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

MARC

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050 4 |a QA433  |b S5.5 1994 
082 0 0 |a 515.63  |b S59 
090 |a QA433  |b S5.5 1994 
099 |a QA433  |a .S535 1994 
100 1 |a Simmonds, James G. 
245 1 2 |a A brief on tensor analysis /  |c James G. Simmonds. 
250 |a 2nd ed. 
260 |a New York :  |b Springer-Verlag,  |c 1994. 
300 |a xiv, 112 p. :  |b ill. ;  |c 24 cm. 
440 0 |a Undergraduate texts in mathematics. 
500 |a Includes index. 
505 0 |t Preface to the Second Edition  |t Preface to the First Edition  |g Ch. I .  |t Introduction: Vectors and Tensors --  |t Three-Dimensional Euclidean Space --  |t Directed Line Segments --  |t Addition of Two Vectors --  |t Multiplication of a Vector v by a Scalar [alpha] --  |t Things That Vectors May Represent --  |t Cartesian Coordinates --  |t The Dot Product --  |t Cartesian Base Vectors --  |t The Interpretation of Vector Addition --  |t The Cross Product --  |t Alternative Interpretation of the Dot and Cross Product. Tensors --  |t Definitions --  |t The Cartesian Components of a Second Order Tensor --  |t The Cartesian Basis for Second Order Tensors --  |g Ch. II.  |t General Bases and Tensor Notation --  |t General Bases --  |t The Jacobian of a Basis Is Nonzero --  |t The Summation Convention --  |t Computing the Dot Product in a General Basis --  |t Reciprocal Base Vectors --  |t The Roof (Contravariant) and Cellar (Covariant) Components of a Vector --  |t Simplification of the Component Form of the Dot Product in a GeneralBasis --  |t Computing the Cross Product in a General Basis --  |t A Second Order Tensor Has Four Sets of Components in General --  |t Change of Basis -- 
505 8 0 |g Ch. III.  |t Newton's Law and Tensor Calculus --  |t Rigid Bodies --  |t New Conservation Laws --  |t Nomenclature --  |t Newton's Law in Cartesian Components --  |t Newton's Law in Plane Polar Coordinates --  |t The Physical Components of a Vector --  |t The Christoffel Symbols --  |t General Three-Dimensional Coordinates --  |t Newton's Law in General Coordinates --  |t Computation of the Christoffel Symbols --  |t An Alternative Formula for Computing the Christoffel Symbols --  |t A Change of Coordinates --  |t Transformation of the Christoffel Symbols --  |g Ch. IV.  |t The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem --  |t The Gradient --  |t Linear and Nonlinear Eigenvalue Problems --  |t The Del Operator --  |t The Divergence, Curl, and Gradient of a Vector Field --  |t The Invariance of [actual symbol not reproducible] --  |t The Covariant Derivative --  |t The Component Forms of [actual symbol not reproducible] --  |t The Kinematics of Continuum Mechanics --  |t The Divergence Theorem --  |t Differential Geometry --  |t Index. 
520 |a 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 the reader has a basic knowledge of calculus and linear algebra, as well as a familiarity with fundamental ideas of mechanics and geometry. In this second edition, new exercises have been added and there is a new section on differential geometry which introduces ideas that find application in theories of curved continua (membranes and shells) and in general relativity. 
650 0 |a Calculus of tensors. 
650 4 |a Cálculo de tensores 
905 |a LIBROS 
902 |a Juan Pascual García L. 
949 |a Biblioteca UAM Iztapalapa  |b Colección General  |c QA433 S5.5 1994 

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