# Calculus of Variation

1. Jul 8, 2006

### zeithief

Hi all, I'm a maths and physics student from college. I have been asked by tutor to make a small report on the uses of calculus of variation which has an impact of society... I have been searching up and down but cant find anything specific or easy enough to understand on the internet.. I was wondering if anyone here has some website for me to refer to or any ideas on what i can do. Thanks in advance :D

2. Jul 8, 2006

### arildno

Since a heck of a lot of the fundamental equations in physics can be regarded as derivable from a principle of variation, the calculus of variation can be regarded as having the same applicability as physics has..

For further note, do not post your questions in the tutorials section.

3. Jul 8, 2006

### zeithief

can you like point out an specific case in which the application of calculus of variation which has an impact of society? and sorry, i didnt saw the homework section!!

4. Jul 8, 2006

### arildno

Can you point to a specific case where physics has impact on our society?
One classic example is elasticity theory, another is the concept of geodesics, as they appear in general relativity.
A third example is Fermat's principle for the propagation of light.

5. Jul 8, 2006

### zeithief

ok! thanks!

6. Nov 15, 2006

### Jheriko

You should search the web for "the action principle" and the "Euler-Lagrange equation" which make use of functional derivatives. "Feynman path integrals" are a more well known example and give a nice example of the functional integral.

These methods are very important in quantum mechanics, which has had a huge effect on society, e.g. technology, philosophy, entertainment, etc..

7. Nov 21, 2006

### Agnostic

Do a search on the "the brachystochrone problem" or Hamiltonâ€™s Principle...

8. Nov 21, 2006

### Hurkyl

Staff Emeritus
You mean "The brachistrone problem"

9. Nov 22, 2006

### Agnostic

No. I mean exactly what I said :)

brachysto / chrone

Greek for: Shortest / Time

The actual originial correct spelling is brachistochrone.