The films
Thirty-four short films
All 34 films are in production. Håkan records each until it's right, so they arrive one at a time. Each appears here, and on its function's page, the day it's finished.
Subtitles appear here, in their own band below the picture.
How the subtitles work
Håkan's films are films of mathematics, so nothing may cover the picture. Subtitles are a real text track (searchable, toggleable, accessible), rendered in a dedicated band below the frame, synchronised with the speech.
Press play on the demo to see the mechanism.
What's this?The idea of the table, in a few minutes.
What it's notWhat the table doesn't try to be.
Table toursA guided walk through the families.
Example 1A first worked example.
Example 2A second worked example.
Example 3A third worked example.
Example 4A fourth worked example.
Absolute value & the sign function|x| and sign x, the simplest special functions.
RootsThe non-singular roots, x^(1/2) and friends.
Singular trigonometric functionstan, cot, sec, csc, and their asymptotes.
Negative integer powers1/x, 1/x² and the rest of family 2.
Logarithm primitivesx(ln|x|−1) and the chain of repeated primitives.
More rootsThe singular roots: negative fractional powers.
Trigonometric inversesarcsin to arcsec.
Hyperbolic functionssinh, cosh and the rest of family 7.
The half circle function√(1−x²), a function whose graph is a half circle.
More bounded trigonometric functionssin 2x, cos 3x, sin nx…
Geometric series1/(1−x) and the power series column.
The Gaussian and relatede^(−x²) and Φ(x).
Hyperbolic inversesarsinh, arcosh, artanh, arcoth, as logarithms.
Extra special roots and rationalsThe tail of family 11.
Linear combinationsBuilding new functions from old ones.
Impulse “functions”δ(x) and its derivatives, and why the quotes.
Impulse trainsΣ δ(x−k) and the Dirac comb.
Fourier seriesInfinite linear combinations of sin nx and cos nx.
The Dirichlet kernelsin((n+½)x)/sin(x/2).
Laplace & Fourier transformThe two transform relations, side by side.
What is a function?The definition, in plain words.
PropertiesThe ~30 properties and their glyphs.
RelationsThe 7 relations and their colours.
Relations of propertiesWhich properties imply which.
NumbersN, Z, Q, R, C: the building blocks.
A squareHow to read one square of the table.
New functionsFive ways to build new functions from two old ones.