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Introducing vector fields
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Classroom Contents
APEX Calculus - Vector Calculus
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- 1 Parametric curves and arc length
- 2 Line integrals of functions
- 3 Example: line integral of a function
- 4 Introducing vector fields
- 5 The 'del' operator
- 6 The gradient vector field
- 7 Divergence of a vector field
- 8 Curl of a vector field
- 9 Some divergence examples
- 10 Interpreting curl
- 11 Line integrals of scalar fields, revisited
- 12 Line integrals of vector fields
- 13 Line integral example 1
- 14 Line integral example 2
- 15 Terminology for curves
- 16 Properties of line integrals
- 17 Fundamental Theorem of Calculus
- 18 FTC example 1
- 19 FTC example 2
- 20 FTC example 3
- 21 FTC example 4
- 22 Conservative vector fields and independence of path
- 23 Further terminology for curves in the plane
- 24 Green's Theorem
- 25 Verifying Green's Theorem with an example
- 26 Sketching the proof of Green's Theorem
- 27 Green's Theorem for multiply-connected domains: an example
- 28 Using Green's Theorem to find the area under a cycloid
- 29 Green's Theorem and polygon areas
- 30 Parametric surfaces
- 31 Tangent and normal vectors for parametric surfaces; surface area
- 32 Surface area
- 33 Surface area of a sphere
- 34 Surface integral of a scalar field
- 35 Surface integrals of vector fields
- 36 Surface integral example
- 37 Computing flux across a cube (surface with 6 faces!)
- 38 Some surface integrals over spheres
- 39 The Divergence Theorem
- 40 Gauss' Law
- 41 Stokes' Theorem
- 42 Using Stokes' Theorem: Example 1
- 43 Using Stokes' Theorem: Example 2
