Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.

# Calculus One

Instructor: Thomas Evans

**490,092** already enrolled

## Course

## Skills you'll gain

- Category: Derivative
- Category: Calculus
- Category: Antiderivative
- Category: Integral

## Details to know

64 quizzes, 15 assessments

## Course

## There are 16 modules in this course

Welcome to Calculus! Join me on this journey through one of the great triumphs of human thought.

#### What's included

2 videos2 readings

Functions are the main star of our journey. Calculus isn't numbers: it's relationships between things, and how one thing changing affects something else.

#### What's included

13 videos5 quizzes

People have thought about infinity for thousands of years; limits provide one way to make such ponderings precise. Continuity makes precise the idea that small changes in the input don't affect the output much.

#### What's included

15 videos4 quizzes

It is time to change topics, or rather, to study change itself! When we wiggle the input, the output value changes, and that ratio of output change to input change is the derivative.

#### What's included

13 videos4 quizzes

With the product rule and the quotient rule, we can differentiate products and quotients. And since the derivative is a function, we can differentiate the derivative to get the second derivative.

#### What's included

14 videos5 quizzes

The chain rule lets us differentiate the composition of two functions. The chain rule can be used to compute the derivative of inverse functions, too.

#### What's included

13 videos5 quizzes

So far, we can differentiate polynomials, exponential functions, and logarithms. Let's learn how to differentiate trigonometric functions.

#### What's included

14 videos5 quizzes

Derivatives can be used to calculate limits via l'Hôpital's rule. Given a real-world equation involving two changing quantities, differentiating yields "related rates."

#### What's included

11 videos3 quizzes

In the real world, we must makes choices, and wouldn't it be great if we could make the best choice? Such optimization is made possible with calculus.

#### What's included

12 videos4 quizzes

Replacing the curved graph by a straight line approximation helps us to estimate values and roots.

#### What's included

13 videos5 quizzes

Antidifferentiation is the process of untaking derivatives, of finding a function whose derivatives is a given function. Since it involves working backwards, antidifferentiation feels like "unbreaking a vase" and can be just as challenging.

#### What's included

14 videos4 quizzes

By cutting up a curved region into thin rectangles and taking a limit of the sum of the areas of those rectangles, we compute (define!) the area of a curved region.

#### What's included

14 videos6 quizzes

Armed with the Fundamental Theorem of Calculus, evaluating a definite integral amounts to finding an antiderivative.

#### What's included

13 videos4 quizzes

Substitution systematizes the process of using the chain rule in reverse. Considering how often we used the chain rule when differentiating, we will often want to use it in reverse to antidifferentiate.

#### What's included

12 videos3 quizzes

Integration by parts is the product rule in reverse. Integrals of powers of trigonometric functions can be evaluated.

#### What's included

10 videos4 quizzes

We have already used integrals to compute area; integration can also be used to compute volumes.

#### What's included

10 videos3 quizzes

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