Need calculus of variations book for a laymen

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Discussion Overview

The discussion revolves around finding accessible resources for learning calculus of variations, particularly for individuals with a background in physics who may not have formal training in this area. Participants express a desire for practical understanding rather than rigorous theoretical details, especially in the context of analytical mechanics and quantum field theory (QFT).

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant notes difficulty in understanding variations of functions compared to derivatives and integrals, expressing a need for practical resources to aid in learning.
  • Another participant suggests that calculus of variations is typically a graduate-level topic and may not have simplified resources available.
  • A recommendation is made for "The Calculus of Variations" by van Brunt, highlighting its inclusion of physical examples and the option to skip theoretical sections.
  • Another participant mentions "A First Course in the Calculus of Variations" by Mark Kot as a potential resource.
  • One participant is writing lecture notes on mathematical topics for QFT, including a section on calculus of variations, and shares a link to their work.
  • There are inquiries about the accessibility of the shared lecture notes, with some participants expressing frustration over the need for a Dropbox account to access the file.

Areas of Agreement / Disagreement

Participants generally agree on the need for practical resources for learning calculus of variations, but there is no consensus on specific recommendations or the accessibility of shared materials.

Contextual Notes

Some participants express uncertainty about the availability of beginner-friendly resources and the challenges of accessing shared documents, indicating limitations in the discussion regarding resource accessibility.

MichPod
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While trying to study textbooks on analytical mechanics or QFT I realized that I simply cannot operate with variations of functions in the same way I can operate with derivatives and integrals. I have never learned calculus of variations in university and, frankly, I am not much interested in this topic by itself, but I need it to go further in my attempts to learn physics.

So can anybody recommend a good practical book or may be video-course on this subject? Again, I do not need very fine details and rigorous proofs, but I need to gain practical ability to understand this stuff and gain some intuition with it. I see that some physics textbook try to introduce calculus of variations just as part of the text, but I fail to understand it to a satisfactory level.
 
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MichPod said:
While trying to study textbooks on analytical mechanics or QFT I realized that I simply cannot operate with variations of functions in the same way I can operate with derivatives and integrals. I have never learned calculus of variations in university and, frankly, I am not much interested in this topic by itself, but I need it to go further in my attempts to learn physics.

So can anybody recommend a good practical book or may be video-course on this subject? Again, I do not need very fine details and rigorous proofs, but I need to gain practical ability to understand this stuff and gain some intuition with it. I see that some physics textbook try to introduce calculus of variations just as part of the text, but I fail to understand it to a satisfactory level.
The calculus of variations is often a graduate-level course. It's pretty abstract stuff, and I doubt there's a Calculus of Variations for Dummies out there.

Now, there are certain physical problems which can be handled by the C of V which may be a little easier to understand than QFT, problems like the brachistochrone.

http://mat.uab.cat/matmat/PDFv2007/v2007n05.pdf
 
Why don't you try The Calculus of Variations by van Brunt. It has physical examples and you can skip over the theory if bored.
 
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malawi_glenn said:
I am actually in the progress writing "Lecture notes" about mathematical topics for basic Quantum Field Theory.

https://www.dropbox.com/s/u3c4wzdbaqbjumq/QFT_notes.pdf?dl=0

Now I so happens that I am almost finished with the section regarding calculus of variations :)
Is there any way you could share it publicly? I do not have a dropbox account and it does not let me download it. Thanks.
 
smodak said:
Is there any way you could share it publicly? I do not have a dropbox account and it does not let me download it. Thanks.
strange that one needs a dropbox account in order to obtain access to a shared file, it has never happened to me before

no I do not want to do that because it is not finished yet
 
malawi_glenn said:
strange that one needs a dropbox account in order to obtain access to a shared file, it has never happened to me before

no I do not want to do that because it is not finished yet
Ok, I will open a free account. Thanks for sharing.
 

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