Calculus on Manifolds, Fall 2019

Calculus on Manifolds

V. Ivanov


Syllabus of the Course


Recommended textbooks

Manifolds
  1. P.Gadea, J.Munoz, I.Mykytyuk, Analysis and Algebra on Differentiable Manifolfds
  2. J.Lee, Introduction to Smooth Manifolds
  3. J.Munkres, Analysis on Manifolds
  4. L.Nicolaescu, Lectures on the Geometry of Manifolds, https://www3.nd.edu/~lnicolae/Lectures.pdf
  5. M.Spivak, A Comprehensive Introduction to Differential Geometry
  6. L.Tu, An Introduction to Manifolds
Recalling Linear Algebra
  1. S. Axler, Linear Algebra Done Right.
  2. S. Freidberg, A. Insel, L. Spence, Linear Algebra. (The sections without an asterisk)

Homework Assignments

  1. Problem Set 1, due September 19, pdf file, tex file
  2. Problem Set 2, due September 26, pdf file, tex file
  3. Problem Set 3, due October 3, pdf file, tex file
  4. Problem Set 4, due October 10, pdf file, tex file
  5. Problem Set 5, due October 17, pdf file, tex file
  6. Problem Set 6, due October 31, pdf file, tex file
  7. Problem Set 7, due November 7, pdf file, tex file
  8. Problem Set 8, due November 14, pdf file, tex file
  9. Problem Set 9, due November 21, pdf file, tex file
  10. Problem Set 10, due November 28, pdf file, tex file
  11. Problem Set 11, due December 5, pdf file, tex file