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A brief on tensor analysis

Author: James G Simmonds
Publisher: New York ; Berlin : Springer, 1994.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : 2. ed

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated  Read more...


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Genre/Form: 0 Gesamtdarstellung
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: James G Simmonds
ISBN: 038794088X 9780387940885 354094088X 9783540940883 0387906398 9780387906393 9781461264248 1461264243
OCLC Number: 246731444
Description: XIV, 112 Seiten : Diagramme.
Contents: I Introduction: Vectors and Tensors.- Three-Dimensional Euclidean Space.- Directed Line Segments.- Addition of Two Vectors.- Multiplication of a Vector v by a Scalar ?.- 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.- Exercises.- 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 General Basis.- Computing the Cross Product in a General Basis.- A Second Order Tensor Has Four Sets of Components in General.- Change of Basis.- Exercises.- 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.- Exercises.- 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 ? * v, ? x v, and ?v.- The Covariant Derivative.- The Component Forms of ? * v, ? x v, and ?v.- The Kinematics of Continuum Mechanics.- The Divergence Theorem.- Differential Geometry.- Exercises.
Series Title: Undergraduate texts in mathematics.
Responsibility: James G. Simmonds.
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