About this site
This site is part of a public library of interactive explanations. It is free, has no ads and needs no sign-up. It explains calculus through its two central ideas, slope and accumulation, with figures you drag instead of formulas to memorize.
How the mathematics is checked§
Every figure is driven by a small numerical engine. Its derivatives apply the exact differentiation rules to the formula and check the result by Ridders’ extrapolation of symmetric difference quotients (which alone serves where the rules do not apply); its integrals use adaptive Simpson quadrature with a Richardson correction; its limits extrapolate one-sided samples. The engine is tested twice: by its author against worked examples and exact derivatives and integrals, and by an independent test suite written from the published methods and reference values, without reading the engine’s code. Every factual claim, from the error bound of the midpoint rule to the date of Leibniz’s first paper, is recorded in a claims register with its source and checked by a reviewer who did not write it. What each figure simplifies is stated next to the figure and collected on the sources page.
Numbers, not formulas§
The calculators on this site are numerical: they return the derivative of x² sin x at x = 1 as 2.2232442755…, not as the formula 2x sin x + x² cos x. That is a deliberate choice. Numerical methods work for functions that have no formula, and they can be explained in a paragraph and checked by anyone. Each calculator reports an error estimate and says when it cannot give an answer, for example at a corner, a jump or a point where the function is undefined.
Design§
The yellow is borrowed from the covers of serious mathematics books; the text and equations are set in STIX Two, a typeface designed for scientific publishing, with labels in Public Sans. Colours in the figures have fixed meanings across every chapter: blue for the function, vermilion for slopes and derivatives, green for areas and accumulation, magenta for secants and approximations.
Found an error?§
Please open an issue on the source repository. Corrections are welcome and are credited.
Reuse§
Text and figures are licensed CC BY 4.0; code is MIT. Teachers may use and adapt any of it, with attribution.