Vector Calculus

This course presents the main ideas of vector calculus through line and surface integrals, including integrals of functions and vector fields. It develops Green’s, Stokes’, and the Divergence theorem with examples involving curves, surfaces, areas, and volumes.

Syllabus

Parametric Equations.
What is a Line Integral ?.
Line integral of a function.
Line Integral over a line.
Line Integral Example.
Line Integral Derivation.
Integral over a helix .
Line integral with respect to x.
Line integral of a vector field.
FTC Line Integrals.
Fundamental Theorem of line integrals.
Crazy hard or hardly crazy ?.
Don't use FTC.
Path Independence.
Green's Theorem.
Green's Theorem.
Quick Area of Ellipse.
Area of a polygon.
Winding number.
Parametric surfaces.
Tangent plane to a surface.
Surface area of a sphere.
Surface Area of a donut.
What is a Surface Integral?.
Surface integral of a function.
Surface integral of a vector field.
Surface integral over a curve.
Stokes Theorem.
Stokes Theorem.
Stokes Theorem.
Integral over a barrel.
The Divergence Theorem.
Divergence Theorem.
Derivative of volume is surface area.
The hardest question on the hardest calc 3 test.
Volume of a polyhedron.
Vector Calculus Overview.