So welcome back, and now let's get started with our first real numerical lecture of this course.
So this whole section is about the concept of fitting a function to data, and we will start out this
section by implementing the concept of a serious expansion, which means that you can basically approximate
any function by your so-called Taylor series.
So if you haven't heard about this, that's no problem.
I will teach you what it is and how we can implement this.
And in the second part of the section, we will deal with interpolation, which means that when you
have multiple data points, you can calculate more data points in between and we can do this mathematically
by using linear cubic spleens.
And this will really fit your data perfectly.
However, the problem is it will basically just connect the dots, and this is not really what is good
in terms of a physical background.
So then the third part of the section is about really fitting a physically relevant model function to
our data.
So we will define an error which we will then minimize.
And so we will get the ideal model function with the ideal parameters to describe our data.
And of course, this concept is extremely relevant even in the scientific background, and I will show
you that we can use this concept for a very difficult problem later on in the course.
So in one of the very late sections of the course, we will consider coupled harmonic oscillators,
and we will then fit a function to this data to better understand it.