Dive deep into the world of surface integrals in this comprehensive 4.5-hour tutorial on Multivariable Calculus. Explore parameterized surfaces, calculate surface areas, and understand surface orientations through practical examples. Master surface integrals over scalar and vector fields, and delve into advanced concepts like Stoke's Theorem and the Divergence Theorem. Learn to verify these theorems with multiple examples and understand their limitations. Enhance your mathematical skills with hands-on practice in solving complex problems involving surface integrals, preparing you for advanced applications in physics and engineering.
Overview
Syllabus
Multivariable Calculus | Parameterized surfaces.
Multivariable Calculus | The area of a parameterized surface..
Multivariable Calculus | Surface area of a parameterized surface, example..
Multivariable Calculus | The orientation of a parametric surface with examples..
Multivariable Calculus | Surface integral example 1..
Multivariable Calculus | Surface integral example 2..
Multivariable Calculus | Surface integrals over vector fields..
Multivariable Calculus | Two surface integrals over vector fields..
Multivariable Calculus | Stoke's Theorem.
Multivariable Calculus | Verifying Stoke's theorem, example 1..
Multivariable Calculus | Stoke's theorem verification example 2..
Multivariable Calculus | The Divergence Theorem.
Multivariable Calculus | Verifying the Divergence Theorem.
Multivariable Calculus | When the divergence theorem doesn't apply..
Multivariable Calculus | Two Stoke's theorem examples..
Multivariable Calculus | Divergence Theorem Example.
Taught by
Michael Penn
