Vector Calculus Syllabus

This syllabus and other course materials can be found on the web at http://cc.kzoo.edu/~barth/mat600.html

MAT 600 Vector Calculus
Fall 1997
Eric Barth
Olds-Upton Hall, Room 203H
Phone: 337-7060
email: barth@kzoo.edu

Purpose
An extension of Calc III focusing on generalizations of the derivative, the integral and the fundamental theorem of calculus in the vector language of Linear Algebra. With emphasis on physical motivation and applications.

Goals

develop geometric, analytical and physical understanding of higher dimensional mathematical objects

bring ideas from Real Analysis, Linear Algebra and Electrodynamics into a common context

continued development of skills for lively communication of mathematics in writing and speaking.

Texts

Vector Calculus
Jerrold E. Marsden and Anthony Tromba
W. H. Freeman, Fourth Edition 1996 Div, Grad, Curl and All That
H. M. Schey
W. W. Norton, Third Edition 1997

Topics we will consider

How things get complicated in more than one dimension:
Arithmetic in Euclidean space, functions & maps, scalar and vector fields, non-Cartesian coordinates M & T, Ch. 1
What's the dimension of this derivative?
Jacobian, gradient, path and velocity M & T, Ch. 2
Old faces, new spaces:
Newton's Method, Taylor's Theorem & Inverse Functions in more than one dimension M & T, Ch. 3
Divergence and Curl:
Two new ways to generalize the scalar derivative M & T, Ch. 4
Integration & changing variables M & T, Chs. 5 & 6
Path, Line and Surface Integrals M & T, Ch. 7
Theorems of Green, Gauss and Stokes:
The fundamental theorems of vector calculus M & T, Ch. 8
How does all this fit together?
Maxwell's Equations for the electromagnetic field Schey

Workload with relative contribution to course grade

Daily homework due at the beginning of class
Four 30-minute quizzes
Classroom presentations + Final Exam 50%
25%
25%

The items in boldface constitute the heart of the course. We will explore the remaining material as an enriched survey of Calc III.

Last update:

	How things get complicated in more than one dimension: Arithmetic in Euclidean space, functions & maps, scalar and vector fields, non-Cartesian coordinates	M & T, Ch. 1
	What's the dimension of this derivative? Jacobian, gradient, path and velocity	M & T, Ch. 2
	Old faces, new spaces: Newton's Method, Taylor's Theorem & Inverse Functions in more than one dimension	M & T, Ch. 3
	Divergence and Curl: Two new ways to generalize the scalar derivative	M & T, Ch. 4
	Integration & changing variables	M & T, Chs. 5 & 6
	Path, Line and Surface Integrals	M & T, Ch. 7
	Theorems of Green, Gauss and Stokes: The fundamental theorems of vector calculus	M & T, Ch. 8
	How does all this fit together? Maxwell's Equations for the electromagnetic field	Schey