Advanced Math · Level 5
5.1 Vector Calculus
Extend multivariable calculus to vector fields, then apply your new skills by exploring Maxwell's equations.
Vector Calculus in a Nutshell
Calculus of Motion
Space Curves
Integrals and Arc Length
Frenet Formulae
Parametric Surfaces
Vector Fields
Jack and the Beanstalk
Electrostatic Bootcamp
Introducing Surface Integrals
Flux (Part I)
Flux (Part II)
Surface Integrals
Divergence (Part I)
Divergence (Part II)
The Divergence Theorem
The Divergence Theorem and Fluids
Flows & Divergence
Work (Part I)
Work (Part II)
Line Integrals
Path Independence
Curl
Stokes' Theorem
Swirls and Curls
Differential Forms (Optional)
The Laplacian
Gaussian Integrals (Part I)
Gaussian Integrals (Part II)
Fourier Transform
The Diffusion Equation
The Wave Equation
Maxwell's Equations (Part I)
Maxwell's Equations (Part II)
More Electrostatics!
Course description
Change is deeply rooted in the natural world. Fluids, electromagnetic fields, the orbits of planets, the motion of molecules; all are described by vectors and all have characteristics depending on where we look and when. In this course, you'll learn how to quantify such change with calculus on vector fields. Go beyond the math to explore the underlying ideas scientists and engineers use every day.
Topics covered
- Curl
- Differential Forms
- Divergence Theorem
- Flux
- Fourier Transform
- Line Integrals
- Maxwell's Equations
- Parametric Surfaces
- Space Curves
- Stokes' Theorem
- Surface Integrals
- Vector Fields
Prerequisites and next steps
You’ll need a solid understanding of algebra, as well as the basics of functions, limits, derivatives, and integrals.