微積分和數學分析引論：第1卷(英文版)（簡體書）

During the latter part of the seventeenth century the new mathe-matical analysis emerged as the dominating force in mathematics.It is characterized by the amazingly successful operation with infinite processes or limits. Two of these processes, differentiation and inte- gration, became the core of the systematic Differential and Integral Calculus, often simply called Calculus, basic for all of analysis.The importance of the new discoveries and methods was immediately felt and caused profound intellectual excitement. Yet, to gain mastery of the powerful art appeared at first a formidable task, for the avail-able publications were scanty, unsystematic, and often lacking in clarity. Thus, it was fortunate indeed for mathematics and science in general that leaders in the new movement soon recognized the vital need for writing textbooks aimed at making the subject ac-cessible to a public much本書在內容以及形式上有如下三個特點：一是引領讀者直達本學科的核心內容；二是注重應用，指導讀者靈活運用所掌握的知識；三是突出了直覺思維在數學學習中的作用。作者不掩飾難點以使得該學科貌似簡單，而是通過揭示概念之間的內在聯繫和直觀背景努力幫助那些對這門學科真正感興趣的讀者。
本書第一章主要圍繞著一元函數展開討論，二、三、四章分別介紹了微積分的基本概念、運算及其在物理和幾何中的應用，隨後講述了泰勒展開式、數值方法、數項級數、函數項級數、三角級數，最後介紹了一些與振動有關的類型簡單的微分方程。
本書各章均提供了大量的例題和習題，其中一部分有相當的難度，但絕大部分是對內容的補充。另外，本書附有一本專門的習題冊，並且給出了習題的提示與解答。
本書適合於多種學科界的讀者，如數學工作者、科學工作者、工程技術人員等。
目次：預備知識；微積分學基本思想；微分法和積分法；在物理和幾何中的應用；泰勒展開式；數值方法；無窮和與無窮乘積；三角級數；關於振動的最簡單類型的微分方程；傳記材料目錄；索引。

Chapter 1 Introduction
1.1 The Continum of Numbers
1.2 The Concept of Function
1.3 The Elementary Functions
1.4 Sequences
1.5 Mathematical Induction
1.6 The Limit of a Sequence
1.7 Further Discussion of the Concept of Limit
1.8 The Concept of Limit for Functions of a Continuous Variable
Supplements
S.1 Limits and the Number Concept
S.2 Theorems on Continuous Functions
S.3 Polar Coordinates
S.4 Remarks on Complex Numbers
PROBLEMS
Chapter 2 The Fundamental Ideas of the Integral and Differential Calculus
2.1 The Integral
2.2 Elementary Examples of Integration
2.3 Fundamental Rules of Integration
2.4 The Integral as a Function of the Upper Limit (Indefinite Integral)
2.5 Lograithm Defined by an Integral
2.6 Exponential Function and Powers
2.7 The Integral of an Arbitrary Power of
2.8 The Derivative
2.9 The Integral,the Primitive Function,and the Fundamental Theorems of the Calculus
PROBLEMS
Chapter 3 The Technipues of Calculus
Chapter 4 Applications in Physics and Geometry
Chapter 5 Taylors Expansion
Chapter 6 Numerical Methods
Chapter 7 Infinite Sums and Products
Chapter 8 Trigonometric Series
Chapter 9 Differential Epuations for the Simplest Types of Vibration
List of Biograpical Dates
Index