Does anyone know of any books on analysis, linear algebra, differential equations, and probability theory?
I need books for mathematics to then get into the theoretical mechanics of physics. Does anyone know any books about it?
btw I'm 14 so I don't have that much previous knowledge in mathematics if there is a book that doesn't require that much previous knowledge that would be really cool
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Mathematics is heavily interrelated. You should at least be able to calculate reasonably well with variables and parameters and understand them to keep up with these topics. Then it's also not a bad idea if you know what limits are, ie, have some familiarity with infinitely large and small values.
Unfortunately, I can't recommend any books. However, you can find plenty of videos and tutorials online that explain it all very simply.
https://www.nachhilfe-team.net/lernen-leicht-machen/analysis/
Mechanics on this basis is then relatively easy to understand and you can see that physics also makes more sense if you consider, for example, speed as the derivative of distance with respect to time.
For self-study, I recommend: 'Mathematics for Physicists and Engineers' by Klaus Weltner, Volumes 1 and 2.
https://portal.dnb.de/opac/simpleSearch?query=weltner+mathematik+physiker+ingenieure
Here are the tables of contents of the two volumes:
https://d-nb.info/1023059576/04
https://d-nb.info/1018407979/04
The earlier editions are also great, and you can get them used at a reasonable price.
Thanks 🙂
At 14, you don't really need anything like that in school, and textbooks are expensive. You could go to a university library and look at math textbooks there; the content is almost the same everywhere.
I didn't even say that I need it for school and I just find the topic exciting and would like to know more about it.
Analysis, linear algebra, differential calculus, etc. require prior knowledge.
To learn the basics, I would stick to textbooks. Advanced mathematics is usually not something you can simply Google, especially without the basics.
Yes, of course, that's why there are books that explain the basics. In an emergency, I still have a cell phone and wifi?
Analysis 1, Analysis 2
Otto Forster
Linear algebra and geometry
Wilhelm Klingenberg
Ordinary differential equations
Wolfgang Walter
These were the standard works for mathematicians and physicists for me, but that was a while ago.
These books are very advanced and unsuitable for those asking questions without any prior knowledge. Books for getting started with "theoretical mechanics" always require prior knowledge of mathematics and physics. I would recommend building the foundations and delving deeper into the mathematics later. As a good book for getting started with proof-oriented mathematics, I can recommend "The Book of Proof" by Richard Hammack. A version of it is available for free online.