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