Looking for simple materials for calculus of variations

In summary, the conversation discusses learning the calculus of variations in physics and recommendations for materials on the topic. The experts suggest starting with Arfken's book, with the caveat that it may not go into enough detail for some individuals. They also mention the Dover book by Elsgolc as another resource. Additionally, they bring up the importance of understanding the subtleties of the topic, which can be found in books like Landau Lifshitz and Gerald Sussman's "Structure and Interpretation of Classical Mechanics."
  • #1
Haorong Wu
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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.
 
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  • #3
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.
 
  • #4
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.
 
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1. What is calculus of variations?

Calculus of variations is a branch of mathematics that deals with finding the optimal solutions to problems involving functions. It involves finding the function that minimizes or maximizes a given functional, which is a mathematical expression involving a function and its derivatives.

2. What are some real-world applications of calculus of variations?

Calculus of variations has many applications in physics, engineering, economics, and other fields. Some examples include finding the path of least resistance for an object moving through a medium, determining the shape of a soap bubble, and optimizing the trajectory of a rocket.

3. What are some simple materials that can be used to learn calculus of variations?

Some simple materials that can be used to learn calculus of variations include textbooks, online resources, and video lectures. Khan Academy, MIT OpenCourseWare, and Coursera are some popular online platforms that offer free courses on calculus of variations.

4. Is calculus of variations difficult to learn?

Like any other branch of mathematics, calculus of variations can be challenging to learn. However, with dedication and practice, it can be understood by anyone with a strong foundation in calculus and basic mathematical concepts.

5. What are some common techniques used in solving problems in calculus of variations?

Some common techniques used in solving problems in calculus of variations include the Euler-Lagrange equation, the method of variation of parameters, and the calculus of variations on a finite interval. These techniques involve manipulating and solving differential equations to find the optimal solutions to a given problem.

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