內容大鋼
R.庫朗、F.約翰著的《微積分和數學分析引論(第1卷)(英文版)》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，但絕大部分是對正文內容的補充。
目錄
Chapter 1 Introduction
1.1 The Continuum of Numbers
a. The System of Natural Numbers and Its Extension. Counting and Measuring
b. Real Numbers and Nested Intervals
c. Decimal Fractions. Bases Other Than Ten
d. Definition of Neighborhood
e. Inequalities
1.2 The Concept of Function
a. Mapping-Graph
b. Definition of the Concept of Functions of a Continuous Variable. Domain and Range of a Function
c. Graphical Representation. Monotonic Functions
d. Continuity
e. The Intermediate Value Theorem. Inverse Functions
1.3 The Elementary Functions
a. Rational Functions
b. Algebraic Functions
c. Trigonometric Functions
d. The Exponential Function and the Logarithm
e. Compound Functions,Symbolic Products, Inverse Functions
1.4 Sequences
1.5 Mathematical Induction
1.6 The Limit of a Sequence
1.7 Further Discussion of the Concept of Limit
a. Definition of Convergence and Divergence
b. Rational Operations with Limits
c. Intrinsic Convergence Tests. Monotone Sequences
d. Infinite Series and the Summation Symbol
e. The Number e
f. The Number r as a Limit
1.8 The Concept of Limit for Functions of a Continuous Variable
a. Some Remarks about the Elementary Functions
Supplements
S.1 Limits and the Number Concept
a. The Rational Numbers
b. Real Numbers Determined by Nested Sequences of Rational Intervals
c. Order, Limits, and Arithmetic Operations for Real Numbers
d. Completeness of the Number Continuum. Compactness of Closed Intervals. Convergence Criteria
e. Least Upper Bound and Greatest Lower Bound
f. Denumerability of the Rational Numbers
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
Chapter 3 The Techniques of Calculus
Chapter 4 Applications in Physics and Geometry
Chapter 5 Taylor' s Expansion
Chapter 6 Numerical Methods
Chapter 7 Infinite Sums and Products
Chapter 8 Trigonometric Series
Chapter 9 Differential Equations for the Simplest Types of Vibration
List of Biographical Dates
Index
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