Math 522 - Second Semester Advanced Calculus

The following is an approximate list of topics covered in each lecture. Topics might change along the semester and it is the responsability of the student to keep track of any updates.

Topics and approximate lecture schedule

  1. Linear transformations
    2 lectures.
  2. Differentiation
    3 lectures
  3. The contraction principle; The inverse function Theorem
    1 lecture
  4. The implicit function Theorem
    2 lectures
  5. The rank Theorem
    1 lectures
  6. Determinants
    1 lecture
  7. Derivatives of higher order; Differentiation of integrals
    1-2 lectures
  8. Integration
    1 lecture
  9. Primitive mappings
    1 lecture
  10. Partition of unity; Change of variables
    1 lecture
  11. Differential forms
    4 lectures
  12. Simplexes and Chains
    3 lectures
  13. Stokes Theorem
    1 lecture
  14. Closed forms and exact forms
    2 lectures
  15. Vector analysis; Green Theorem; Divergence Theorem
    3 lectures

    16. Midterms:

    First midterm - Tuesday February 24, in class.

    Second midterm - Tuesday April 14, in class.

    Distribution of grades:

    Each midterm will be worth 100 points, the homework 100 points and the Final 150 points, for a total of 450 points.

    Homework:

    Homework will be assigned after each lecture and collected every week or two weeks. We will have a grader who will grade under my supervision.