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 larger than the very small intellectual elite of the early days. One of the greatest mathematicians of modern times,Leonard Euler, established in introductory books a firm tradition and these books of the eighteenth century have remained sources of inspira-tion until today, even though much progress has been made in the clarification and simplification of the material. presented as a unified.
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 x
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 Taylor's 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