This course on Vector Calculus aims to teach students how to evaluate line integrals of scalar functions, line integrals of vector fields, fundamental theorems for line integrals, Green's theorem, scalar surface integrals, and applications of Stokes' theorem and the Divergence theorem. Students will learn to apply these concepts to solve problems involving vector fields, surfaces, and curves. The course uses a combination of theoretical explanations, examples, and problem-solving exercises. It is intended for learners interested in advanced calculus topics and applications in physics, engineering, and related fields.
Overview
Syllabus
Line Integrals of Scalar Functions: Evaluate Line Integrals : Contour Integrals.
Line Integral of a Vector Field :: F(x,y,z) = sin(x) i + cos(y) j + xz k.
Fundamental Theorem for Line Integrals :: Conservative Vector Field Line Integral.
Green's Theorem Examples.
Scalar Surface Integral ∫∫ x^2yz dS where S is part of the plane z=1+2x+3y.
Scalar Surface Integral ∫∫xy dS, S is the triangular region (1,0,0), (0,2,0), (0,0,2).
Evaluate the Surface Integral over the Helicoid r(u,v) = ucos v i + usin v j + v k.
Find the Flux of the Vector Field F = x i + y j + z^4 k Through the Cone with Downward Orientation.
Use Stokes' Theorem to Evaluate the Surface Integral.
Divergence Theorem:: Find the flux of F = ( cos(z) + xy^2, xexp(-z), sin(y)+x^2z ).
Taught by
Jonathan Walters
