Vector analysis is concerned with the differentiation and integration of vector fields. It plays a vital role in problems of physics and engineering, particularly in fluid dynamics, elasticity and electromagnetics. Vector analysis also serves as a bridge between multivariable calculus and differential geometry.
Topics covered include:
- brief review of multivariable calculus
- line integrals
- Inverse and implicit function theorems
- Div, grad, and curl
- Gauss' theorem, Stokes' theorem and Green's identities
- Introduction to the exterior derivative and differential forms
- Introduction to calculus on manifolds
- The equations of elasticity, fluid dynamics, and electromagnetics
Prerequisites
- Calculus I/II/III, Analysis I.
- General Physics I, II (PHYS-UA 91, PHYS-UA 93) are not required, but recommended as they provide useful context.
Textbook
The course textbook is Vector Calculus by Jerrold E. Marsden ad Anthony J. Tromba.Recommended Texts
- Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, by H. M. Schey - an excellent introduction to applications of vector calculus in classical physics.
- Calculus on Manifolds, by M. Spivak - an excellent (but terse) introduction to the "modern" view of multivariable calculus and differential geometry.
Assignments and grading
There will be regular (weekly or biweekly) assignments, an in-class midterm and an in-class final.Grading will be based 30% on assignments, 30% on the midterm, and 40% on the final. Please see NYU's Academic integrity policies.