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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.

Interactive
quizzes

19

Concepts and
exercises

210+
  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

    Limits

    Limits: the very heart of calculus.

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      What is a Limit?

      Gain limit intuition with a no-frills example.

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      How are Limits found?

      Compute limits with continuity.

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      How are Limits defined?

      Learn limit precision with lemmings!

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      When do Limits exist?

      Dive deeper into limits and why they matter.

  3. 3

    Derivatives

    Rates of change, tangent lines, and applications.

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      What is a Derivative?

      Discover a crucial calculus idea with a microscope.

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      How are Derivatives found?

      Practice fundamental skills for computing derivatives.

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      What are Derivatives for?

      Explore the many uses for derivatives.

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      Application: Optimization

      Use derivatives to solve a challenging real-world problem.

  4. 4

    Integrals

    Discover why reversing a derivative is important, too.

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      Antiderivatives

      Build skills for “undoing” differentiation.

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      What is an Integral?

      Explore integrals with an ancient geometry problem.

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      How are Integrals found?

      Unlock integrals with the most important theorem in calculus.

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      Application: Gabriel's Horn

      Explore a paradoxical shape with calculus!

  5. 5

    Infinite Sums

    Unending sums and their place in the real world.

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      Sequences

      Step into calculus with geometry and science problems.

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      What is an Infinite Sum?

      Understand the meaning of infinite sums with thought experiments.

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      The Tower of Lire

      What do divergent sums have to do with real life?

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      What are Infinite Sums for?

      Solve a fundamental physics problem with series!

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