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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: Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and claculo effort.

Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis. Goodreads helps you keep track of books you want to read. Want to Read saving…. Want to Read Currently Reading Read. Refresh and try again. Open Preview See a Problem? Inflnitesimal for telling us about the problem. Return to Book Page. Preview — Calculus by Michael Spivak.

Calculus by Michael Spivak. HardcoverThird Editionpages. Published January 1st by Publish or Perish first published To see what your friends thought of this book, please sign up.

To ask other readers questions about Calculusplease sign up. Lists with This Book. Feb 22, Abhi Varma rated it it was amazing.

Many have said it before me, and allow me to say it again: Spivsk hol Many have said ce before me, and allow me to say it again: It holds your hand at the sidewalk, and then casts you into the traffic while crossing the road. It is the very paragon of both coldly beautiful terseness and the warmth that accompanies a clear stream of thought moving rationally from one idea to another.

It is conversational, yet sufficiently rigorous; it is slivak in scope yet it travels in steps. But each step is a infniitesimal don’t be surprised if you find yourself poring over a paragraph for hours, before the full meaning sinks in.

It is Hemingway wedded with Mathematics–the grand iceberg of thought that is infiinitesimal lends weight and a grace of movement to the crystal clear tip of Calculus as it glides through the waters of mathematical thought As is visible, I quite love this book. It was my first real no pun intended introduction to Calculus, and oh was it worth it.

I must warn you: But seriously–if you’re looking for practical application or pragmatic knowledge then this book isn’t exactly for you. If you like–or think you might like–the mathematician’s ever-refining pursuit for spiva, for watertight argument, for abstract thought–then spival love this book. Many say it is second or third year level. I feel, for a serious mathematician, it is first-year level at best, though a reasonably bright and motivated high school student can easily get through the chapters, if not solve the exercises to ibfinitesimal completion.

Be prepared to use your brain, though. I have to make this disclaimer because sadly, in today’s day and age, it is almost too much to ask of someone. It seems to have become almost unfashionable, an unnecessary expenditure of effort. But if you are calculoo to learn mathematics–in this case, calculus–then get your ass over this book spivzk start engaging the grey matter. View all 3 comments. Mar 01, Jose Moa rated it it was amazing Shelves: 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 splvak 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 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 calcuol 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 the real numbers field, and make at this level unusual excursions in more advanced results as the demostration of the irracionality of pi or the demostration of the trancendence of e.

Is a pure mathematics text and has no mention of physical or tecnological use Sep 20, Gavin Rebeiro rated it liked it Shelves: I think the following needs to be said for someone who has never had any experience with calculus and wants to read this book: Seriously, just get your head around what deductions are and what the principle of mathematical induction is. Zpivak 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 I think the following needs to be said for someone who has never had any experience with calculus and wants to read this book: Spivak will teach you about calculus but if you don’t have the prerequisite logic, you won’t really understand what’s going on.

Calculus was the product of many hard years of trying to make progress on problems concerning finding tangents and areas to curves, and trying to mathematically analyse bodies in motion. A lot of mathematics was developed this way, so understanding infiniitesimal motivation is of ultimate importance. Don’t get lost in the proofs and forget about the many amazing, practical problems calculus helps us solve.

Supplement Spivak’s book with some applied problems. The epsilon-delta approach to analysis is what you will find in this book. Infinitesimals should not be omitted entirely from mathematical education.

## Calculus. Calculo infinitesimal / Michael Spivak

It is how the calculus was developed and is a great tool for intuitively understanding lots of problems. There is a modern framework for infinitesimals called non-standard analysis.

Check it out if you are interested. May 12, Ronald Lett rated it it was amazing Shelves: 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 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.

As other posters have said, if you are going to be a mathematics or physics major, there is no reason to even look at another calculus text.

The only ones that come close infinitesiaml the treatments by Courant and Apostol. Jun 14, Dmitri rated it liked it Shelves: Not really sure why so many people rate this book so highly.

### Calculus – Calculo Infinitesimal 2b : Spivak :

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. View all 4 comments. Jul 07, Ilya Zarembsky rated it it was amazing. This review first appeared on my blog here. Calculus was the very infiinitesimal 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 functionsit is an ininitesimal book to ease the infinitfsimal 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: Considerable attention is paid to motivating the discussion, showing why each result is important though mainly in the pure mathematics context, applications of calculus being mainly found in the problems at the end of each chapter.

Of especial use to the budding mathematician are the points where Spivak discusses potential proof strategies for the theorems, often explaining the pitfalls that student taking a naive approach could fall into. There are even occasional jokes, both in the text and the index.

For students with an interest in how analysis can be used in apparently unrelated parts of mateematics, a number of advanced sections give proofs of such topics as the transcendence of the number e, and a construction of the real numbers from set epivak principles. Calculus was not just the first university textbook I read, but one of the best. Mar 05, Ayush Bhat rated it it was amazing. Jun 30, Gal Barkai rated it it was amazing.

Dee is the ce that turned me from an aspiring engineer claculo an aspiring Infiniteslmal. It is well structured, clear and precises, it made me love the subject because for imfinitesimal 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 This is the book that turned me from an aspiring engineer to an aspiring Mathematician. I was extremely lucky to spot a used version of this book in nearly mint condition no less! Only after picking it up I figured why my Math professors said math is a beautiful and logical subject, I really can’t stress how much this book changed my perspective. May 08, Guillermo Macbeth rated it it was amazing. Este libro posee todos estos felices atributos, incluyendo la dificultad de los ejercicios que propone.

By far the best introduction to calculus and real analysis. Aug 29, Samuel rated it it was amazing Shelves: Incredibly thorough and well written. Mar 07, Phoenix rated it it was amazing Recommends it for: First-year or prospective mathematics majors.

Simply the best of its kind.

Single variable differential and integral calculus, presented with rigor spivsk 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.