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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