Elementary Calculus (Classic Reprint)

PREFACE
This book is adapted to the use of students in the first year
in technical school or college, and is based upon t.he experIence
of the authors m teaching calculus to students ill the Massaohusetts
Institute of Technology immedIately upon entrance.
It is accordingly assumed that the student has had collegeentrance
algebra, mcludmg graphs, and 'an elementary course
In trigonometry, but that he has not studIed analytIC geometry.
The first three chapters form an introductory course ill
whICh the fundamental ideas of the calculus are introduced,
including derivatIve, dIfferential, and the definite mtegral, but
the formal work is restrIcted to that involvmg only the polynomial.
These chapters alone are well fitted for a short course
of about a term.
The defhution of the derivative is obtained through the
concept of speed, using familiar illustrations, and the idea
of a derivative as measuring the rate of change of relate(l
quantities is emphaSIZed. The slope of a cu

Table of Contents

CONTENTS; CHAPTER I RATES; SReTlON; 1 L1mits; 2 A verage speed; 3 True speed; 4 AlgeblalC method; 5 Accelel atwll; G Rate of change; CHAPTER II DIFFERENTIATION; 7 The dE'rivative; 8 Dlfrel'entlation of a polynomIal; 9 Sign of the derivative ; 10 Velocity and acceleratIOn (contmued); 11 Rate of change (contmued); 12 Gl'aphs; 13 Real roots of an equatIOn; 14 Slope of a stra1ght hne; 15 Slope of a curvE'; 16 The second derivatIve; 17 MaxIma and milllma; 18 Integration; HI Area; 20 Drfferentials; 21 AppIOXlmatwns ; General exercises ; CHAPTER III SUMMATION; 22 Area by summation ; 23 The definite integral; 24 The general BummatlOn problem; 25 Pressure; 26 Volume ; General exercises ;