Multivariable Calculus

You already know calculus. Now you’ll learn it in 3D – with applications to physics.

Teacher: Joshua McGrath

How can we write an equation for the tangent plane to an igloo? The volume of a parabolic or elliptical satellite dish? How can we use 3D calculus to describe gravitational, electric and magnetic fields?

This course will be a fundamental introduction to multivariable calculus including physical applications (primarily electromagnetism and Newtonian mechanics). We will begin with a quick review of key topics of single variable calculus and vector algebra including dot and cross products. Primary topics of the course will be: continuity, partial derivatives, Lagrange multipliers, multiple integrals, line integrals, divergence, gradient, curl, Green's theorem, Stokes' theorem, surface integrals, and the divergence theorem. We will rely primarily on electrostatics to help us gain an intuitive understanding of what these theorems of vector calculus mean beyond their formal definitions.

For the application...

Prerequisites

Familiarity with both differential and integral calculus of a single variable. It is expected that you feel comfortable with performing generic differentiation and integration in a single variable as well as what it means to integrate or differentiate.

Relevant experience

Any courses, activities, or independent exploration in higher-level mathematics (calculus and beyond)

Application Question (Core-specific free response)

Describe a problem in mathematics that you enjoyed solving. Why did you enjoy it? Did it help you understand a particular concept? See a topic in a new and different way? Something else? There are no wrong answers, but thoughtful and thorough explanation is appreciated.