Readings for Math 2374
IT Multivariable Calculus and Vector Analysis
Readings marked with an asterisk (*) are required in the sense that they contain content necessary for the online quiz (available only via WebCT).
Lecture 1
Introduction
Practice Quiz (not graded)
Interactive Concept-Visualization Tools
Parametrization of a Line
Matrices and determinants
The cross product
The component formula for the cross product
The scalar triple product
The relationship between determinants and area or volume
Parametrization of a line examples
Cross product examples
Triple scalar product example
Lecture 2
Forming planes*
Forming Planes quiz*
A line, a point, or a plane?
Distance from point to plane
Forming plane examples
Distance from point to plane example
Intersecting planes example
Lecture 3
Multiplying matrices and vectors*
Matrix-vector multiplication quiz*
Dot product in matrix notation
Matrices and linear functions
Examples of n-dimensional vectors
Matrix and vector multiplication examples
Lecture 4
Level sets*
Level sets quiz*
Function notation
Translation, rescaling, and reflection
Quadric surfaces
Level set examples
Lecture 5
Introduction to partial derivatives*
Partial derivatives intro quiz*
Partial derivatives by limit definition
Partial derivative examples
Lecture 6
Differentiability in higher dimensions*
Differentiability quiz*
More on Differentiability
Differentiability examples
Lecture 7
The chain rule*
Chain rule quiz*
Chain rule examples
Parametrized curves and their derivatives
Tangent lines to parametrized curves
Tangent line to parametrized curve examples
Lecture 8
The directional derivative and the gradient*
Gradient and directional derivative quiz*
Directional derivative and gradient examples
Lecture 9
Double integrals*
Double integral quiz*
Double integrals as iterated integrals
Double integrals examples
Lecture 10
Gradient and directional derivative review quiz*
Initial readings and quizzes survey
Double integrals as volume or area
Change order of integration examples
Area of region example
Changing order of integration is not always feasible
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 example
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 integral examples
Lecture 16
The idea behind Green's theorem*
Green's theorem quiz*
Other ways of writing Green's theorem
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 2004-2006 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. Duane Nykamp Duane Nykamp
–>
13974 hits since April 05 2005
| 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 |
