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So welcome back to the final lecture, of course, and to be honest, I can already congratulate you



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because you made it through the most difficult parts of this course and does last lecture very short



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and also very easy.



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So what we have discussed so far is we have started with considering electrode and electromagnetic waves



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in a vacuum.



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So there's more light than we have discussed.



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A special case of Electrostatic and Magneto's static's, which considered time independent fields.



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And then in the last section, I told you that we discussed the most general case, which meant we did



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not consider a vacuum and we did consider time dependent fields.



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However, we still considered kind of a vacuum.



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So what we did is we took a vacuum and then we positioned some charges and some currents inside of this



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vacuum.



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And of course, what you can do is you can you can build every piece of metal, for example, a metal.



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You can take every single electron in this metal and calculate that in the -- potentials and come



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up with the solutions, however, and that it consists of out of so many atoms and especially electrons,



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it's just impossible to do so in this section.



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I will show you a trick how you can consider the Maxwell's equations in matter.



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So here we will not actively consider the electrons in the metal, for example, but we will separate



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them from the actual electrons or charges and currents that we want to consider.



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So we take the matter, the metal, for example, like a background and separate its influence from



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the actual charges and currents that we want to consider.



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And by using this trick, we also introduced the electric polarization and the magnetization and then



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we finally come up with Maxwell's equations in matter.



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And as you will see, they look almost the same as the Maxwell's equations in vacuum.



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So you can really take most of the results that we had previously and just carry them over to matter.