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 2013 34402 (M415) and 34410 (M515)

Syllabus Version 1

  • Calculus on Manifolds
  • MWF 1100-1150 (Deady 209) + F 1500-1550 (Peterson 103)
  • Office hours Monday, Wednesday, Friday 0900-0950
  • 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). I will drop your 2 lowest homework scores in computing the homework average. This is to allow for life's little emergencies in case you have to miss turning in 1 or 2 homeworks. Late homework will not be accepted.
  • Grade: Will be based
    1. 25% on the homework
    2. 25% on the mid term Wednesday 1 May 2013
    3. 50% on the Final Exam 10:15 Thursday 13 June 2013.
  • Note: No class Memorial Day Monday May 27 2013.
    Teaching Associate: Ekaterina Puffini. Academic Calendar


  • Here are tentative reading and homework assignments. Subject to change
    1. Week 1 (1 Apr - 5 Apr 2013): Read 1-34. Do 1.7, 1.10, 1.22, 1.30, 2.4, 2.5, 2.7.
    2. Week 2 (8 Apr - 12 Apr 2013): Read 34-45. Do 2.12, 2.13., 2.21, 2.22, 2.23, 2.24, 2-25, 2-26. Also Extra problem
    3. Week 3 (15 Apr - 19 Apr 2013): 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 (22 Apr - 28 Apr 2013): Read 56-73. Do 3.1-3.10.
    5. Week 5 (29 Apr - 3 May 2013): Read 56-73. Do 1.18, 3.11, 3.12, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19. Exam Wednesday May 01 2013
    6. Week 6 (6 May - 10 May 2013): Do 3.13, 3-20, 3.21, 3.22, 3.23, 3.26, 3.28, 3.29, 3.36.
    7. Week 7 (13 May - 17 May 2013): 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:   Prove or disprove the following assertion: ``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 8 (20 May - 24 May 2013): Assignment #8
    9. Week 9 (25 May - 30 May 2013): Assignment #9
    10. (27 May 2013 is Memorial Day)
    11. Week 10 (03 Jun - 07 Jun 2013): TBA
    12. Week 11 (10 June - 14 June 2013) Final Exam Thursday 13 June 2013 10:15. Owing to faculty legislation, final exams may not be given early under any circumstances
  • Notes available in the class:
    1. Improper Integrals
    2. Change of variable Theorem
    3. Green's, Gauss's, Stokes Theorem
    4. Applications Fundamental Theorem Algebra, Brauer fixed point formula, combing the hair on a billiard ball.
    Mathematics Department Undergraduate Grading Standards November 2011 There are two important issues that this grading policy recognizes. Rubric for applied courses: Modeling, in mathematical education parlance, means the process of taking a problem which is not expressed mathematically and expressing it mathematically (typically as an equation or a set of equations). This is usually followed by solving the relevant equation or equations and interpreting the answer in terms of the original problem.

    Rubric for pure courses:

    Many courses combine pure and applied elements and the rubrics for those courses will have some combination of elements from the two rubrics above. Detailed interpretation of the rubrics depends on the content and level of the course and will be at the discretion of instructors. Whether to award grades of A+ is at the discretion of instructors.

    Course Goals This material was added 24 May 2013 and was not part of the original syllabus. Still, as it perhaps will assist the students in their review, we felt it worth adding. This is a rigorous introduction to the material necessary to understand multi-variable calculus and calculus on manifolds.