An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

Match the descriptions of physical processes to these differential equations.

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

Things are roughened up and friction is now added to the approximate simple pendulum

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

Solve these differential equations to see how a minus sign can change the answer

Get further into power series using the fascinating Bessel's equation.

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

Look at the advanced way of viewing sin and cos through their power series.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

Can you find the differential equations giving rise to these famous solutions?

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

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.