Source recommendation on Differential Geometry

In summary, based on the questions asked, it seems that you want to learn differential geometry and linear algebra concepts. It is best if you consult a book on differential geometry and another one on linear algebra.
  • #1
rajsekharnath
14
2
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.
 
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  • #2
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/
 
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  • #3
Yeah the questions got no replies because I accidentally framed such a big paragraph.
 
Last edited:
  • #4
rajsekharnath said:
Yeah the questions got no replies because I accidentally framed such a big prargraph.
Sarcasm?
 
  • #5
malawi_glenn said:
Sarcasm?
No sir. I just wrote what I thought.
 
  • #6
rajsekharnath said:
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?
 
  • #7
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.
 

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