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
Calculus One
Instructor: Thomas Evans
490,092 already enrolled
Course
Gain insight into a topic and learn the fundamentals
58 hours (approximately)
Flexible schedule
Learn at your own pace
Skills you'll gain
- Category: Derivative
- Category: Calculus
- Category: Antiderivative
- Category: Integral
Details to know
Quizzes and assessments
64 quizzes, 15 assessments
English
Subtitles: French, Portuguese (European),
Course
Gain insight into a topic and learn the fundamentals
58 hours (approximately)
Flexible schedule
Learn at your own pace
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
Instructor
Instructor ratings
4.8 (41 ratings)Offered by
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