Vector Calculus in a Nutshell
Explore the possibilities that come from combining calculus and vectors.
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.
Vector fields, surface integrals, div and curl.
Explore the possibilities that come from combining calculus and vectors.
Look at the world in motion through the lens of vector calculus.
Mix vectors with integrals to uncover an essential tool for applications.
See one of the most important theorems in vector calculus at work.
Force fields, motion through space, and much, much more...
Fly along curves through three dimensions.
Exactly how long is a space curve?
Measure the shape of space curves with vector calculus.
Expand your gallery of shapes to include a few exotic cases.
Combine vectors and functions into a powerful tool for applications.
Learn about Newton's root-finding method and help defeat a vile giant.
Take a lightning tour of the physics that made vector calculus famous.
Part I of the essential vector calculus toolbox.
Experiment with charges moving in electric field and discover the concept of flux.
Use flux to uncover surface integrals and see how they're used to solve important problems.
Master integrals of functions on parametrized surfaces.
Construct a crucial vector derivative through a fundamental law of nature.
What is divergence?
Prove a beautiful integral identity that's essential for real-world applications.
Explore more about the divergence through visuals and geometry.
Part II of the essential vector calculus toolbox.
Explore an important physics application of vector calculus.
Unveil a new kind of integral by delving into a familiar physics concept.
Learn how to integrate along space curves and why it's so useful.
Journey to where calculus and topology meet to discover a crucial property of vector fields.
Construct a derivative that measures the swirl of a vector field.
Uncover the deep connection between curl and line integrals.
Dive deeper into curl with visuals and geometry.
Unify vector calculus into a single master formula.
Solve important real-world problems with vector calculus.
Apply a new derivative to problems in electrostatics and fluid dynamics.
Detour into the world of multivariable calculus to compute an integral crucial for applications.
Use linear algebra and a change of variables to find the most general Gaussian integral.
Apply Gaussian integrals to understand the Fourier transform, a powerful way to solve pdes.
Use the Fourier transform to solve a pde and calculate the speed of scent.
Make waves with Fourier series.
Combine divergence, curl, line and surface integrals to uncover Maxwell's electromagnetic equations.
Use vector calculus to solve electromagnetic problems and unify Maxwell's equations with forms.
Squeeze new pde methods from old vector calculus theorems and solve hard electrostatics problems.