Vector calculus

OpenStax

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1 Examples of vector fields

2 Vector fields in ℝ 2

3 Drawing a vector field

4 Vector fields in ℝ 3

5 Gradient fields

9 Key equations

1 Scalar line integrals

2 Vector line integrals

3 Applications of line integrals

4 Flux and circulation

7 Key equations

Conservative vector fields

Green’s theorem

Divergence and curl

4 Using divergence and curl

9 Key equations

Surface integrals

1 Parametric surfaces

2 Surface area of a parametric surface

3 Surface integral of a scalar-valued function

4 Orientation of a surface

5 Surface integral of a vector field

7 Key equations

Stokes’ theorem

1 Stokes’ theorem

3 Applying stokes’ theorem

4 Interpretation of curl

6 Key equations

The divergence theorem

1 Overview of theorems

2 Stating the divergence theorem

4 Using the divergence theorem

5 Application to electrostatic fields

8 Key equations

9 Chapter review exercises

Source: OpenStax, Calculus volume 3. OpenStax CNX. Feb 05, 2016 Download for free at http://legacy.cnx.org/content/col11966/1.2

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