Beschreibung
InhaltsangabeCALCULUS OF VARIATIONS I - The Lagrangian Formalism: Part I: The First Variation and Necessary Conditions: The First Variation; Variational Problems with Subsidiary Conditions; General Variational Formulas.- Part II: The Second Variation and Sufficient Conditions; Second Variation, Excess Function, Convexity; Weak Minimizers and Jacobi Theory; Weierstrass Field Theory for One-dimensional Integrals and Strong Minimizers. CALCULUS OF VARIATIONS II - The Hamiltonian Formalism: Part III: Canonical Formalism and Hamilton-Jacobi Theory; Legendre Transformation, Hamiltonian Systems, Convexity, Field Theories; Parametric Variational Integrals.- Part IV: Hamilton-Jacobi Theory and Canonical Transformations: Hamilton-Jacobi Theory and Canonical Transformations; Partial Differential Equations of First Order and Contact Transformations.
Autorenportrait
Inhaltsangabeof Calculus of Variations I.- 1. The First Variation.- 2. Variational Problems with Subsidiary Conditions.- 3. General Variational Formulas.- 4. Second Variation, Excess Function, Convexity.- 5. Weak Minimizers and Jacobi Theory.- 6. Weierstrass Field Theory for One-Dimensional Integrals and Strong Minimizers.- Supplement. Some Facts from Differential Geometry and Analysis.- 1. Euclidean Spaces.- 2. Some Function Classes.- 3. Vector and Covector Fields. Transformation Rules.- 4. Differential Forms.- 6. Mean Curvature and Gauss Curvature.
Inhalt
CALCULUS OF VARIATIONS I - The Lagrangian Formalism: Part I: The First Variation and Necessary Conditions:The First Variation; Variational Problems with Subsidiary Conditions; General Variational Formulas.- Part II: The Second Variation and Sufficient Conditions; Second Variation, Excess Function, Convexity; Weak Minimizers and Jacobi Theory; Weierstrass Field Theory for One-dimensional Integrals and Strong Minimizers. CALCULUS OF VARIATIONS II - The Hamiltonian Formalism: Part III: Canonical Formalism and Hamilton-Jacobi Theory; Legendre Transformation, Hamiltonian Systems, Convexity, Field Theories; Parametric Variational Integrals.- Part IV: Hamilton-Jacobi Theory and Canonical Transformations: Hamilton-Jacobi Theory and Canonical Transformations; Partial Differential Equations of First Order and Contact Transformations.
