Advanced Math · Level 1

1.1 Calculus in a Nutshell

Investigate the central ideas of calculus and learn how to put them to use.

Rate of Change

Rate of Change: Practice Questions

Rate of Change: Challenge Questions

Instantaneous Rate of Change

Instantaneous Rate of Change: Practice Questions

Instantaneous Rate of Change: Challenge Questions

The Derivative

The Derivative: Practice Questions

The Derivative: Challenge Questions

Applying the Derivative: Optimization

Optimization: Practice Questions

Optimization: Challenge Questions

What is a Derivative?

What are Derivatives for?

How are Derivatives found?

Application: Optimization

What is an Integral?

How are Integrals found?

Application: Gabriel's Horn


What is an Infinite Sum?

The Tower of Lire

What are Infinite Sums for?

Sine & Cosine

Euler's formula

Taylor Series



Course description

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. Calculus in a Nutshell is a short course with only 19 quizzes. If you want to quickly learn an overview of calculus or review the foundational principles after a long hiatus from the subject, this course ought to be perfect. Calculus Fundamentals and Integral Calculus are the two courses that can follow next in the Calculus sequence. If/when you want to go into more depth and learn a wide spread of specific techniques in differential calculus and integral calculus respectively, that's where you should look. For example, integration techniques like "integration by parts" are only in the Integral Calculus course.

Topics covered

  • Antiderivatives
  • Derivatives
  • Derivative rules
  • The Fundamental Theorem
  • Geometric applications
  • Geometric series
  • Infinite sums
  • Integrals
  • Limits
  • Riemann sums
  • Science applications
  • Tangent lines

Prerequisites and next steps

You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts.


  • Trigonometry
  • Pre-Calculus

Up next

Advanced Math · Level 2

2.1 Calculus Fundamentals

Begin your calculus journey by getting up to speed on limits and derivatives.

Jump ahead