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