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The book explores classical variational calculus, appealing to analysts, geometers, and physicists. Volume 1 focuses on the formal framework and nonparametric field theory, while Volume 2 covers parametric variational problems, Hamilton-Jacobi theory, and first-order partial differential equations. It emphasizes inner variations, revealing insights like monotonicity formulas and conservation laws, particularly through Emmy Noether's principles. Additionally, it examines Legendre-Jacobi theory, one-dimensional field theory, and the role of convexity in variational calculus, highlighting the concept of null Lagrangians.
Nákup knihy
Calculus of Variations I, Mariano Giaquinta, Stefan Hildebrandt
- Jazyk
- Rok vydania
- 2010
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- (mäkká)
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- Titul
- Calculus of Variations I
- Podtitul
- The Lagrangian Formalism
- Jazyk
- anglicky
- Vydavateľ
- Springer Berlin Heidelberg
- Rok vydania
- 2010
- Väzba
- mäkká
- Počet strán
- 508
- ISBN13
- 9783642080746
- Kategórie
- Matematika, Príroda všeobecne
- Anotácia
- The book explores classical variational calculus, appealing to analysts, geometers, and physicists. Volume 1 focuses on the formal framework and nonparametric field theory, while Volume 2 covers parametric variational problems, Hamilton-Jacobi theory, and first-order partial differential equations. It emphasizes inner variations, revealing insights like monotonicity formulas and conservation laws, particularly through Emmy Noether's principles. Additionally, it examines Legendre-Jacobi theory, one-dimensional field theory, and the role of convexity in variational calculus, highlighting the concept of null Lagrangians.