# Roller coaster – Differentiation – Mathematics- Pre-university Calculus – TU Delft

Rollercoasters! Do you love them? Do you like to feel the G-forces and scream

out loud? Or are you too scared? If I see those massive constructions of rollercoasters

I can’t help wondering: how do they invent these rides? And how do you make a rollercoaster spectacular

but safe? I love roller coasters too! The design of a rollercoaster demands both

creativity and thorough calculations. These calculations are strongly related to

the topic of this week: Differentiation. To construct a roller coaster you have to

deal with finding a good trade-off between different requirements. For a thrilling ride you want high speed and

acceleration. But for safety reasons you want to limit the

G-forces that people will experience. We call this an optimisation problem. Differentiation plays a very important role

in solving those problems. Another important aspect is that a roller

coaster track is constructed from basic segments. These segments need to be connected in such

a way that the track is smooth and doesn’t have any kinks or bumps. The slope and direction at the connection

point of any pair of segments should coincide. If not,

the ride would be very unpleasant. Mathematically,

this means precisely that the track should be differentiable. This gives another aspect of roller coaster

design where differentiation comes in. So,

two of the most important ingredients for building a great roller coaster ride are slope

and speed. But what is slope and what is speed exactly? Even to define slope and speed,

we need the concept of differentiation! This week you will learn about differentiation

and its many applications. Enjoy the ride!