Collection
From equation to curve: initial values, linear equations, substitution and the worlds in which they apply.
Apps
An introduction to differential equations: nine running worlds from everyday life, physics, biology, medicine, epidemiology, economics and psychology (coffee, parachute, bacteria, spring, hares and foxes, epidemic, tablets, Solow growth, Romeo and Juliet). Arranged by curve shape, only three shapes remain. In detail: slope arrow = right-hand side of the ODE, draggable initial value, family of solutions, equilibrium.
Differential equationsTry it
Differential equations as a detective story: the culprit is a function, and all we know is something about its derivative. Guessing and checking made visible: the real tangent against the slope the ODE demands. y′ = 5y with eˣ, e⁵ˣ, e⁵ˣ + C and C·e⁵ˣ (family, trajectory), and y′·y = −x: the tangent is perpendicular to the radius, so only circles solve it.
Differential equationsTry it
h″ = −g with a falling ball: integrating twice leaves a family of parabolas with C₁ and C₂. With no condition many balls fall, with only h(0) still a family; only h(0) and h′(0) pick exactly one path. Draggable initial height and velocity (start tangent), boundary value problem with a target after t₁, Earth/Mars/Moon, working with numbers.
Differential equationsTry it
y′ + p(x)·y = q(x) in four steps: the homogeneous family y_h = C·e^(−P(x)) by separation, variation of constants with a runner that wanders across the family (C(x) as a curve in the C plane), the general solution as the family shifted by y_p with the difference of two solutions, and the initial value. Working with numbers; examples y′ + y = x, y′ − 2xy = x, y′ + y/x = x², cooling, RC circuit; game "Build the solution".
Differential equationsTry it
ODEs of the form y′ = f(ax + by + c) in five steps: recognise u = ax + by + c, derive u′ = a + b·f(u), separate and integrate, substitute back, insert the initial value. Two cards x-y and x-u; turning the plane makes the lines u = constant horizontal. Examples y′ = 2x − y (asymptote y = 2x − 2), y′ = (x + y)², y′ = 1/(x − y) + 1, y′ = x + y + 1; games “Find u” and “Where does it go?”.
Differential equationsTry it
ODEs y′ = F(y/x) in the direction field: isoclines are lines through the origin, a dilation maps solutions to solutions (C′ = C − ln λ), and zooming towards the origin leaves the field unchanged. Five-step worked solution with numbers: recognise, u = y/x, separate x·u′ = F(u) − u, substitute back, initial value. Five examples up to the logarithmic spiral, invariant lines F(u) = u, and a “homogeneous?” test with a ray check.
Differential equationsTry it
Explicit Euler step by step: read off the slope at the starting point, follow the tangent for one step size h, new point. The dashed solution curve through each point shows how the method jumps onto neighbouring curves and errors add up. Enter your own right-hand side f(x, y) or pick a preset (slide example, oscillation, growth, decay, logistic); slide the step size, compare with h/2 and h/4, read the error in a log-log plot — order 1, special cases and instability for too large h.
NumericsTry itCollections
Planning and steering projects: the iron triangle, stakeholders, network diagrams, earned value, schedule risk, team size, Kanban and waterfall against Scrum.
8 appsOpen collection
From sequences to loans: arithmetic and geometric growth, savings plans, annuities, compounding within the year and perpetuities.
11 appsOpen collection
Reading the traces: burial mounds in section, radiocarbon dating, settlements in the landscape and the tomb of Tutankhamun.
5 appsOpen collection
Why robot arms are heavy, how six axes guide a hand and how control holds the load.
4 appsOpen collection
Tables, keys, joins, groups and subqueries you can touch: how a database really reads.
7 appsOpen collection
Generative AI in strong images: what it can do, how it writes, why it convinces, how to use it well and where to take care.
7 appsOpen collection
Engine, brakes, high voltage, CAN bus and chassis: technology and diagnostics of the modern vehicle.
9 appsOpen collection
Heat in the city centre: heat islands, shade, trees and unsealing, using the old town of Reutlingen as an example.
5 appsOpen collection
Reading the small print, spotting subscription traps, placing risk figures and making texts understandable.
4 appsOpen collection
Mean, median, mode, box plot and levels of measurement: descriptive statistics to try out.
9 appsOpen collection
From coordinates to the inverse: vectors, dot and cross products, linear equations and matrices in pictures.
12 appsOpen collection
Production principles, waste, one-piece flow, value streams, bills of materials and routing: how a factory is organised.
6 appsOpen collection
What the CRA requires of manufacturers: checking whether it applies, meeting reporting deadlines, keeping software bills of materials.
5 appsOpen collection
Reducing, common denominators, multiplying, dividing and mixed numbers: fractions step by step.
7 appsOpen collection
Proofs of special beauty to touch: Zagier's windmills, the museum guards and Buffon's needle.
3 appsOpen collection
How oscillations break down: coefficients, symmetry, phasor chains, the Gibbs phenomenon and the plucked string.
7 appsOpen collection
What happens inside the machine: objects, methods, operators, slicing and sorting in Python, visible step by step.
9 appsOpen collection
From the Patent Motor Car to the Z3: famous machines and experiments cut open in 3D.
11 appsOpen collection
Keyboard, intervals, scales, chords, the circle of fifths and groove: music theory you hear and play.
9 appsOpen collection
How sound is made and shaped: synthesizers and samplers, envelopes and overtones, waveforms and timbre, voice and orchestra, room acoustics and sound scenography — all audible in your browser.
16 appsOpen collection
Staging space, sight, light, sound and paths: visitor flows, showcase lighting, room acoustics, sound islands, projection mapping and the pavilions of world expos to try out.
15 appsOpen collection
Mathematical questions open for decades, for which an AI model proposed solutions in 2026, as interactive apps: understand the problem, experience the result.
32 appsOpen collection
From neurons and gradients to transformers, RLHF and agents: machine learning you can touch.
44 appsOpen collection
DNA, replication, transcription, translation and cell division as explorable 3D models.
24 appsOpen collection
Perspective, ornament, structure and space: how art and architecture work with mathematics.
21 appsOpen collection
Hyperloop, autonomous vehicles, warehouses and conveyors: logistics as interactive simulation.
17 appsOpen collection
Heart, eye, voice, skeleton and nerves: the human body in 3D, layer by layer.
10 appsOpen collection
Monty Hall, Simpson, Berkson and base rates: where intuition fails us with numbers.
14 appsOpen collection
Planets, stars, black holes and space probes: the cosmos to explore.
10 appsOpen collection
Light switches for nerve cells, a telescope made of ice, mirror-image chemistry and interest rates: the 2026 Nobel Prizes to try out.
8 appsOpen collection
Planted participants, smoke in the room, one dollar for a lie and experimenters who are themselves the subjects: famous social psychology experiments to try yourself.
5 appsOpen collection
Relations, classes, orders, bijections, different infinities and topology: mathematics as the science of structure, hands-on.
11 appsOpen collection
Riemann, P vs NP, Poincaré and other great questions of mathematics, made tangible.
16 appsOpen collection
Counting, arithmetic and shapes: maths for beginners, playful and clear.
6 appsOpen collectionWant to use these apps in your courses? Let’s find out what works for you.
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