Calculus - Fourth Edition


How much do I want to read more? 7/10

I like maths when it starts from scratch, so simple on every step, to reach the complex.
This is very well explained, and rigorous.


PREFACE

Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics.
In addition to devel- oping the students' intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.

Since the most exciting concepts of calculus do not appear until Part III, it should be pointed out that Parts I and II will probably require less time than their length suggests—although the entire book covers a one-year course, the chapters are not meant to be covered at any uniform rate.
A separate answer book contains the solutions of the other parts of these problems, and of all the other problems as well.

PART 1 - PROLOGUE

CHAPTER I BASIC PROPERTIES OF NUMBERS

addition and multiplication, subtraction and division, solutions of equations and inequalities, factoring and other algebraic manipulations—are already familiar to us.
Despite the familiarity of the subject, the survey we are about to undertake will probably seem quite novel; it does not aim to present an extended review of old material, but to condense this knowledge into a few simple and obvious properties of numbers.

(PI) If a, b, and c are any numbers, then:
a + (b + c) = (a + b) + c.

(P2) If a is any number, then:
a + 0 = 0 + a — a.

(P3) For every number a, there is a number —a such that
a + (— a) = (—a) + a = 0.