Explore vector calculus concepts in this comprehensive tutorial covering Stewart Calculus Chapter 16. Delve into line integrals of scalar functions, vector fields, and the Fundamental Theorem for Line Integrals. Learn to apply Green's Theorem, evaluate scalar surface integrals, and calculate flux through various surfaces. Master techniques for solving problems involving helicoids, cones, and complex vector fields. Gain proficiency in using Stokes' Theorem and the Divergence Theorem to evaluate surface integrals and flux. Perfect for students seeking a deep understanding of vector calculus and its applications.
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
