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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.
Buchkauf
Calculus of Variations I, Mariano Giaquinta, Stefan Hildebrandt
- Sprache
- Erscheinungsdatum
- 2010
- product-detail.submit-box.info.binding
- (Paperback)
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- Titel
- Calculus of Variations I
- Untertitel
- The Lagrangian Formalism
- Sprache
- Englisch
- Autor*innen
- Mariano Giaquinta, Stefan Hildebrandt
- Erscheinungsdatum
- 2010
- Einband
- Paperback
- Seitenzahl
- 508
- ISBN13
- 9783642080746
- Kategorie
- Mathematik, Naturwissenschaften
- Beschreibung
- 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.