What is VECTOR CALCULUS?? **Full Course Introduction**

Curves, Parameterizations, and the Arclength Parameterization

What is a LINE INTEGRAL? // Big Idea, Derivation & Formula

Line Integrals: Full Example

Line Integrals in 3D // Formula & Three Applications

Intro to VECTOR FIELDS // Sketching by hand & with computers

The Gradient Vector Field

Line Integrals of Vector Fields // Big Idea, Definition & Formula

Example: Computing the Line Integral of a Vector Field (i.e. Work Done)

Line Integrals with respect to x or y // Vector Calculus

Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus

Flux Integrals // Big Idea, Formula & Examples // Vector Calculus

Conservative Vector Fields // Vector Calculus

The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus

How to Test if a Vector Field is Conservative // Vector Calculus

Finding the scalar potential function for a conservative vector field // Vector Calculus

Curl or Circulation Density of a Vector Field // Vector Calculus

Curl, Circulation, and Green's Theorem // Vector Calculus

Divergence, Flux, and Green's Theorem // Vector Calculus

Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus

Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus

The Surface Area formula for Parametric Surfaces // Vector Calculus

Why is the surface area of a Sphere 4pi times radius squared???

Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus

Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus

Surface Area for Implicit & Explicit Surfaces // Vector Calculus

Computing the Surface Area of an Implicitly Defined Surface

Surface Integrals // Formulas & Applications // Vector Calculus

Orientable vs Non-Orientable Surfaces and the Mobius Strip

Flux of a Vector Field Across a Surface // Vector Calculus

Computing the Flux Across a Surface // Vector Calculus

The CURL of a 3D vector field // Vector Calculus

Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus

Stokes' Theorem Example // Verifying both Sides // Vector Calculus

The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus

Divergence Theorem example: Flux across unit cube // Vector Calculus

Divergence Theorem for regions bounded by two surfaces // Vector Calculus

Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus

A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)