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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.

19

210+
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

### Limits

Limits: the very heart of calculus.

1. Included with

#### What is a Limit?

Gain limit intuition with a no-frills example.

2. Included with

#### How are Limits found?

Compute limits with continuity.

3. Included with

#### How are Limits defined?

Learn limit precision with lemmings!

4. Included with

#### When do Limits exist?

Dive deeper into limits and why they matter.

3. 3

### 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

#### How are Derivatives found?

Practice fundamental skills for computing derivatives.

3. Included with

#### What are Derivatives for?

Explore the many uses for derivatives.

4. Included with

#### Application: Optimization

Use derivatives to solve a challenging real-world problem.

4. 4

### Integrals

Discover why reversing a derivative is important, too.

1. Included with

#### Antiderivatives

Build skills for “undoing” differentiation.

2. Included with

#### What is an Integral?

Explore integrals with an ancient geometry problem.

3. Included with

#### How are Integrals found?

Unlock integrals with the most important theorem in calculus.

4. Included with

#### Application: Gabriel's Horn

Explore a paradoxical shape with calculus!

5. 5

### Infinite Sums

Unending sums and their place in the real world.

1. Included with

#### Sequences

Step into calculus with geometry and science problems.

2. Included with

#### What is an Infinite Sum?

Understand the meaning of infinite sums with thought experiments.

3. Included with