January 29

My Day

Dear Diary! Today was not that eventful either. Over the whole day, I spent most of my time studying or watching YouTube. It was kind of weird. Technically, I did not spend that much time studying, but I feel like, I learned a lot today. I was revisiting my ODE’s lectures, and thought about them for some time. And I gotta say, it all makes sense.

Talking way too much about Math

My first big realization was: I asked myself, how I would plan such a script, and then I compared it, to how the professor did it. And it pretty much overlaps. Look: First you get “elementary methods to solve ODE’s” in order to get a feeling for ODE’s. Then we proved, that they exist, they are unique (under certain conditions) and that the solution depends continuously. That means, if for example, your measurement is a little off, your solution is also only a little off.

Then, once that is done, we go from 1 dimension to multiple. Which also makes sense. Most of the theorems in the 1 dimensional section, are quite similar to the n-dimensional section. Then we look at how to solve these n-dimensional ODE’s.

And for the last section, we look at ODE’s with weird conditions. That would be, “boundary problems”. The difference here is, that in a usual ODE, you have a initial value for each derivative, but for the boundary problems, you have multiple for the same derivative. For example:
– Normal problem: y is the function of your place, then y’ is your speed, y” your acceleration. And then you are given: “You start at 10, move with 5 speed, and accelerate with +2 speed per time”. This is uniquely solvable (for your position i.e. y).
– boundary value problem: same function as above, but “you start with a speed of 2, and after 10 seconds you have a speed of 2.” This is not (necessarily) uniquely solvable.

Back to my Day

Anyway. Most of the afternoon, I studied, solved some exercises, or watched some YouTube. Then, after dinner, I had to go coach my volleyball team. Today was not the best training.

This was kinda understandable, since (1) our next match, is against a really weak opponent, (2) we were only like 8 players and (3) I had a special training, with my middles, and the others had to look for themself.

After the practice, I got home at about 12pm, watched some YouTube, and now I’m writing you. Otherwise, nothing important happened.

Since it’s already way too late, I head to bed now. See you tomorrow and good night! Bye-Bye!