Need calculus of variations book for a laymen

[MichPod]

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.

 

[SteamKing]

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

 

[deskswirl]

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.

 

[smodak]

A First Course in the Calculus of Variations
Mark Kot
https://www.amazon.com/dp/1470414953/?tag=pfamazon01-20

 

[malawi_glenn]

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 :)

 

[smodak]

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.

 

[malawi_glenn]

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

 

[smodak]

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.

 

[malawi_glenn]

Ok, I will open a free account. Thanks for sharing.

https://www.dropbox.com/help/20

One should not have to be logged on to dropbox in order to download files which I have shared link to

lets try again

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

 

[smodak]

https://www.dropbox.com/help/20

One should not have to be logged on to dropbox in order to download files which I have shared link to

lets try again

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

I am not sure if I was doing anything wrong before but it works now. Many Thanks!