Differential Geometry

  • #1
15
1

Main Question or Discussion Point

I am taking my bachelor in geometric quantization but I have no real experience in differential geometry ( a part of my project is to learn that). So I find myself in need of some good books that cover that the basics and a bit more in depth about symplectic manifolds.

If you have any recommendations that would be greatly appreciated.
 

Answers and Replies

  • #2
3
0
A very interesting book, with a quite distinctive approach, is Sussman, Wisdom and Farr's "Functional Differential Geometry", also available free online at https://groups.csail.mit.edu/mac/users/gjs/6946/calculus-indexed.pdf [Broken]

The different thing about this book is that it is supported by software examples throughout, which you can run on MIT-Scheme's "scmutils/mechanics" software to check your understanding.

I have just started it myself. You may find you need another text, too, with a more conventional approach, but this one is really fun. They have stated that a lot of their inspiration came from Spivak's approach in "Calculus on Manifolds", so this may be just what you want.

Incidentally, Sussman and Wisdom, with Mayer, have done another quite well-known book, "Structure and Interpretation of Classical Mechanics", which gives the same practical, unambiguous treatment to Lagrange, Hamilton and dynamics in general.
 
Last edited by a moderator:
  • #3
15
1
Thanks for the tip. I will check out the book.
 
  • #4
3
0
Hi Fgard,
Once you've had a chance to have a good look at it, I'd appreciate your opinion/feedback.
Like I said, it's quite an unconventional approach, so you may need to get your head around their style a bit, but really cool once you get going.

ScmUtils is a bit of an albatross, but does work well once you set it up. I know that there are people working on porting it to more modern envirnmonents :wink:, so hopefully this approach will catch on in the future...
 

Related Threads on Differential Geometry

  • Last Post
Replies
10
Views
1K
Replies
19
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
9
Views
4K
  • Last Post
2
Replies
40
Views
9K
  • Last Post
Replies
4
Views
11K
Replies
12
Views
1K
Replies
6
Views
4K
Top