張量分析簡論(第2版‧英文版)（簡體書）

本書是Springer數學本科生教程系列之一，適合於工程、物理、數學以及相關應用學科的高年級本科生。本書可以作為學習連續介質力學和廣義相對論的很好的過度。這部簡明的教程還包括了一些給出解答的問題和一些練習。讀者有基本微積分和線性代數的知識，並對力學和幾何的基本觀點熟悉將會更容易學習理解本書內容。本書是第2版，增加了不少新的練習，也增加了一部分專門講述微分幾何，這可以引導讀者學習在彎曲連續理論中的應用。目次：導論：向量和張量；一般理論和張量表示法；牛頓定律和張量分析；梯度、Del算子、共變微分法和散度定理。

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　Newtons Law and Tensor Calculus
　Rigid Bodies
　New Conservation Laws
　Nomenclature
　Newtons Law in Cartesian Components
　Newtons Law in Plane Polar Coordinates
　The Physical Components of a Vector
　The Christoffel Symbols
　General Three-Dimensional Coordinates
　Newtons 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