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So now it is time to learn about one of the most important concepts of theoretical and numerical physics.

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These are differential equations.

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So here we have to combine the concept of integration and of differentiation, so we have to really

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apply what we have learned before.

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So once again, like for discussions about the derivatives and the integrals, we will first discuss

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the background and the numerical pot.

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We will learn about different methods and we will actually implement these methods ourselves, as well

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as loading them from the Non-PO module.

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So these methods have different accuracy as before, but this time since solving differential equations

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takes quite a lot of time.

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We also have to care about the speed of the calculation.

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So, of course, the higher the accuracy, the slower the calculation will be.

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So we will always have to find a sweet spot and we have to consider the tradeoff between accuracy and

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speed.

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And we will discuss this a bit and learn about the different methods.

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And of course, we will also discuss examples here.

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So we will apply the methods to radioactive decay, to the free fall and to the pendulum.

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So all of these are described by differential equations, and we can solve them numerically using our

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methods.

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So this is here only the first part about differential equations.

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So we will consider here only a single dimension.

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And quite simple examples.

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So this is here really about learning the basics and understanding what is going on.

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And then in the next section, we will go to more difficult examples.

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And then we will actually solve differential equations with several particles at the same time and also

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in multiple dimensions.