Where Can I Find Helpful Texts on Calculus of Variations?

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SUMMARY

This discussion centers on finding recommended texts for studying Calculus of Variations. A key suggestion is Weinstock's "Calculus of Variations with Applications to Physics and Engineering," noted for its accessibility. Participants also mention challenges faced while reading Nakahara's "Geometry, Topology and Physics," particularly in understanding variations related to tensors and the Einstein-Hilbert action. The conversation highlights the need for clearer resources in this specialized area of mathematics.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with tensor calculus
  • Knowledge of variational principles in physics
  • Basic understanding of differential geometry
NEXT STEPS
  • Research "Calculus of Variations with Applications to Physics and Engineering" by Weinstock
  • Study tensor calculus to improve understanding of variations with respect to tensors
  • Explore variational principles in the context of general relativity
  • Review Nakahara's "Geometry, Topology and Physics" focusing on chapter 10 for deeper insights
USEFUL FOR

Students and professionals in mathematics and physics, particularly those interested in the applications of Calculus of Variations in theoretical physics and engineering.

Son Goku
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Could anybody recommend any texts on Calculus of Variations?

Unlike most areas of mathematics I'm finding it difficult to obtain standard texts.
 
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An easy book on the subject is Weinstock's "Calculus of Variations with Applications to Physics and Engineering".

Daniel.
 
dextercioby said:
An easy book on the subject is Weinstock's "Calculus of Variations with Applications to Physics and Engineering".

Daniel.
Thanks. I hit a wall when reading Nakahara's Geometry, Topology and Physics. In chapter 10 he takes the variation of the action of a scalar field and the Einstein-Hilbert action, equates them both to zero and ends up with the Field Equations.

My basic problem is I don't know how to take a variation with respect to a tensor, such as the metric.
 

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