V63.0224 Vector Analysis
| Term: | Spring 2011 |
| Lectures: | MW 2:00pm-3:15pm in WWH 1302 |
| Recitations: | Tue 8:00am-9:15am in WWH |
| Instructor: | Prof. F. Greenleaf |
| Office: | WWH 613 |
| Office hours: | TBA |
| Phone: | 212-998-3173 |
| Email: | greenleaf@cims.nyu.edu |
Prerequisites
Passing V63.0325 Analysis I with a grade of C or better
Description of the course
Brief review of multivariate calculus: partial derivatives, chain rule, Riemann inetgral, 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.
Course Details
Textbook and Materials
Analysis on manifolds, J. Munkres, Westview/Perseus Press
Homework
Assigned weeklyExams
The final exam is scheduled for 5/16 from 2 to 3:50 pm.
Grading policy
To be determined
Detailed Topics
Calendar
| Week | Topic |
|---|---|
| 1 | Review of calculus |
| 2 | Partial derivatives |
| 3 | Integration techniques |
| 4 | Optimization |
| 5 | Implicit functions |
| 6 | Introduction to manifolds |
| 7 | Vector fields, differential forms |
| 8 | Line integrals |
| 9 | Integration of forms |
| 10 | Gauss' theorem |
| 11 | Stokes' theorem |
| 12 | Applications |
| 13 | Review of the course |