A Tour of the CalculusWere 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 
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LibraryThing Review
User Review  TheDivineOomba  LibraryThingThis is book that started of interesting, between the calculus theories, and the stories told, but than the book started going into complicated math theories, that made my brain recoil in an attempt to understand, I gave up. Read full review
LibraryThing Review
User Review  br77rino  LibraryThingLike the 4 other reviewers here have said: too wordy. There is poetry in calculus, but not this much. Still, there are little gems scattered around making it sort of worthwhile. But this is no "Journey Through Genius." Read full review
Contents
10  
chapter  16 
chapter  22 
The Unbearable Smoothness of Motion  30 
Thirteen Ways of Looking at a Line  41 
Real World Rising  54 
Forever Familiar Forever Unknown  61 
Some Famous Functions  75 
Wrong Way Rolle  190 
The Mean Value Theorem  198 
The Song of Igor  217 
Area  244 
Those Legos Vanish  253 
The Integral Wishes to Compute an Area  268 
The Integral Wishes to Become a Function  274 
Between the Living and the Dead  282 
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Common terms and phrases
affirms algebra antiderivative antidifferentiation appears area underneath argument average speed axis c h a pter calculus Cartesian coordinate system Cauchy century clock comes concept connection coordinate axis Dedekind defined definite integral derivative Descartes difference differentiation distance elementary functions equation Euclidean geometry existence exponential functions expressed f is continuous fact falling object familiar finite formula fractions func function f fundamental theorem Galileo's law Hafez the Intelligent idea identity Igor imagine infinitely instantaneous speed intellectual irrational numbers Leibnitz limit logarithmic look mathe mathematical mathematician matician mean value theorem natural numbers Newton notation polynomial position function precisely rational numbers real numbers real world realvalued function rectangles represent reveals Riemann Rolle's theorem secant lines sense sequence simply slope space square root straight line strange subinterval suggests symbols takes things tion trigonometric functions underneath a curve underneath the curve velocity Waldburger