So now it is time to learn about one of the most important concepts of theoretical and numerical physics.
These are differential equations.
So here we have to combine the concept of integration and of differentiation, so we have to really
apply what we have learned before.
So once again, like for discussions about the derivatives and the integrals, we will first discuss
the background and the numerical pot.
We will learn about different methods and we will actually implement these methods ourselves, as well
as loading them from the Non-PO module.
So these methods have different accuracy as before, but this time since solving differential equations
takes quite a lot of time.
We also have to care about the speed of the calculation.
So, of course, the higher the accuracy, the slower the calculation will be.
So we will always have to find a sweet spot and we have to consider the tradeoff between accuracy and
speed.
And we will discuss this a bit and learn about the different methods.
And of course, we will also discuss examples here.
So we will apply the methods to radioactive decay, to the free fall and to the pendulum.
So all of these are described by differential equations, and we can solve them numerically using our
methods.
So this is here only the first part about differential equations.
So we will consider here only a single dimension.
And quite simple examples.
So this is here really about learning the basics and understanding what is going on.
And then in the next section, we will go to more difficult examples.
And then we will actually solve differential equations with several particles at the same time and also
in multiple dimensions.