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Calculus

4.50  ·  Rating details ·  806 ratings  ·  42 reviews

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rot

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Hardcover, Third Edition, 670 pages
Published January 1st 1994 by Publish or Perish (first published 1967)
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Average rating 4.50  · 
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 ·  806 ratings  ·  42 reviews


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Abhi Varma
Feb 22, 2014 rated it it was amazing
Many have said it before me, and allow me to say it again: this is the Calculus book. Yes, it really does start you off with (a + b) + c = a + (b + c), and then takes you through a nice variety of topics on a breathtaking journey through epsilon-delta proofs, axiomatic deductions and then inductions, the irrationality of pi, the transcendental nature of e, all sorts of sequences and series, and of course--the main 'body' of calculus that is the practice of integration and differentiation. It hol ...more
Jose Moa
Mar 01, 2016 rated it it was amazing
Shelves: science, mathematics
For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises.

Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of
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Mark Moon
Superb! A pleasure to read, and a pleasure to teach from. I wish I'd learned calculus from this book. Of all the excellent things about it, the best is the selection of exercises. They range from elementary ones useful for practicing the mechanical aspects of the subject to extremely challenging and abstract ones that connect the material in the book to more advanced concepts. ...more
Gavin Rebeiro
Sep 20, 2017 rated it liked it
I think the following needs to be said for someone who has never had any experience with calculus and wants to read this book:

1) If you are thinking of reading this book because you are attracted to its "pure" approach, learn some logic. Seriously, just get your head around what deductions are and what the principle of mathematical induction is. I recommend a Fitch-style natural deductive system. Spivak will teach you about calculus but if you don't have the prerequisite logic, you won't really
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Ilya Zarembsky
Jul 07, 2011 rated it it was amazing
Beautiful and merciless
Gal Barkai
Jun 30, 2016 rated it it was amazing
This is the book that turned me from an aspiring engineer to an aspiring Mathematician. It is well structured, clear and precises, it made me love the subject because for the first time I saw it presented for the logical wonder it is, and as an assortment of formulas to be used. Not to mention the generous margins for scribbling (a homage to Diophantus and Fermat perhaps) practically beg the reader to try his hand in proving the theorems and exercises stated in it.

I was extremely lucky to spot
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Ronald Lett
May 12, 2011 rated it it was amazing
Shelves: analysis
This is a beautiful exposition of the theory of calculus from the axiomatic approach with full motivation and proof of the major theorems and some interesting facts that are seldom presented at this level. The proofs and exercises are the most elegant that I have seen in any calculus text, as is Spivak's hallmark. All that is necessary is a solid understanding of high school pre-calculus and mathematical curiousity. As other posters have said, if you are going to be a mathematics or physics majo ...more
Parsa
May 05, 2018 rated it it was amazing
I first read this in high school. But it turns out that I didn't really understand it. Now that I'm done with first year university, I realize what a gem this book truly is.
Very well written, well motivated introduction to analysis, with good problems. I also absolutely love the little annotated bibliography near the end, which you can find here :
https://pctex.org/mathpop/wp-content/...
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Dmitri
Jun 14, 2012 rated it liked it
Shelves: math
Not really sure why so many people rate this book so highly. Apart from the gratuitous waste of page real estate there is also some confusing notation as well as an overall feel that is a lot more academic than practical.
Simon Mcleish
Jul 18, 2017 rated it it was amazing  ·  review of another edition
Shelves: owned
This review first appeared on my blog here.

Calculus was the very first textbook I read for my university degree. As well as being a fine description of the basics of analysis (mostly real, with a toe in the deep water of complex functions), it is an excelent book to ease the transition from mathematics as taught at school level to the rigours of university mathematics.

