A brief on tensor analysis /

Intended for advanced undergraduates in engineering, physics, mathematics, and applied sciences, A Brief on Tensor Analysis can serve as a springboard for studies in continuum mechanics and general relativity. This concise but informal text includes worked-out problems and exercises. It assumes that...

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Detalles Bibliográficos
Clasificación:QA433 S5.5 1994
Autor principal: Simmonds, James G.
Formato: Libro
Idioma:Inglés
Publicado: New York : Springer-Verlag, 1994.
Edición:2nd ed.
Colección:Undergraduate texts in mathematics.
Temas:
Calculus of tensors.
Cálculo de tensores
Tabla de Contenidos:
  • Preface to the Second Edition Preface to the First Edition Ch. I . Introduction: Vectors and Tensors
  • Three-Dimensional Euclidean Space
  • Directed Line Segments
  • Addition of Two Vectors
  • Multiplication of a Vector v by a Scalar [alpha]
  • Things That Vectors May Represent
  • Cartesian Coordinates
  • The Dot Product
  • Cartesian Base Vectors
  • The Interpretation of Vector Addition
  • The Cross Product
  • Alternative Interpretation of the Dot and Cross Product. Tensors
  • Definitions
  • The Cartesian Components of a Second Order Tensor
  • The Cartesian Basis for Second Order Tensors
  • Ch. II. General Bases and Tensor Notation
  • General Bases
  • The Jacobian of a Basis Is Nonzero
  • The Summation Convention
  • Computing the Dot Product in a General Basis
  • Reciprocal Base Vectors
  • The Roof (Contravariant) and Cellar (Covariant) Components of a Vector
  • Simplification of the Component Form of the Dot Product in a GeneralBasis
  • Computing the Cross Product in a General Basis
  • A Second Order Tensor Has Four Sets of Components in General
  • Change of Basis
  • Ch. III. Newton's Law and Tensor Calculus
  • Rigid Bodies
  • New Conservation Laws
  • Nomenclature
  • Newton's Law in Cartesian Components
  • Newton's Law in Plane Polar Coordinates
  • The Physical Components of a Vector
  • The Christoffel Symbols
  • General Three-Dimensional Coordinates
  • Newton's Law in General Coordinates
  • Computation of the Christoffel Symbols
  • An Alternative Formula for Computing the Christoffel Symbols
  • A Change of Coordinates
  • Transformation of the Christoffel Symbols
  • Ch. IV. The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem
  • The Gradient
  • Linear and Nonlinear Eigenvalue Problems
  • The Del Operator
  • The Divergence, Curl, and Gradient of a Vector Field
  • The Invariance of [actual symbol not reproducible]
  • The Covariant Derivative
  • The Component Forms of [actual symbol not reproducible]
  • The Kinematics of Continuum Mechanics
  • The Divergence Theorem
  • Differential Geometry
  • Index.

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