Section 16.1 Vector Fields
Section 16.2 Line Integrals
- Line Integrals – The Main Idea
- Evaluating a Line Integral over a Union of Curves
- More Line Integrals
- Line Integrals in Space
- Line Integrals of Vector Fields and Work – The Main Idea
- More Line Integrals of Vector Fields and Work
- Even More Line Integrals of Vector Fields
- Alternate Notation for the Line Integral of a Vector Field
Section 16.3 The Fundamental Thm for Line Integrals
- Fundamental Theorem for Line Integrals – The Main Idea
- Three Special Line Integral Theorems
- Cross Partials Test for Conservative Fields
- Find a Potential Function for the Field – Another Ex
Section 16.4 Green’s Theorem
- Green’s Theorem – The Main Idea
- Green’s Theorem and Areas
- Two Examples using Green’s Theorem
- Green’s Theorem with a Union of Regions
- Green’s Theorem – Another Ex
Section 16.5 Curl and Divergence
- Curl – The Main Idea
- Curl and Conservative Vector Fields
- Divergence – The Main Idea
- Divergence and Curl Examples
- Other Forms of Green’s Theorem
Section 16.6 Parametric Surfaces
- Parametric Surfaces – The Main Idea
- Parametric Representation Examples
- Tangent Planes to a Surface
- Surface Area (Note: The last integral should have +1, not -1.)
Section 16.7 Surface Integrals
- Surface Integrals – The Main Idea
- Surface Integral Example using Spherical Coordinates
- Surface Integral Applications
- Surface Integral Two Ways
- Surface Integrals of Vector Fields