Differential equations

problem
Bird-brained

Age

16 to 18

Challenge level

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
problem
What's my equation?

Age

16 to 18

Challenge level

Can you find the differential equations giving rise to these famous solutions?
problem
A different differential equation

Age

16 to 18

Challenge level

Explore the properties of this different sort of differential equation.
problem
The real hydrogen atom

Age

16 to 18

Challenge level

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms
problem
Predator - prey systems

Age

16 to 18

Challenge level

See how differential equations might be used to make a realistic model of a system containing predators and their prey.
problem
The not-so-simple pendulum 2

Age

16 to 18

Challenge level

Things are roughened up and friction is now added to the approximate simple pendulum
problem
Bessel's equation

Age

16 to 18

Challenge level

Get further into power series using the fascinating Bessel's equation.
problem
The not-so-simple pendulum 1

Age

16 to 18

Challenge level

See how the motion of the simple pendulum is not-so-simple after all.
problem
Reaction rates

Age

16 to 18

Challenge level

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
problem
Earth orbit

Age

16 to 18

Challenge level

Follow in the steps of Newton and find the path that the earth follows around the sun.