A Tour of the Calculus

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Overview

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of ...

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A Tour of the Calculus

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Overview

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe.

"An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."—New York Times Book Review

In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity. Charts and graphs throughout.

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Editorial Reviews

Library Journal
Berlinski (Black Mischief: The Mechanics of Modern Science, LJ 2/15/86) presents an unconventional work on the foundations of calculus. It is in part an informal history of the subject, the author inrerweaves the historical fragments with expository sections that explain the concepts from a modern viewpoint. He gives special attention (very appropriately) to the concept of limits and to several of the fundamental theorems that underpin calculus. He also shows how differential calculus deals with rates of change and how integral calculus works to determine areas under curves. Writing in a breezingly informal style, the author includes a plethora of humorous asides as well as a number of clearly fictitious anecdotes. At times his prose gets a bit too ripe, but the overall effect is to make the book quite readable. The work should be especially useful for providing perspective to college and advanced high school students currently learning calculus. Recommended for all public and college libraries.-Jack W. Weigel, Univ. of Michigan Lib., Ann Arbor
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Product Details

  • ISBN-13: 9780679747888
  • Publisher: Knopf Doubleday Publishing Group
  • Publication date: 1/28/1997
  • Series: Vintage Series
  • Edition description: Reprint
  • Pages: 352
  • Sales rank: 359,314
  • Product dimensions: 5.16 (w) x 8.00 (h) x 0.70 (d)

Table of Contents

Introduction xi
A Note to the Reader xv
The Frame of the Book xvii
Chapter 1 Masters of the Symbols 3
Chapter 2 Symbols of the Masters 9
Chapter 3 The Black Blossoms of Geometry 16
Chapter 4 Cartesian Coordinates 21
Chapter 5 The Unbearable Smoothness of Motion 30
Chapter 6 Yo 35
Chapter 7 Thirteen Ways of Looking at a Line 40
Chapter 8 The Doctor of Discovery 44
Chapter 9 Real World Rising 54
Chapter 10 Forever Familiar, Forever Unknown 61
Chapter 11 Some Famous Functions 75
Chapter 12 Speed of Sorts 92
Chapter 13 Speed, Strange Speed 106
Chapter 14 Paris Days 118
Chapter 15 Prague Interlude 129
Chapter 16 Memory of Motion 155
Chapter 17 The Dimpled Shoulder 173
Chapter 18 Wrong Way Rolle 190
Chapter 19 The Mean Value Theorem 198
Chapter 20 The Song of Igor 217
Chapter 21 Area 244
Chapter 22 Those Legos Vanish 252
Chapter 23 The Integral Wishes to Compute an Area 268
Chapter 24 The Integral Wishes to Become a Function 274
Chapter 25 Between the Living and the Dead 282
Chapter 26 A Farewell to Continuity 304
Epilogue 311
Acknowledgments 313
Index 315
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Customer Reviews

Average Rating 4.5
( 8 )
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Sort by: Showing all of 8 Customer Reviews
  • Anonymous

    Posted July 8, 2006

    Before you pick up that textbook...

    ...read this book! Undoubtedly the best book on mathematics I've read. Hugely entertaining in its whimsical style. Read it if you want to know exactly WHY you are studying calculus.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted January 1, 2003

    Amazing book for anyone interested in math

    This book is for ANYONE interested in math. I am 14 and I LOVED this book. Now I am looking for some real calculus textbooks. A must read.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted September 13, 2000

    A Must Read

    I have read, and re-read 'A Tour of the Calculus' several times; each time gleaning something new are more subtle than the last. Berlinski has extracted and distilled the essence of the alculus, the continuum, and indeed that of 'real' numbers and functions. I was inspired by this book to revisit elementary analytic functions, this time from an elevated view. How function approximation leads to orthogonal function spaces to fourier series/transform (a special case) to wavelet transforms (the true general case). An outstanding work by Berlinski; at times I laughed out loud when reading the anectdotes, especial about the waiter in Prague - 'nicht da'. Doesn't exist... I heartily recommend 'A Tour of the Calculus'; if you don't find it enlightening and entertaining, you're probably a college professor at a public university :o).

    1 out of 1 people found this review helpful.

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  • Posted December 13, 2011

    Worst Book I Ever Read

    I LOVE math. But this book was more prose than interesting content.

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  • Posted August 13, 2011

    Phenomenally written

    As an old but devoted student of mathematics and science, I was easily drawn to this book by title and synopsis. Neither hinted at what a master of language, of storytelling, of visual creation Mr. Berlinski is. In addition to a wonderful tour, a revisiting of the calculus I enjoyed in my youth, he provided the gift of pleasurable excursions in history, biography, and philosophy. I was brokenhearted when the last page was turned.

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  • Anonymous

    Posted March 30, 2004

    Calculus BY a Poet?

    In college thirty years ago, I took a notorious 'gut' course, 'math for poets'. I never thought I would end up reading a book about math written BY a poet...Berlinski is absolutely fabulous, explaining the relationship between calculus and real world applications with great literacy and humor. Make no mistake - this book is NOT a simplification of calculus (I doubt such a thing would be possible). Rather, it is, as its title states, a 'tour', a fanciful, insightful, reasonably accessible introduction to calculus and an appreciation of its power and beauty. And that beauty is what this book is all about.

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  • Anonymous

    Posted March 31, 2012

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  • Anonymous

    Posted May 11, 2011

    No text was provided for this review.

Sort by: Showing all of 8 Customer Reviews

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