本书在内容以及形式上有如下三个特点：一是**读者直达本学科的核心内容；二是注重应用，指导读者灵活运用所掌握的知识；三是突出了直觉思维在数学学习中的作用。作者不掩饰难点以使得该学科貌似简单，而是通过揭示概念之间的内在联系和直观背景努力帮助那些对这门学科真正感兴趣的读者。
本书各章均提供了大量的例题和习题，其中一部分有相当的难度，但绝大部分是对内容的补充。另外，本书附有一本专门的习题册，并且给出了习题的提示与解答。
本书适合于多种学科界的读者，如数学工作者、科学工作者、工程技术人员等。
本书为全英文版。

Chapter 1 Functions of Several Variables and Their Derivatives
1.1 Points and Points Sets in the Plane and in Space
a.Sequences of points.Convergence
b.Sets of points in the plane
c.The boundary of a set.Closed and open sets
d.Closure as set of limit points
e.Points and sets of points in space
1.2 Functions of Several Independent Variables
a.Functions and their domains
b.The simplest types of functions
c.Geometrical representation of functions
1.3 Continuity
a.Definition
b.The concept of limit of a function of several variables
c.The order to which a function vanishes
1.4 The Partial Derivatives of a Function
a.Definition.Geometrical representation
b.Examples
c.Continuity and the existence of partial derivatives
d.Change of the order of differentiation
1.5 The Differential of a Function and Its Geometrical Meaning
a.The concept of differentiability
b.Directional derivatives
c.Geometric interpretation of differentiability,The tangent plane
d.The total differential of a function
e.Application to the calculus of errors
1.6 Functions of Functions (Compound Functions) and the Introduction of New Independent Variables
a.Compound functions.The chain rule
b.Examples
c.Change of independent variables
1.7 The Mean Value Theorem and Taylor's Theorem for Functions of Several Variables
a.Preliminary remarks about approximation by polynomials
b.The mean value theorem
c.Taylor's theorem for several independent variables
1.8 Integrals of a Function Depending on a Parameter
a.Examples and definitions
b.Continuity and differentiability of an integral with respect to the parameter
c.Interchange of integrations.Smoothing of functions
1.9 Differentials and Line Integrals
a.Linear differential forms
b.Line integrals of linear differential forms
c.Dependence of line integrals on endpoints
1.10 The Fundamental Theorem on Integrability of Linear Differential Forms
a.Integration of total differentials
b.Necessary conditions for line integrals to depend only on the end points
c.Insufficiency of the integrability conditions
d.Simply connected sets
e.The fundamental theorem
APPENDIX
……
Chapter 2 Vectors, Matrices, Linear Transformations
Chapter 3 Developments and Applications of the Differential Calculus
Chapter 4 Multiple Integrals
Chapter 5 Relations Between Surface and Volume Integrals
Chapter 6 Differential Equations
Chapter 7 Calculus of Variations
Chapter 8 Functions of a Complex Variable
List of Biographical Dates
Index