A space for curiosity

Explore mathematics.

Try an idea. See what changes. Discover why.

Start with the basics
Open the editor
f(x) = x² x = 1.00 y = 1.00

Explore the curve, point by point

Use the arrow keys to move the point. Home and End move to the ends of the curve.

z = sin(x) cos(y)3D

A new dimension to explore

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Course outline

Explore the calculus syllabus. Start with the available experiment. More lessons and exercises will follow.

01Before calculus
  1. Read a point on a graph Available
  2. Meet the function families Available

    Before continuity and limits, learn to recognize the seven function families in the syllabus, identify allowed inputs, and evaluate simple examples.

02Limits and continuity
  1. Continuity and discontinuities Available

    Explore what happens near x = 0. Compare the value at the point with the values approached from the left and right.

  2. Limits of functions of one variable Available
  3. Asymptotes Available

03Derivatives
  1. Growth rates and difference quotients Available
  2. From secant to tangent Available
  3. Comparing functions Available

    Overlay curves and compare their values at the same point. Explore how their separation and the slope of f(x) change.

  4. Derivatives of elementary functions Available

    Linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.

  5. Sum, product, and quotient rules Available
  6. Composition and the chain rule Available
  7. Derivatives of inverse functions Available

04Studying functions
  1. Increasing, decreasing, maxima, and minima Available
  2. Concavity, convexity, and inflection points Available

05Integrals
  1. Area under a curve Available
  2. The definite integral: geometric and physical meaning Available
  3. Antiderivatives and the indefinite integral Available

    Properties and the constant of integration.

  4. Elementary integration methods Available
  5. Integration by parts Available
  6. The fundamental theorem of calculus Available

06Applications of integration
  1. Areas and volumes using antiderivatives Available
  2. First and second moments Available

07Practice and review
  1. Mixed practice Available

    Choose an approach, solve mixed problems, and find the topics to revisit.

Concept map

Explore mathematics

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Tab to a topic and press Enter. On the map background, use arrow keys to pan, plus or minus to zoom, and zero to reset.

Calculus
Before calculus
Limits and continuity
Derivatives
Studying functions
Integrals
Applications of integration
Practice and review

Follow a connection. Discover how the ideas fit together.