Readings for Math 2374

IT Multivariable Calculus and Vector Analysis

These are web readings designed to introduce some topics in Multivariable Calculus and Vector analysis. Those readings marked with an asterisk (*) were designed to be read before students attended lecture, so they are intended to be somewhat readable introductions to the basic ideas. The readings err on the side of qualitative description rather than getting all technical details precise. The quizzes are available (on WebCT) only to students enrolled in Math 2374 as incentive to read the initial readings before lecture.

You can also view the readings organized by topic.

Lecture 11

Lecture 12

Triple integrals*
Triple integral quiz*
Triple integral examples

Lecture 13

The length of a path*
Length of path quiz*
Physical interpretation of a parametrization and its derivative
Length of a path examples

Lecture 14

The idea of divergence and curl*
Divergence and curl quiz*
Vector fields
The components of the curl
More details on the components of the curl
Divergence and curl notation
Divergence and curl example
Subtleties about divergence
Subtleties about curl

Lecture 15

Path integral of a scalar-valued function*
Path integral quiz*
Path integral examples
Line integral of a vector field
Alternate notation for line integrals
Line integrals as circulation
Line integral examples

Lecture 16

The idea behind Green's theorem*
Green's theorem quiz*
Other ways of writing Green's theorem
Green's theorem with multiple boundary components
Using Green's theorem to find area
Sketch of proof for circulation per unit area
Green's theorem examples

Lecture 17

Path-independent or conservative vector fields*
Path-independence quiz*
An example of a conservative vector field
Path-independence implies no circulation
Understanding the conditions for path-independence
Finding the potential function for path-independent vector fields
Path-independence example in three dimensions

Lecture 18

Lecture 19

Change of variables in double integrals*
Change of variables 2D quiz*
Change of variables examples

Lecture 20

Change of variables in triple integrals*
Change of variables 3D quiz*
Spherical Coordinates
Change of variables examples

Lecture 21

Parametrized surfaces*
Parametrized surface quiz*
Parametrized surface examples

Lecture 22

Surface area of parametrized surfaces*
Surface area quiz*
Surface area calculation
Normal vector of parametrized surfaces
Surface area example

Lecture 23

Surface integrals*
Surface integral quiz*
Orienting surfaces
A surface that is not orientable
Parametrization of a plane
Plane parametrization example
Surface integral examples

Lecture 24

The idea of Stokes' theorem*
Stokes' theorem quiz*
Stokes theorem examples

Lecture 25

Lecture 26

The idea of the divergence theorem*
Divergence theorem quiz*
Divergence theorem examples

Lecture 27

Taylor's theorem*
Taylor theorem quiz*
Taylor polynomial example

Lecture 28

Local extrema*
Extrema quiz*
Extrema examples

Lecture 29

Lecture 30

Review quiz*
The integrals
The fundamental theorems
Length, area, and volume factors

© Copyright 2004-2007 Duane Nykamp. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License. Though not required, I'm always interested in hearing from people who want to use this work. I ask that you obtain permission before making a derivative work as this material is typically undergoing revision.

04080 hits since

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.

nykamp@math.umn.edu