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So welcome back, and now let's get started with our first real numerical lecture of this course.

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So this whole section is about the concept of fitting a function to data, and we will start out this

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section by implementing the concept of a serious expansion, which means that you can basically approximate

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any function by your so-called Taylor series.

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So if you haven't heard about this, that's no problem.

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I will teach you what it is and how we can implement this.

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And in the second part of the section, we will deal with interpolation, which means that when you

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have multiple data points, you can calculate more data points in between and we can do this mathematically

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by using linear cubic spleens.

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And this will really fit your data perfectly.

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However, the problem is it will basically just connect the dots, and this is not really what is good

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in terms of a physical background.

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So then the third part of the section is about really fitting a physically relevant model function to

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our data.

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So we will define an error which we will then minimize.

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And so we will get the ideal model function with the ideal parameters to describe our data.

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And of course, this concept is extremely relevant even in the scientific background, and I will show

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you that we can use this concept for a very difficult problem later on in the course.

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So in one of the very late sections of the course, we will consider coupled harmonic oscillators,

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and we will then fit a function to this data to better understand it.