MATH-UA 224 Vector Analysis

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4 points. Offered in the spring.

Course Description

Brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Lagrange multipliers. Inverse and implicit function theorems and their applications. Introduction to calculus on manifolds: definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss' and Stokes' theorems on manifolds.

Prerequisites

Passing MATH-UA 325 Analysis with a grade of C or better.