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Need calculus of variations book for a laymen

  • Calculus
  • Thread starter MichPod
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  • #1
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Main Question or Discussion Point

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 learnt 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.
 

Answers and Replies

  • #2
SteamKing
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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 learnt 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
 
  • #3
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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.
 
  • #5
malawi_glenn
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  • #6
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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.
 
  • #7
malawi_glenn
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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
 
  • #8
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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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