MATH 3210 - Manifolds and Differential Forms

(MQR-AS, SMR-AS)

Fall. 4 credits. Student option grading.

Prerequisite: multivariable calculus and linear algebra (e.g., MATH 2210-MATH 2220, MATH 2230-MATH 2240, or MATH 1920 and MATH 2940).

Staff.

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, this course investigates 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 area forms and volume forms, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space, or hyperspace. The course re-examines the integral theorems of vector calculus (Green, Gauss, and Stokes) in the light of differential forms and applies them to problems in partial differential equations, topology, fluid mechanics, and electromagnetism.