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# Calculus Fundamentals

## Understand the mathematics of continuous change.

Calculus is the mathematical study of things that change: cars accelerating, planets moving around the sun, economies fluctuating. To study these changing quantities, a new set of tools - calculus - was developed in the 17th century, forever altering the course of math and science.

This course sets you on the path to calculus fluency. The first part provides a firm intuitive understanding of limits, the central idea underlying the entire subject. The second part applies limits to define derivatives, an indispensable tool for measuring change. By the end of the course you'll have practical calculus experience that any aspiring scientist, engineer, or mathematician needs.

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1. 1

### Introduction

Learn about the basics of limits!

1. #### Indeterminate Forms

Examine the speed of motion from the perspective of calculus.

2. #### Limits Intuition

Take your first step towards mastering limits.

3. #### Limits of Functions

Learn the essentials of computing limits.

2. 2

### Computing Limits

Master the infinitesimal.

1. Included with

#### Infinite Limits

Discover how limits tame the infinite.

2. Included with

#### Continuity

When does a function's graph come in pieces?

3. Included with

#### Computing Limits I

Take limits of algebraic expressions.

4. Included with

#### Computing Limits II

Learn limit techniques to conquer derivatives.

3. 3

### Derivatives

Making quantitative sense of the moment when everything's changing.

1. Included with

#### The Derivative at a Point

Learn what derivatives can do for you.

2. Included with

#### First Examples of Derivatives

Gain hands-on experience with a few basic derivatives.

3. Included with

#### What Derivatives Tell Us

What's the point of taking a derivative, anyway?

4. Included with

#### The Second Derivative

Try taking a derivative's derivative, and explore what it can do for you.

4. 4

### Computing Derivatives

The practitioner's toolkit: the product rule, chain rule, and more.

1. Included with

#### Polynomials

Apply your calculus skills to find shortcuts for polynomial derivatives.

2. Included with

#### Products, Reciprocals, and Quotients

Find the derivatives of compound functions that are made by multiplying and dividing simpler pieces.

3. Included with

#### Trigonometric Functions

Step away from algebraic expressions and into the world of trigonometric derivatives.

4. Included with

#### The Chain Rule

Break a complicated derivative problem into a chain of simpler ones.

5. 5

### Linear Approximation and Applications

Linear approximation, implicit differentiation, L'Hôpital's Rule, and some physics!

1. Included with

#### Linear Approximation

Apply tangent lines to the classic root-finding problem.

2. Included with

#### Pendulums: An Application

Use rates of change to model the swing of a pendulum.

3. Included with