This course on Multivariable Calculus with a focus on Surface Integrals aims to teach students the concepts and applications of parameterized surfaces, surface area calculations, orientation of parametric surfaces, surface integrals over vector fields, Stoke's Theorem, and the Divergence Theorem. By the end of the course, students will be able to calculate surface integrals, apply Stoke's Theorem and the Divergence Theorem, and solve related mathematical problems. The course utilizes examples and practice problems to help students understand and apply the theoretical concepts effectively. This course is intended for learners interested in advanced calculus topics and applications in fields such as mathematics, physics, engineering, and related disciplines.
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
