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So we have just learned about derivatives, so of course, the next step will be integrals.

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And you probably know that an integral basically serves to calculating the area under a curve, at least

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in one dimension.

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This is the case.

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And to do this, there exist different integration methods.

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So just like for the derivatives, we can apply different methods to achieve higher accuracy.

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So I think you already have a good feeling about this from the previous section about derivatives.

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So after we are done with this numerical part or with the theoretical part, the background, we will

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then turn to physical examples.

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So we will calculate the rotational energy and the moment of inertia of different objects.

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So we will explore, for example, why a stick rotates at a different and velocity compared to a sphere,

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even though both of them have the same energy.

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But then we will discuss a different physical problem, and here we will even combine the concept of

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derivatives and integrals.

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So we will calculate the magnetic field of a charged wire.

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So you probably know this example from school already, but actually, to calculate it, you really

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need these concepts that are quite advanced.

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So it's not at all easy to calculate this magnetic field.

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And after we are done with this, I will just introduce to you another concept that is based on integration,

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and this is called the full year transport.

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So whenever you have a periodic signal, for example sound, then you can calculate the full you transform

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to determine the characteristic frequencies of this sound or of this periodic signal.

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And this will be a concept that is based on integrals, and we will apply it later on in the course

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to a very difficult example where we will then calculate really the eigen frequencies of several coupled

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harmonic oscillators.