Textbook: Calculus on Manifolds, by Michael Spivak. We will also use some material from Introduction to Analysis in Several Variables, by Michael E. Taylor, also available as a preprint.
The topics we will cover include differentiation and integration of functions on Euclidean space, including an introduction to differential forms and manifolds, with examples from differential equations, geometry, and physics.
Grading will be based on
Homework is due on paper at the beginning of class on Wednesdays. Here are the assignments and associated handouts:
Homework 1, due January 27th. See also this handout from Rudin on length of a curve, and also notes on geodesics.
Homework 2, due February 3rd.
Homework 3, due February 10th. See also notes on interchanging derivatives and inverse and implicit functions.
There will be no homework due February 17th, but the first midterm will be Monday February 15th.
Homework 4, due February 24th. See also notes on ordinary differential equations.
Homework 5, due March 3rd.
Homework 6, due March 10th. See also notes on geodesics and this handout from Shifrin's Multivariable mathematics on manifolds in Rn.
Homework 7, due March 17th. See also notes on geodesics.
Homework 8, due March 24th. See also notes on geodesics.
There is no homework due March 31st or April 7th, but the second midterm is on Monday, April 5th. See also notes on partitions of unity.
Homework 9, due April 14th.
Homework 10, due April 21st. See also notes on differential forms.
There is no homework due April 28th, but the final is on Friday, May 7th.
Finally, a list of general policies and procedures can be found here.