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# Calculus in a Nutshell

## Focus on the core ideas at the heart of calculus.

Calculus has such a wide scope and depth of application that it's easy to lose sight of the forest for the trees.

This course takes a bird's-eye view, using visual and physical intuition to present the major pillars of calculus: limits, derivatives, integrals, and infinite sums. You'll walk away with a clear sense of what calculus is and what it can do.

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1. 1

### Introduction

Can we introduce all of calculus in less than an hour? Maybe!

1. #### Derivatives in a Nutshell

Take the first steps into the world of calculus.

2. #### Integrals in a Nutshell

Learn about the derivative's partner, the integral.

3. #### Infinite Sums in a Nutshell

How does calculus confront the infinite?

2. 2

### Derivatives

Rates of change, tangent lines, and applications.

1. Included with

#### What is a Derivative?

Discover a crucial calculus idea with a microscope.

2. Included with

#### What are Derivatives for?

Explore the many uses for derivatives.

3. Included with

#### How are Derivatives found?

Practice fundamental skills for computing derivatives.

4. Included with

#### Application: Optimization

Use derivatives to solve a challenging real-world problem.

3. 3

### Integrals

Discover why reversing a derivative is important, too.

1. Included with

#### What is an Integral?

Explore integrals with an ancient geometry problem.

2. Included with

#### How are Integrals found?

Unlock integrals with the most important theorem in calculus.

3. Included with

#### Application: Gabriel's Horn

Explore a paradoxical shape with calculus!

4. 4

### Infinite Sums

Unending sums and their place in the real world.

1. Included with

#### Sequences

Learn to solve geometry and science problems with sequences.

2. Included with

#### What is an Infinite Sum?

Understand the meaning of infinite sums with thought experiments.

3. Included with

#### The Tower of Lire

What do divergent sums have to do with real life?

4. Included with

#### What are Infinite Sums for?

Solve a fundamental physics problem with Taylor series!

5. 5

The farthest reaches of single-variable calculus.

1. Included with

#### Sine & Cosine

Explore the quintessential models of periodic change with calculus.

2. Included with

#### Euler's formula

Recreate one of the most beautiful results in all of math.

3. Included with