Newbie questions about core mechanics topics

[whirlpoolm51]

I am a newbie to physics forums and I would like to say thank you to the creators of this site because it is going to be a huge help to me and my future endeavors into physics! I honestly do not know how it took me so long to find a forum with this kind of topic as I have been a member of cloudy nights forums for some time now and no one ever mentioned it!

Sorry about the long intro but I will get to the point.

While I have a pretty good understanding of the universe and all objects in it I lack the mathematical understanding that it truly takes to see it for what it really is!

Honestly, I had to start from scratch when it came to my knowledge of mathematics but I am slowly but surely filling my head with everything from basic algebra to calculus , differential equations , linear algebra , topology etc etc

I started this thread because I would like to know what exactly are some of the main and most important topics of classical mechanics I should learn first before delving into general relativity and quantum mechanics.

I have a boat load of books on mathematics of physics ,cosmology , classical physics, string theory , m-theory , quantum mechanics , QED , QCD, quantum and classical field theory etc etc. I literally have over 300 books on every subject you could imagine , but what's funny is most of them are introductions to the mathematics that do not understand at all lol I just simply bought them because I love books and I want to have every little piece of information I could possibly need right at my fingertips!

My main interest is cosmology right now but I am going to be getting into quantum mechanics and the harder but yet fun stuff once I feel my knowledge of mathematics is prepared.

 

[Drakkith]

Welcome to PF!

Any textbook on Introductory Mechanics would be a good place to start learning classical mechanics.

 

[MuIotaTau]

I've had three courses on introductory mechanics, the first from an algebra based text called Physics of Everyday Phenomena by Griffith, the second from a calculus based book called Fundamentals of Physics by Halliday (my first courses in E&M, thermal physics, and optics also came from this book), and finally Introduction to Mechanics by Kleppner and Kolenkow. I recommend the last text most highly, but which you are most comfortable with depends on your level of comfort with calculus. K&K are very good at bring explicit with their calculations, though, and their selection of problems are fairly challenging while not being excessively so, so I definitely recommend it.

As far as concepts go, the standard laundry list I'm familiar with should include kinematics, conservation of energy and momentum, general energy principles, rotational mechanics (including conservation of angular momentum), and non-inertial reference frames.

I also want to emphasize the importance of understanding classical mechanics before delving deep into the harder stuff (QM, GR, QFT, etc.). Clearly you're aware of this, but I still think it's important to note that there is very little you can learn about mechanics that will not enhance your understanding of modern physics.