This course on Vector Calculus aims to teach students the main concepts and theorems associated with vector calculus, such as line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Students will learn about parametric equations, line integrals, surface integrals, and various applications of these concepts. The teaching method includes theoretical explanations, examples, derivations, and applications to real-world problems. This course is intended for learners interested in advanced mathematics, particularly those studying calculus or related fields.
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
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