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# Vector Calculus

## Complete the multivariable calculus saga with vector fields.

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.

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1. 1

### Introduction

Vector fields, surface integrals, div and curl.

1. #### Vector Calculus in a Nutshell

Explore the possibilities that come from combining calculus and vectors.

2. 2

### Vector-valued Functions

Force fields, motion through space, and much, much more...

1. Included with

#### Calculus of Motion

Look at the world in motion through the lens of vector calculus.

2. Included with

#### Space Curves

Fly along curves through three dimensions.

3. Included with

#### Integrals and Arc Length

Exactly how long is a space curve?

4. Included with

#### Frenet Formulae

Measure the shape of space curves with vector calculus.

3. 3

### Surface Integrals and Divergence

Part I of the essential vector calculus toolbox.

1. Included with

#### Introducing Surface Integrals

Mix vectors with integrals to uncover an essential tool for applications.

2. Included with

#### Flux (Part I)

Experiment with charges moving in electric field and discover the concept of flux.

3. Included with

#### Flux (Part II)

Use flux to uncover surface integrals and see how they're used to solve important problems.

4. Included with

#### Surface Integrals

Master integrals of functions on parametrized surfaces.

4. 4

### Line Integrals & Curl

Part II of the essential vector calculus toolbox.

1. Included with

#### Work (Part I)

Explore an important physics application of vector calculus.

2. Included with

#### Work (Part II)

Unveil a new kind of integral by delving into a familiar physics concept.

3. Included with

#### Line Integrals

Learn how to integrate along space curves and why it's so useful.

4. Included with

#### Path Independence

Journey to where calculus and topology meet to discover a crucial property of vector fields.

5. 5

Solve important real-world problems with vector calculus.

1. Included with

#### The Laplacian

Apply a new derivative to problems in electrostatics and fluid dynamics.

2. Included with

#### Gaussian Integrals (Part I)

Detour into the world of multivariable calculus to compute an integral crucial for applications.

3. Included with