Unlike many writers of textbooks in mathematics, Spivak makes a big effort to give more than a dry exposition: theorem - proof -
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Ayush Bhat
Mar 05, 2017 rated it it was amazing
Love his VERY detailed treatment to the topic of Infinite Series.
Jesse
Mar 12, 2019 rated it it was amazing
This is the best math book I've ever read ...more
Alex
Aug 07, 2011 rated it it was amazing
A solid text and reference on the topic. Were I to want to re-learn calculus, I'd start here. ...more
Eric
Aug 04, 2019 rated it really liked it
Shelves: mathematics
Bought this particular textbook because of its connection with the Hampshire College Summer Studies in Mathematics program, if I remember (the index of this, or another, of Spivak's books has an in-joke listing for "Yellow Pigs", not a would-be counterculture insult but rather one of the two mascots of that program, along with the number 17.) As a general thing - it's been a long time since I read this textbook but I have good memories of it. ...more
Kent Sibilev
Jan 09, 2020 rated it it was amazing
It is a very good introduction to Calculus. Considering that this book is a bit old and consequently uses unusual notations, the explanations are extremely good and the author's approach reminds me of the best Leonard Euler's texts. ...more
Joe Richardson
Aug 22, 2020 rated it it was amazing
Shelves: 2020-top-10
There's nothing I can adequately say about this. Calculus explained lucidly. I didn't know that had every been done. This book makes you go from struggling in abstraction to realizing that the whole field is intuitive and useful. ...more
Samuel
Aug 29, 2018 rated it it was amazing
Shelves: math-misc, classic
Incredibly thorough and well written.
George Menegakis
By far the best introduction to calculus and real analysis
Cameron
Jul 25, 2020 rated it really liked it
can't go wrong with Spivak ...more
Faizan
Jul 31, 2020 rated it it was amazing
I had to study this book during my 1st semester of electrical engineering degree & it really was worth but excruciatingly difficult.
Ankit Ranjan
Sep 28, 2020 rated it it was amazing  ·  review of another edition
The calculus book I wish I had in high school.
Aryan Kumar Prasad
Dec 18, 2020 rated it it was amazing  ·  review of another edition
Shelves: acadmic
If a textbook have a simple name, its going to be tough and rewarding.
Henry Cooksley
Like putting an everyday object under a microscope: very interesting, but now there are many more interesting objects I want to put under a microscope.

One day I will return to Spivak's Calculus to complete all the exercises; the suggested reading offers some reassurance that readers who have got as far as completing all the exercises probably know a lot more about advanced mathematics (e.g. functional analysis) than is covered by this book. The reason for this is suggested by the final item of t
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K. P.
Mar 07, 2013 rated it it was amazing
Recommends it for: First-year or prospective mathematics majors
Recommended to K. P. by: Arunas Liulevicius
Simply the best of its kind. Single variable differential and integral calculus, presented with rigor and style.

Many calculus texts motivate the study of the material with physics problems. Spivak does not, although he does point out the applications. Rather, the development of the calculus here proceeds from mathematical considerations. Because of this, the book is certain to be useful to mathematics students--those approaching calculus for the first time, or those who wish to gain deeper insig
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Thomas
Aug 22, 2013 rated it it was amazing
This is a very good introduction to calculus and higher mathematics. Unlike most other calculus textbooks on the market, it does not burden the reader with mathematical topics that are inessential and at the same time it provides all the necessary tools in calculus to study other branches of mathematics. At the same time, the author proceeds at a leisurely pace and provides a lot of good calculus/analysis problems. As an aside, there is an answer book that enhances its value.
arash
Mar 20, 2007 rated it it was amazing
Shelves: arash
It is such a very very good and usefull book in Calculus course.solving its problems cause to understand the fandumenal concepts of calculus.It's a Berekley Univ book and it covers even Analysis(1). ...more
Tim
Apr 23, 2007 rated it it was amazing
A must have, in my opinion. Spivak's writing is casual and thoughtful while the exercises are unique and forward thinking. ...more
Michael
Aug 29, 2008 rated it it was amazing  ·  review of another edition
Shelves: math, nonfiction
This is really a beautiful book and it's clear that a lot of love went into every page. ...more
Jonathanstray Stray
By far THE BEST textbook I've ever read on any subject, and this one is teaching calculus. I don't know why there are any other (single variable) calc textbooks, this is the one. ...more
Alex
Aug 07, 2011 rated it it was amazing
A solid text and reference on the topic. Were I to want to re-learn calculus, I'd start here. ...more
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Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. He is the author of the five-volume Comprehensive Introduction to Differential Geometry. He received a Ph.D. from Princeton University under the supervision of John Milnor in 1964.

His book Calculus takes a very rigorous and theoretical approach to
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