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.

Interactive
quizzes

27

Concepts and
exercises

310+
  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.

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      Infinite Limits

      Discover how limits tame the infinite.

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      Continuity

      When does a function's graph come in pieces?

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      Computing Limits I

      Take limits of algebraic expressions.

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      Computing Limits II

      Learn limit techniques to conquer derivatives.

  3. 3

    Derivatives

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

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      The Derivative at a Point

      Learn what derivatives can do for you.

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      First Examples of Derivatives

      Gain hands-on experience with a few basic derivatives.

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      What Derivatives Tell Us

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

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      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.

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      Polynomials

      Apply your calculus skills to find shortcuts for polynomial derivatives.

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      Products, Reciprocals, and Quotients

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

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      Trigonometric Functions

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

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      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!

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      Linear Approximation

      Apply tangent lines to the classic root-finding problem.

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      Pendulums: An Application

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

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      Optimization

      Find extreme values with derivatives, one of the most important uses of calculus.

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      Implicit Differentiation

      Compute rates of change of related quantities.