Table of Contents
Introduction
Line Integrals
Surface Integrals
Vector Derivative Operators
Introduction
Vectors
Vectors
(Lecture)
Dot Product
(Lecture)
Law of Cosines
(Lecture)
Which Way is North?
(
SGA
)
Differentials and Derivatives
Differentials I
(Lecture)
Differentials II
(Lecture)
Polar Coordinates
(
SGA
)
Coordinates
(Lecture)
Curvilinear Coordinates
(
SGA
)
Vector Differentials
(Lecture)
Polar Coordinates
(Lecture)
Surfaces
Surfaces
(
SGA
: 30+ min)
Surfaces
(SWBQ: 10 min)
Representations of surfaces
(Lecture)
Surfaces
(Lecture)
Contour Maps
(Lecture)
Gradient and Directional Derivatives
Gradient
(Lecture)
Properties of the Gradient
(Lecture)
The Hill
(
SGA
)
Directional Derivatives
(Lecture)
The Puddle
(
SGA
)
Vector Fields
(Lecture)
Polar and Curvilinear Coordinates
The Area of a Circle
(SWBQ: 10 min)
Polar Coordinates
Curvilinear Coordinates
Area and Volume Elements
(
SGA
)
The Cone
(
SGA
: 1 hour)
Integrals in Polar Coordinates
(Lecture)
Integrals in Curvilinear Coordinates
(Lecture)
Line Integrals
Line Integrals
Line Integrals I
(Lecture)
The Valley
(
SGA
)
Line Integrals II
(Lecture)
Use What You Know
(Lecture)
Path Independence
(Lecture)
The Wire
(
SGA
)
Conservative Vector Fields
Conservative Vector Fields
(Lecture)
Finding Potentials
(Lecture)
Surface Integrals
Surfaces
Cross Product
(Lecture)
Surfaces
(Lecture)
Surface Elements
(Lecture)
The Cone
(
SGA
)
Flux
Flux
(Lecture)
Surface Integrals I
(Lecture)
Surface Integrals II
(Lecture)
The Fishing Net
(
SGA
)
Vector Derivative Operators
Divergence and Curl
Divergence
(Lecture)
Divergence
(
SGA
) [divergence only]
Divergence Thm
(Lecture)
Curl
(Lecture)
Curl
(
SGA
) [curl only]
Curl and Divergence
(Lecture)
Other Coords
(Lecture)
Theorems
Stokes' Theorem
(Lecture)
Stokes' Theorem
(
SGA
)
Product Rules
(Lecture)
Stokes' Theorem
(Lecture)
Applications
Second Derivatives
(Lecture)
Change of Variables
(Lecture)
Change of Variables
(
SGA
) [optional]