Introduction to Tensor Analysis and the Calculus of Moving Surfaces

• Κύριος συγγραφέας: Grinfeld, Pavel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2013.
• Θέματα: Mathematics.; Matrix theory.; Algebra.; Differential geometry.; Calculus of variations.; Differential Geometry.; Calculus of Variations and Optimal Control; Optimization.; Linear and Multilinear Algebras, Matrix Theory.

This text is meant to deepen its readers’ understanding of vector calculus, differential geometry and related subjects in applied mathematics. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the pri...

Πίνακας περιεχομένων:

• Preface
• Why Tensor Calculus?
• 1. Rules of the Game
• 2. Coordinate Systems and the Role of Tensor Calculus
• 3. Change of Coordinates
• 4. Tensor Description of Euclidean Spaces
• 5. The Tensor Property
• 6. Covariant Differentiation
• 7. Determinants and the Levi-Civita Symbol
• 8. Tensor Description of Surfaces
• 9. Covariant Derivative of Tensors with Surface Indices
• 10. The Curvature Tensor
• 11. Covariant Derivative of Tensors with Spatial Indices
• 12. Integration and Gauss's Theorem
• 13. Intrinsic Features of Embedded Surfaces
• 14. Further Topics in Differential Geometry
• 15. Classical Problems in the Calculus of Variations
• 16. Equations of Classical Mechanics
• 17. Equations of Continuum Mechanics
• 18. Einstein's Theory of Relativity
• 19. The Rules of Calculus of Moving Surfaces
• 20. Applications of the Calculus of Moving Surfaces.