This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Vector calculus: course

### From Mathematics Is A Science

## 1 Description

This is a two-semester course in n-dimensional calculus with a review of the necessary linear algebra. It covers the derivative, the integral, and a variety of applications. An emphasis is made on the coordinate free, vector analysis.

## 2 Prerequisites

## 3 Lectures

- Introduction to vector calculus
- Linear algebra of Euclidean space (review)
- Geometry of Euclidean space (review)
- Linear functions in Euclidean space (review)
- Parametric curves as vector valued functions
- Functions of several variables
- Gradient
- Extrema of functions of several variables
- Vector functions
- Derivative as a linear operator
- Integration in dimension n
- Vector integrals
- Stokes theorem
- Independence of path

## 4 Exercises

- Functions of several variables: exercises
- Vector calculus: exercises
- Vector calculus: review
- Vector calculus: test 1
- Vector calculus: test 2
- Vector calculus: final
- Vector calculus: exam 1
- Vector calculus: exam 2
- Vector calculus: midterm
- Vector calculus: exam 3
- Vector calculus: exam 4
- Vector calculus: midterm 2
- Vector calculus: final 2

## 5 Notes

The content is based on the complete set of lecture notes for a course taught by Peter Saveliev in Fall 2009/Spring 2010 at Marshall University.

Text: Calculus Two by Flanigan and Kazdan.

Alternative is a more analytic than geometric approach, see Real analysis: course.