Course Description

This course is a generalization of Math 52 multivariable calculus. We define manifolds and differentiable maps between them. We integrate functions on manifolds and then define differential forms. After defining derivative of differential forms, we prove Stokes Theorem and discuss deRham complex.

For a more detailed syllabus see the schedule of topics.


  • Multi Variable Calculus (Math 51, 52, or equivalent).
  • Linear maps and their matrices and determinants.
  • Some exposure to mathematical reasoning is recommended.


The text for the course is Analysis on Manifolds, by James R. Munkres.
The text is required and is available at the bookstore.
While preparing for the classes I will also look into Calculus on Manifolds by Michael Spivak.


Grades will be based on the following components:
  • Class Participation: 2%
  • Homeworks: 24%
  • Midterm: 30%
  • Final Exam: 44%

Students with Documented Disabilities    

Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066, URL:

Affordability of Course Materials

Stanford University and its instructors are committed to ensuring that all courses are financially accessible to all students. If you are an undergraduate who needs assistance with the cost of course textbooks, supplies, materials and/or fees, you are welcome to approach me directly. If would prefer not to approach me directly, please note that you can ask the Diversity & First-Gen Office for assistance by completing their questionnaire on course textbooks & supplies: or by contacting Joseph Brown, the Associate Director of the Diversity and First-Gen Office (; Old Union Room 207). Dr. Brown is available to connect you with resources and support while ensuring your privacy.