Need guidance on where to start on the study of the variational principle

In summary, the individual was struggling with the mathematics involved in their physics experiments and sought guidance from a professor who recommended researching the variational principle. However, the individual found the material to be beyond their current knowledge in Calculus II. They were directed to a resource that provides a straightforward explanation of the topic, with a suggestion to first learn the necessary concepts from Calculus 3 and/or Ordinary Differential Equations. They also expressed a need for additional resources.
  • #1
Nano-Passion
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I was experimenting with some physics and the mathematics started to get a bit tougher than what I'm used to. I had a professor who looked at what I'm doing, offered to guide me, and told me to do some research on the variational principle.

At the moment, I am in Calculus II. I did a couple searches, and the material I found is well beyond my knowledge at this moment. Can someone help direct me to a proper place to start on this study.
 
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  • #2
This looks like a straightforward explanation (well, straightforward in the sense that it
doesn't obscure things with "advanced" notation for no particular reason).
http://www.math.umn.edu/~olver/am_/cvz.pdf

If you don't understand this, first learn what you need from Calc 3 and/or ODEs.
 
  • #3
AlephZero said:
This looks like a straightforward explanation (well, straightforward in the sense that it
doesn't obscure things with "advanced" notation for no particular reason).
http://www.math.umn.edu/~olver/am_/cvz.pdf

If you don't understand this, first learn what you need from Calc 3 and/or ODEs.

Yes there is a bunch of calculus 3 there that I see. Thanks for the link.
 
  • #4
Anyone else? I need a supplement.
 

1. What is the variational principle?

The variational principle is a fundamental principle in physics and mathematics that states that the actual behavior of a physical system is the one that minimizes or maximizes a certain physical quantity, known as the action. It is often used in the study of systems with continuous symmetries, such as classical mechanics and quantum mechanics.

2. Why is the variational principle important?

The variational principle is important because it allows us to find the most accurate and efficient solutions to problems in physics and mathematics. It also provides a powerful framework for understanding the underlying structure and behavior of physical systems.

3. How do I start studying the variational principle?

The best way to start studying the variational principle is to have a strong foundation in mathematics, particularly in calculus and differential equations. It is also helpful to have a basic understanding of classical mechanics and quantum mechanics. From there, you can begin to explore the variational principle through textbooks, online resources, and practice problems.

4. What are some real-world applications of the variational principle?

The variational principle has many applications in various fields, including classical mechanics, quantum mechanics, electromagnetism, and optics. It is used to derive the equations of motion for physical systems, calculate the energy levels of atoms and molecules, and optimize systems in engineering and physics.

5. Are there any challenges in studying the variational principle?

Like any other mathematical and physical concept, the variational principle can be challenging to understand and apply. It requires a strong understanding of advanced mathematics and may take time to fully grasp. It is also important to carefully consider the boundary conditions and constraints of a problem when applying the variational principle.

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