Differential Equations & Transforms
Where things that change over time settle, bounce, or swing, and how the Laplace transform turns them into algebra
5 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Linear EquationsPC cooling: passive, air, or water?
Heat flows through the cooler like current through a resistor: temperature rise = watts × °C/W. Water adds mass, so it heats up slower.
Differential Equations & TransformsWhen will my coffee wear off?
Each cup rises, then fades by half every few hours. Cups stack, and the Laplace transform says why they simply add.
Exponents & LogarithmsRapid cooling: 135 °F to 70 °F in two hours
Cooling slows as food nears the fridge temperature. A logarithm says how long it takes, and why shallow pans win.
Differential Equations & TransformsDoor closer: slam, bounce, or glide
One damping knob turns a slam into a glide. Where two dots (the poles) sit tells you which.
Differential Equations & TransformsWhy the shower goes hot, then cold
You react to water that left the tap seconds ago. Delay plus impatience makes the swing, and one number predicts it.