Can I start self studying DG and GR with my background?

[TheKracken]

Hello, so I will be starting Calculus 3 (vector and multivariable calc) and physics 1 (intro calculus based mechanics) this next semester.

I am interested in using this next semester to go further into both of those topics and I am curious how I would start? I am interested in studying Calc 3 further mathematically (differential manifolds ) and further in Mechanics and GR ( General Relativity)

My current background is just Calc 1&2 though we did do some basic differential equations in Calc 2

 

[homeomorphic]

Math and physics require patience. You can't expect it to happen overnight. I think it can be a delicate balancing act as far as wanting to get ahead versus spreading yourself too thin and moving too fast. You're definitely leaning towards jumping the gun on all those subjects.

You're going to want to do special relativity before tackling GR (and subjects like E&M and more advanced classical mechanics are also helpful to know first, not to mention the intro calculus-based physics). Also, you should probably concentrate on calc 3 before doing differential geometry. You're going to need linear algebra before you do differential geometry, as well. I would focus on your classes first, and if you find that you have them completely under your control, THEN you can think about going the extra mile and getting ahead.

One thing you could do is read Visual Complex Analysis. You'll have to excuse my recommending it yet again, but the reason why I bring it up is that you could already start reading it very easily with your current background because it only requires calc 1-2 (as opposed to more rigorous Complex Analysis books, and the other non-rigorous ones are probably kind of crappy, but VCA is a classic), and you'll find complex analysis useful later on. It will also boost your geometric intuition greatly, which is very useful later on.

 

[TheKracken]

VCA, will this be helpful in my physics courses at all or is it strictly a proof based text? Also, as I understand you took up a lot of self studying of physics and right now I am debating about if I should take the extra year and a half onto my degree for a double major or if I should just take Calc3 and LA DEQ's this next semester, transfer and hopefully come back around to physics later on?

 

[homeomorphic]

VCA, will this be helpful in my physics courses at all or is it strictly a proof based text?

It's not exactly proof-based--just gives visual arguments and the exercises are sort of conceptual ones that might require a little computation, but maybe not formal proofs for answers. And yes, it comes up in physics. The book even explains some of the applications to physics.

Three math classes and a physics class might be a lot, but I think linear algebra might be another good one to throw in, since it might shed some light on calc III.

In my undergrad, I didn't self-study physics that much. I just took classical mechanics and worked through the textbook for intro physics III, which I didn't take, plus I was an EE major for a long time, so there was a little physics in there, particularly in electromagnetism. I self-studied physics more in grad school.

 

[Matrix0]

Yes, you can definitely start self-studying differential geometry (DG) and general relativity (GR) with your background in Calculus 1 and 2. However, it would be beneficial to have a strong understanding of multivariable calculus and basic differential equations before diving into these topics. I suggest reviewing your knowledge in these areas before starting your self-study.

To begin your self-study in DG and GR, I recommend starting with introductory textbooks or online resources that cover the basics of these subjects. It would also be helpful to familiarize yourself with the mathematical notation and concepts used in these fields. Additionally, it may be beneficial to supplement your self-study with practice problems and exercises to solidify your understanding.

It's great that you have a specific interest in studying differential manifolds and GR. As you continue your self-study, you may find it helpful to focus on one topic at a time and build your knowledge gradually. Don't be afraid to ask for help or clarification if you come across any difficult concepts.

Overall, with dedication and hard work, you can definitely start self-studying DG and GR with your background in Calculus 1 and 2. Good luck on your journey!