Dive into a comprehensive 9-hour video playlist exploring the fundamental concepts of vector calculus. Learn about parametric equations, line integrals, surface integrals, and the pivotal theorems of Green, Stokes, and Divergence. Master techniques for calculating line integrals of functions and vector fields, understand path independence, and explore surface integrals over curves and surfaces. Tackle challenging problems, including area calculations for ellipses and polygons, surface area computations for spheres and donuts, and volume determinations for polyhedrons. Gain a solid foundation in vector calculus through detailed explanations, derivations, and practical examples, culminating in an overview that ties all concepts together.
Overview
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.
Taught by
Dr Peyam
