Peter B Gilkey
202 Deady Hall,1-541-346-4717 (office phone) 1-541-346-0987 (fax) email: gilkey@darkwing.uoregon.edu
Mathematics Department, University of Oregon, Eugene Oregon 97403 USA

Math 4/515 Introductory Analysis III Spring  2009

Syllabus Version 1

  • Calculus on Manifolds MWF 1300-1350 + Friday 1500-1550 (Problem Session).
  • Office hours Monday 0900-0950, Wednesday, Friday 1100-1150 or by appointment.
  • Text: Spivak: Calculus on manifolds (paperback). (Benjamin/Cummings Publishing Company).
  • Homework will be due each Monday on the material of the subsequent week. The Friday discussion hour is an opportunity for you to ask questions about the homework. The homework problems will be challenging and it is essential that you have thought about the homework before comming to the discussion hour. You should also feel free to ask questions regarding the lecture that have come up then (or during class of course).
  • Grade: Will be based
    1. 25% on the homework
    2. 25% on the mid term Friday May 01
    3. 50% on the Final Exam 15:15 Thursday June 11. Owing to faculty legislation, final exams may not be given early under any circumstances
  • Notes: No class Memorial Day Monday May 25 2009. Teaching Associate: Ekaterina Puffini. Academic Calendar

    • Here are tentative reading and homework assignments. Subject to change
    1. Week 1 Mar 30-Apr 03: Read 1-34. Do 1.7, 1.10, 1.22, 1.30, 2.4, 2.5, 2.7.
    2. Week 2 Apr 06-Apr 10: Read 34-45. Do 2.12, 2.13., 2.21, 2.22, 2.23, 2.24, 2-25, 2-26. Also extra problems -- see PDF and TEX
    3. Week 3 Apr 13-Apr 17: Read 46-56. Do 2.29, 2.30, 2.31, 2.32, 2.35, 2.36, 2.37 [not part b], 2.38, 2.39
    4. Week 4 Apr 20-Apr 24: Read 56-73. Do 3.1-3.10.
    5. Week 5 Apr 27-May 01: Read 56-73. Do 1.18, 3.11, 3.12, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19. Exam Friday May 01
    6. Week 6 May 4-May 8: Do 3.13, 3-20, 3.21, 3.22, 3.23, 3.26, 3.28, 3.29, 3.36.
    7. Week 7 May 11-May 15: Do 1.17, 3.30, 3.31, 3.32, 3.33, 3.34, 3.37, 3.38
      1. Problem A1:  Prove or disprove the following assertion: ``Let U be a bounded open subset of R-n. Then the characteristic function of U is integrable in the extended sense over U.
      2. Problem A2: If U is any unbounded open subset of R-n, then the characteristic function of U is not integrable in the extended sense over U.
      3. Reference the Change of Variable Theorem
    8. Week 8 May 18-May 22. TBA
    9. Week 9: May 26-May 29. TBA (Monday 25 is Memorial Day)
    10. Week 10: June 1-June 5. TBA
    11. Week 11 June 9-June 13  Final Exam 15:15 Thursday June 11. Owing to faculty legislation, final exams may not be given early under any circumstances

    To rest on the blue of the day, like an eagle rests on the wind, over the cold range, confident on its wings and its breadth.
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