Online calculus of variations resource

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SUMMARY

The discussion focuses on advanced resources for studying calculus of variations, specifically seeking materials that extend beyond basic concepts like Euler and Lagrange. A recommended online resource is a curated list found at http://www.geocities.com/alex_stef/mylist.html. Additionally, the book "Calculus of Variations" (ISBN: 0486414485) is highlighted for its clear approach and comprehensive treatment of both proofs and computational problems. This book effectively motivates the study of optimization and gradually introduces more complex functionals.

PREREQUISITES
  • Basic understanding of calculus and differential equations
  • Familiarity with optimization techniques
  • Experience with mathematical analysis
  • Knowledge of functionals and their properties
NEXT STEPS
  • Explore advanced topics in "Calculus of Variations" by Gelfand and Fomin
  • Research optimization methods in functional analysis
  • Study the application of calculus of variations in physics and engineering
  • Learn about numerical methods for solving variational problems
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are looking to deepen their understanding of advanced calculus of variations and its applications in optimization problems.

Terilien
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Are there any advanced resources on the topic that go beyond the basic concepts. I'm interested in learning the more advanced applied and theoretical concepts(beyond euler and lagrange).
 
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It's not an online source, but it's dirt cheap:

https://www.amazon.com/dp/0486414485/?tag=pfamazon01-20

This book is great- it really only requires a little bit of experience with analysis, the approach is very motivated and clear, and for problems it has both proofs and computation. The thing that I love most about this book is the very natural way that it proceeds- you start with the motivation for developing this calculus (optimization), then you treat the simplest of functionals. After this you bit by bit treat more general functionals. After you get your hands dirty with these problems, you then confront deeper more theoretical ideas which were motivated by the problems.
 

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