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

Math 4/515 Introductory Analysis III Spring 2010 CRN 33749 and 33757

Syllabus as of 7 May 2010

  • Calculus on Manifolds MWF 0800-0850 (Dea 209) + Friday 1500-1550 (Problem Session Dea 306)
  • Office hours Monday, Wednesday, Friday 1000-1050 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 7 May 2010 (Take home)
    3. 50% on the Final Exam Wednesday 9 June 10:15 2010. Owing to faculty legislation, final exams may not be given early under any circumstances
  • Notes: No class Memorial Day Monday May 31 2010. Teaching Associate: Ekaterina Puffini. Academic Calendar

    • Here are tentative reading and homework assignments. Subject to change
    1. Week 0 Mar 22-Mar 26: Read 1-34.
    2. Week 1 Mar 29-Apr 02 Read 34-45. 2.12, 2.13., 2.21, 2.22, 2.23, 2.24, 2-25, 2-26. Also extra problems
    3. Week 2 Apr 05-Apr 09: 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 3 Apr 12-Apr 16: Read 56-73. Do 3.1-3.10.
    5. Week 4 Apr 19-Apr 23: Read 56-73. Do 1.18, 3.11, 3.12, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19.
    6. Week 5 Apr 26-Apr 30: Do 3.13, 3-20, 3.21, 3.22, 3.23, 3.26, 3.28, 3.29, 3.36.
    7. Week 6 May 3-May 7: Do 1.17, 3.30, 3.31, 3.32, 3.33, 3.34, 3.37, 3.38. Homework is due Wednesday May 12. Problem Session is Sunday May 9 -- 10:00 to 10:50 my office.
      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.
    8. Week 7 May 10-May 14: HW7M4515S10.pdf
    9. Week 8 May 17-May 21: HW8M4515S10.pdf
    10. Week 9 May 25-May 28: HW9M4515S10.pdf
    11. Week 10 June 2-June 4. (Memorial day 31 June 2010)
    12. Week 11 June 8-June 12  Final Exam Wednesday 9 June 10:15 2010. Owing to faculty legislation, final exams may not be given early under any circumstances
  • Notes available in the class:
    1. Change of variable Theorem
    2. Green's, Gauss's, Stokes Theorem

    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.
    Web page spun on 17 May 2010 by Peter B Gilkey 202 Deady Hall, Department of Mathematics at the University of Oregon, Eugene OR 97403-1222, U.S.A. Phone 1-541-346-4717 Email:peter.gilkey.cc.67@aya.yale.edu of Deady Spider Enterprises