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Introduction to Vector Calculus
Trefor Bazett
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Preface
About This Video Text
Overview of Vector Calculus
1
Line Integrals
1.1
Review of Curves and Parameterizations
1.1
Post-Video Activities
1.2
Introduction to Line Integrals
1.2
Post-Video Activities
1.3
Example Computing a Line Integral
1.3
Post-Video Activities
1.4
Line Integrals in 3D
1.4
Post-Video Activities
2
Vector Fields
2.1
Intro to Vector Fields
2.1
Post-Video Activities
2.2
Gradient Vector Field
2.2
Post-Video Activities
2.3
Line Integral of a Gradient Vector Field
2.3
Post-Video Activities
2.4
Example: Line Integral of a Vector Field
2.4
Post-Video Activities
2.5
Line Integrals with respect to x or y
2.5
Post-Video Activities
2.6
Circulation and Flow
2.6
Post-Video Activities
2.7
Flux
2.7
Post-Video Activities
3
Conservative Vector Fields
3.1
Intro to Conservative Vector Fields
3.1
Post-Video Activities
3.2
Fundamental Theorem of Line Integrals
3.2
Post-Video Activities
3.3
How to Test if a Vector Field is Conservative
3.3
Post-Video Activities
3.4
Finding the scalar potential function for a conservative vector field
4
Green's Theorem
4.1
Circulation Density and Curl
4.1
Post-Video Activities
4.2
Green's Theorem (Circulation Form)
4.2
Post-Video Activities
4.3
Divergence and Green's Theorem (Divergence Form)
4.3
Post-Video Activities
4.4
Example using Green's Theorem
4.4
Post-Video Activities
5
Surfaces
5.1
Describing Surfaces Explicitly, Implicitly and Parametrically
5.1
Post-Video Activities
5.2
Surface Area Formula for Parametric Surfaces
5.2
Post-Video Activities
5.3
Surface Area of a Sphere
5.3
Post-Video Activities
5.4
Two Surface Area Examples (Parametric)
5.4
Post-Video Activities
5.5
Surface Area Formulas for Implicit and Explicit Descriptions
5.5
Post-Video Activities
5.6
Surface Area Example (Implicit)
5.6
Post-Video Activities
6
Surface Integrals
6.1
Surface Integrals
6.1
Post-Video Activities
6.2
Orientable vs Non-orientable Surface
6.2
Post-Video Activities
6.3
Flux Across a Surface
6.3
Post-Video Activities
6.4
Example: Flux Across a Surface
7
Stokes' Theorem
7.1
Curl of a Vector Field
7.1
Post-Video Activities
7.2
Stokes' Theorem
7.2
Post-Video Activities
7.3
Stokes' Theorem Example
8
Divergence Theorem
8.1
The Divergence Theorem
8.1
Post-Video Activities
8.2
Divergence Theorem Example
8.2
Post-Video Activities
8.3
Regions with Two Boundaries
8.4
Gauss' Law
8.4
Post-Video Activities
8.5
A Unified Perspective
8.5
Post-Video Activities
Section
7.3
Stokes' Theorem Example
Let's verify Stokes' Theorem by computing both side of the equation in a concrete example.
Learning Objectives:
Compute both sides of Stokes' Theorem
