Natalie, welcome you in this course, and I'm very thankful for your participants.
Let us first discuss about the structure.
In the beginning, we will learn how to use Python and Jupyter notebooks.
We will discover how you can install the Python programming language and how you can set up your first
Jupyter notebook.
And then I have added a two hour crash course where we will discuss concepts like Nampai functions,
arrays and the visualization.
So this is especially for the students that are new to Python or that don't have so much experience
with it.
If you are unsure if you should watch these videos, then I have prepared some quizzes, coding exercises
and solutions so you could just jump right into these quizzes and challenges and see if you manage or
not.
And then with the third section, the actual course starts.
We will begin by discussing series expansion and interpolation, and this also contains topics such
as Blind's solving linear equations systems and also filling data.
Then we will turn to two very important concepts derivatives and integrals, and in both cases, we
will first discuss different methods with different accuracy.
So there exist different methods to calculate numerically a derivative or also an integral.
And then we will really turn to actual physical examples, such as calculating the velocity and the
acceleration from a data file.
And then we will calculate the rotational motion or rotational energy and the corresponding moment of
inertia, and we will also calculate the magnetic field of a wire.
For this, we even need the derivative concepts in multiple dimensions, such as gradients, divergences
and kernels.
And then for the integrals.
As the last lecture, we will discuss future transforms that we will need later on.
So then come Sections six and seven, which are actually the longest and most important sections of
this course.
Here we will discover all the properties of differential equations.
We will begin very mathematical and we will really program an Euler method and a quarter for five method
ourselves.
And of course, we will also discover the methods are provided by Nampai and by Python in general to
solve problems such as the radioactive decay, the fall and pendulum motion.
So these are all pretty basic and in one dimension.
But then we will make things more difficult and go to multiple dimensions, and we will simulate a rolling
ball.
We will simulate a chaotic Lorence system and we will discover the butterfly effect.
We will solve the heat equation where we will investigate how temperature propagates over time in the
sample, and we will then solve the famous three body problem at the example of Sun, Earth and Moon.
And we will actually even add a fourth body, which will be a rocket ship with which we fly to the Moon.
Then in section eight, we will solve and discuss an eigenvalue problem.
The coupled motion of harmonic oscillators.
So for example, you have several pendulums and you a couple of them, and this gives rise to a very
complicated type of motion, which is hard to understand.
However, we actually have three tools at our hands from the previous lectures, so these are calculating
the eigenvalues of a matrix using a fit of procedure and calculating to fully transform it.
In all cases, we will get very similar solutions, and we will really be able to understand the complicated
behavior.
And then the last real section of this course is about Monte-Carlo methods.
This is where we exploit randomness to get extra results.
And first, we will test this at a mathematical example.
We will calculate the numerical value of PI, and then we will actually simulate the collective magnetism
of many small individual magnets that form a ferromagnetic and also an antifa magnet.
So that's the main part of the course.
And then I have two additional add on sections, which are for the advanced students that want to see
what is even beyond these previous topics that I have just explained.
So this is about quantum physics, where I have actually a whole course here on Udemy.
So this is just a teaser on how to solve the Schrodinger equation, which is the differential equation
that describes the quantum behavior of electrons, for example.
And then section 11 is really state of the art research here, we will discuss the electronic properties
of graphene and for this topic, the Nobel Prize was awarded quite recently.
So you see, it's really a difficult topic and state of the art research, but with our tools that we
have employed so far, we can really tackle these problems and understand what is going on.
So I hope you are excited.
And let's jump right into the topic.
And in the next lecture, I will explain to you how you can install Python and Jupyter Notebook to get
started.