A Brief on Tensor Analysis

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 stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

ISBN	038794088X	Volumes	1
ISBN13	9780387940885 (What's this?)	Weight (grammes)	366
Publisher	Springer-Verlag New York Inc.	Published in	New York, NY
Imprint	Springer-Verlag New York Inc.	Series editor	Ewing, J.H., Ewing, J.H., Ewing, J.H.
Format	Hardback	Series title	Undergraduate Texts in Mathematics
Publication date	01 Aug 1997	Previous ISBN	9783540940883
Library of Congress	QA433.S535	Height (mm)	234
DEWEY	515.63	Width (mm)	156
DEWEY edition	DC21	Spine width (mm)	11
Pages	146	Academic level	Undergraduate, Postgraduate, Professional / Scholarly

	Preface to the Second Edition
	Preface to the First Edition
Ch. I	Introduction: Vectors and Tensors	1
	Three-Dimensional Euclidean Space	3
	Directed Line Segments	3
	Addition of Two Vectors	4
	Multiplication of a Vector v by a Scalar [alpha]	5
	Things That Vectors May Represent	5
	Cartesian Coordinates	6
	The Dot Product	7
	Cartesian Base Vectors	10
	The Interpretation of Vector Addition	10
	The Cross Product	11
	Alternative Interpretation of the Dot and Cross Product. Tensors	15
	Definitions	16
	The Cartesian Components of a Second Order Tensor	17
	The Cartesian Basis for Second Order Tensors	19
Ch. II	General Bases and Tensor Notation	25
	General Bases	25
	The Jacobian of a Basis Is Nonzero	27
	The Summation Convention	27
	Computing the Dot Product in a General Basis	28
	Reciprocal Base Vectors	28
	The Roof (Contravariant) and Cellar (Covariant) Components of a Vector	30
	Simplification of the Component Form of the Dot Product in a General Basis	31
	Computing the Cross Product in a General Basis	32
	A Second Order Tensor Has Four Sets of Components in General	34
	Change of Basis	36
	More...

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