Looking for simple materials for calculus of variations

Click For Summary

Discussion Overview

The discussion revolves around finding accessible materials for learning the calculus of variations, particularly in the context of physics. Participants share their experiences and recommendations for resources that focus on practical calculations rather than deeper mathematical theory.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about simple materials for learning calculus of variations, specifically for physics applications, and mentions Arfken's "Mathematical Methods for Physicists" as a potential resource.
  • Another participant agrees that Arfken's book is suitable but emphasizes the importance of its detail for the individual learner's needs. They also recommend Elsgolc's Dover book as an alternative.
  • A third participant shares their experience of learning calculus of variations from physics texts, specifically mentioning Landau Lifshitz and Goldstein's works, while cautioning that some derivations may be unclear.
  • This participant also suggests Sussmann's "Structure and Interpretation of Classical Mechanics" for a deeper understanding of the subtleties involved in the calculus of variations, noting that typical physics courses may overlook these aspects.

Areas of Agreement / Disagreement

Participants generally agree on the suitability of Arfken's book, but there is no consensus on the best resource, as different participants recommend various texts based on their personal experiences and learning preferences.

Contextual Notes

Some participants express concerns about the clarity of derivations in certain texts, indicating that the effectiveness of the materials may depend on the learner's background and the depth of understanding they seek.

Haorong Wu
Messages
419
Reaction score
90
Hi, there. I have not systematically learned the calculus of variations. I would like to learn it now. Are there simple materials for the purpose of learning how to do the calculation in physics? No need for deeper consideration in mathematics.

Is Mathematical methods for physicists by Arfken sufficient?

Thanks in advance.
 
Physics news on Phys.org
caz said:
Arfken is fine. The real question is does it go into enough detail for YOU?

I always liked the Dover book by Elsgolc
https://www.amazon.com/dp/0486457990/?tag=pfamazon01-20
Thanks! I will try Arfken's book first. If that is not enough, I will consult Dover's book.
 
I've always learned calculus of variations directly from one of the physics books and found it to be adequate at a physicist's level (ability to push symbols and calculate). I learned it from Landau Lifshitz vol. 1 from the principle of least action calculation there. Goldstein Classical mechanics has a more verbose version of the same derivation. But beware that all those derivations are iffy.

For more subtle explanations of what is really going on (which is important but maybe not needed on the first run), you can consult the "structure and interpretation of classical mechanics" by Gerald Sussmann. What I found out was that a lot of the important subtleties are swept under the rug due to time in the typical physics course, but gerald sussman really emphasizes those.
 
  • Like
Likes   Reactions: Haorong Wu

Similar threads

  • · Replies 26 ·
Replies
26
Views
6K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
5
Views
3K
Replies
9
Views
4K
  • · Replies 5 ·
Replies
5
Views
5K
  • · Replies 13 ·
Replies
13
Views
6K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K