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General information

Course description

A manifold is a type of subset of Euclidean space that has a well-defined tangent space at every point. Such a set is amenable to the methods of multivariable calculus. After a review of some relevant calculus, we will investigate manifolds and the structures that they are endowed with, such as tangent vectors, boundaries, orientations, and differential forms. The notion of a differential form encompasses such ideas as surface and volume forms, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space or hyperspace. We will re-examine the integral theorems of vector calculus (Green, Gauss and Stokes) in the light of differential forms and apply them to problems in partial differential equations, topology, fluid mechanics and electromagnetism.


Multivariable calculus and linear algebra as taught in 2210-2220, or 2230-2240, or 2930-2940.


Weekly homework usually due on Wednesday. You can turn in your homework paper in class or before 03:00 pm at my office, Malott Hall 551. The first homework will be due 3 September. No homework due 1 October and 5 November (because of prelims).

A selection of each assignment will be graded by the TA and returned in class. Each assignment will be worth 20 points. We will drop the lowest homework grade (or absence).


There will be two in-class prelims and a final exam. The schedule is on the Exams page.

No books or calculators will be allowed on the exams.

You may bring a one-sided letter size paper of notes to each prelim exam and a two-sided letter size paper of notes to the final.

If you require special accommodation on exams, such as extended time or quiet time, you must obtain a Faculty Notification Letter from Student Disability Services and contact the professor at least one week before the exam to make the necessary arrangements.


Homework 100 points, prelims 100 points each, final 200 points. Expected median course grade: B+.

Academic integrity

You are encouraged to discuss homework problems with your classmates. Copying other people's solutions is not allowed however and will be penalized by the grader.

You are expected to abide by the CU Code of Academic Integrity.