time as they indicate. You must arrange this well in advance of a test (in particular: no retakes). Click to Disability Support Services for further information.

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