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  • 张量分析简论(第2版)(英文版)[平装]
  • 共2个商家     15.20元~17.29
  • 作者:西蒙兹(Simmonds.J.G.)(作者)
  • 出版社:世界图书出版公司;第1版(2009年6月1日)
  • 出版时间:
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  • 包装:
  • ISBN:9787510004889

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    《张量分析简论(第2版)(英文版)》是由世界图书出版公司出版的。

    作者简介

    作者:(美国)西蒙兹(Simmonds.J.G.)

    目录

    Preface to the Second Edition
    Preface to the First Edition
    CHAPTER 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

    CHAPTER 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

    CHAPTER 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

    CHAPTER 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 lnvariance of V. v, V x v, and Vv
    The Covariant Derivative
    The Component Forms of V- v, V x v, and Vv
    The Kinematics of Continuum Mechanics
    The Divergence Theorem 
    Differential Geometry 
    Exercises
    Index

    序言

    When I was an undergraduate, working as a co-op student at North Ameri-can Aviation, I tried to learn something about tcosors. In the AeronauticalEngineering Department at MIT, I had just finished an introductory coursein classical mechanics that so impressed me that to this day I cannot watch aplane in flight——especially in a turn——without imaging it bristling with vec-tors. Near the end of the course the professor showed that, if an airplane istreated as a rigid body, there arises a mysterious collection of rather simple-looking integrals called the components of the moment of inertia tensor.Tensor——what power those two syllables seemed to resonate. I had heard theword once before, in an aside by a graduate instructor to the cognoscenti inthe front row of a course in strength of materials. "What the book calls stressis actually a tensor...." With my interest twice piqued and with time off from fighting the brush-fires of a demanding curriculum, I was ready for my first serious effort atself-instruction. In Los Angeles, after several tries, I found a store with a bookon tensor analysis. In my mind I had rehearsed the scene in which a graduatestudent or professor, spying me there, would shout, "You're an under-graduate. What are you doing looking at a book on tensors?" But luck wasmine: the book had a plain brown dust jacket. Alone in my room, I turnedimmediately to the definition of a tensor:. "A 2rid order tensor is a collectionof na objects that transform according to the rule..." and thence followed aninscrutable collection of superscripts, subscripts, overbars, and partial deriv-atives. A pedagogical disaster! Where was the connection with those beauti-ful, simple, boldfaced symbols, those arrows that l could visual/ze so well? I was not to find out until after graduate school. But it is my hope that,with this book, you, as an undergraduate, may sail beyond that bar on whichI once foundered. You will find that I take nearly three chapters to prepare.

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