本书是Springer数学本科生教程系列之一，适合于工程、物理、数学以及相关应用学科的高年级本科生。本书可以作为学习连续介质力学和广义相对论的很好的过度。这部简明的教程还包括了一些给出解答的问题和一些练习。读者有基本微积分和线性代数的知识，并对力学和几何的基本观点熟悉将会更容易学习理解本书内容。

本书是第2版，增加了不少新的练习，也增加了一部分专门讲述微分几何，这可以引导读者学习在弯曲连续理论中的应用。

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