Classical Source recommendation on Differential Geometry

[rajsekharnath]

I am intending to join an undergrad course in physics(actually it is an integrated masters course equivalent to bs+ms) in 1-1.5 months. The thing is, in order to take a dive into more advanced stuff during my course, I am currently studying some of the stuff that will be taught in the first year, and that is classical mechanics and electrodynamics at that moment, so I studied the first two chapters of Griffith's book of Electrodynamics(some part of the electrostatics chapter is due), and I studied the variational calculus chapter from Taylor's book of Classical mechanics and right now I am studying the first chapter of Classical mechanics by H. Goldstein(because I was interested), so far I have reached the point where he derives the Lagrange Equation from D'Alembert's principle, but now I am getting stuck because he is talking about some differential geometry which I know nothing about. So I have mainly two questions:
1.Which book should I consult to learn some basic and intermediate differential geometry? I heard V. Arnold's book on mathematical methods for mechanics is a great one, but should I go for reading a little bit of that considering I do not have that much time? Any recommendations of source is welcome.
Also, I found out the college I will be going into, uses Taylor's book for Classical mechanics, so my plan is to supplement Taylor with H. Goldstein as I am interested in the more canonical and comprehensive stuff it provides.
2.I also came across to know that I will be needing a thorough hold on linear algebra to progress on the later chapters of Goldstein and in the advanced books of Quantum Mechanics which I am willing to catch up later, so I also seek source recommendations on that.

 

[malawi_glenn]

Very hard to read post because
1) just a big paragraph
2) there are two questions here - book on differential geometry and book on linear algebra

Perhaps its best if you list the concepts in differential geometry you seek to learn.

Anyway, I recommend these:
Differential Geometry of Curves and Surfaces, by Tapp, Springer
Elementary linear algebra, by Anton (any edition should suffice)

Also check out free "books" here https://www.physicsforums.com/threa...-math-books-and-lecture-notes-part-1.1044710/

 

[rajsekharnath]

Yeah the questions got no replies because I accidentally framed such a big paragraph.

 

[malawi_glenn]

Yeah the questions got no replies because I accidentally framed such a big prargraph.

Sarcasm?

 

[rajsekharnath]

Sarcasm?

No sir. I just wrote what I thought.

 

[malawi_glenn]

No sir. I just wrote what I thought.

Did you assume my gender? ;)

Now what about those concepts in diff geom, what are the ones you want to learn?

 

[rajsekharnath]

Well, the point where I got stuck in Goldstein's book is where he just derives the D'Alembert's principle Eqn 1.52, he says:"Note that in system of Cartesian co-ordinates the partial derivative of T with respect to q^j vanishes. Thus speaking in the language of differential geometry, the term arises from the curvature of the co-ordinates q^j."
I do not understand the second line he says and I wanted to know what I need to learn(and from which book, if it requires) in order to understand the line.
And as of the case of assuming your gender, I am sorry sir. Oh I did that again accidentally!
Sorry again.