Side 02
Calculus
Ten canonical function families examined through the same ten calculus lenses. The aim is to make change, accumulation and local behaviour visible by holding the questions constant while the functions change.
The route through calculus.
Calculus is easier to retain when its ideas are learned as a dependency chain rather than a bag of procedures. Each stage below answers one new question while reusing the previous stage.
The whole Side.
Read down a function to see its calculus profile, or across a lens to see how the same idea behaves under different functions. Every intersection opens into a compact explanation.
Function families.
These are the recurring shapes calculus keeps returning to. Learning their behaviour makes later differentiation, integration and approximation less mechanical.
Calculus lenses.
The same ten questions are asked of every function. Together they form a compact checklist for reading almost any one-variable function.
Compare.
Select two to four function families and any lenses. This is where the Side Studies method becomes most useful: the question stays fixed, so the structural difference is harder to miss.
Functions
Lenses
Local behaviour.
Pick a function and a point. The playground evaluates the function, its first derivative and the tangent line there. It is deliberately small: one point, one local story.