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Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, Medieval contributions and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.
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Customer Reviews (12)

Propaganda history
This is not a history of the calculus, but rather a profoundly biased and small-minded quasi-history of its foundations. Boyer kneels before the modern theory of the foundations of the calculus with religious awe, and crusades on its behalf with exceptional arrogance and obliviousness to reason. The purpose of a history of the calculus, according to Boyer, is apparently to condemn the infidels for their "misapprehension ... as to the logical basis of the calculus" (p. 8). His so-called "history" is in reality a thinly veiled sermon on the sins of the "logically unsatisfactory" (p. 4) and the "logically irrelevant" (p. 8).

Newton and Leibniz are chastised because they "did not fully recognize the need" for "the rigorous formulation of the concepts involved" (p. 47) and "were insensible to the delicate subtleties required in the logical development of the subject" (p. 5). To any sane person these historical facts show that there was in fact no such "need" and that Boyer's favourite "subtleties" were in fact not "required" at all. But not so to Boyer, who apparently considers his own intellect so superior that he has nothing to learn from Newton and Leibniz.

For a more specific illustration of Boyer's simplistic and dogmatic mindset, we may consider his appraisal of Berkeley's "objection to Newton's infinitesimal conceptions as self-contradictory" as "well taken" and "pertinent" (p. 226). Here it is useful to make a comparison with complex numbers (as Leibniz himself suggested, p. 215). The rules for discarding infinitesimals do not prove that infinitesimal calculus is self-contradictory any more than the fallacious reasoning that -2 = Sqrt(-2)Sqrt(-2) = Sqrt((-2)(-2)) = Sqrt(4) = 2 proves that complex numbers are self-contradictory. In both these cases, all that is shown is that these new entities do no obey all the laws of ordinary numbers. But no one ever claimed that they should, so there is nothing "self-contradictory" or "logically unsatisfactory" about either of these situations, as is obvious to anyone who, unlike Boyer and Berkeley, is not blinded by dogma.

A little technical on the historical side...
Boyer is a historian of mathematics, and I have his larger history text, which I like much better. I honestly expected a history of the calculus to be more of a fascinating read. The author does an excellent job of taking you through some of the finer points of this history and reasons why, for example, Archimedes should not be given credit for discovering the calculus, but why there is some justification for such a claim. The thing is, these finer points of the history are mentioned quite frequently even with regard to mathematicians whom I have never heard of. It seems that someone is always saying that so-and-so really discovered the calculus, and Boyer always points out why in fact they did not. The writing also can be rather verbose at times (this is sometimes entertaining). I do not see this text as appealing to a lay reader with an interest in the history of one of the greatest intellectual acheivements of all time: the calculus. I see this as appealing more to historians of mathematics or other such related fields. I started this book twice, and the second time, I made it about three fifths of the way through. It's hard to read a lot at once. It's a history book, not a book about the history. There are a fair amount of diagrams, and the math is interesting, if at times confusing, to follow. I can't say that my understanding of calculus is much deeper after reading the majority of the book, though it certainly does have a larger and more technical context.

More history, less real mathematics?
Only two things made me give the bookbetter than two stars:
the idea of an error term to:
d(x^n)/dx=n*x^(n-1)+error(f(x,n)).
And the mention of harmonic triangle:
t(n,m)=1/(n*Binomial[n,m])
The question of what would mathematics be like without Leibniz and Newton
and calculus really takes us back to what mathematics was like in 1600:
geometry, algebra and number theory. That mathematics had such a great part in the industrial revolution by making physics, a science based mainly on derivative calculus, makes me think that we would have sailing ships and horses still.
The fact that he pretty much leaves out fractional calculus is another
strike against him presenting a true history of calculus.

Mildly instructive
but atrociously written: this book is an epitome of the shift/reduce conflict -- some paragraphs defy parsing altogether. Overall OK if you're into calculus to the point of worrying about its history or if you want to get to understand how, and even more why it came about. Although the hows definitely prevail over the whys here, unfortunately. The book is far from flawless, but still, if you can get through the stultifying writing, it will enlarge somewhat your overall conceptual view of calculus. Recommended? Perhaps. If you have time.

Fascinating material, questionable presentation
The first thing I noticed about this book is that it is written with an intellectually arrogant, indecipherable style which (I hope) would today prevent its being published at all.Here is a paragraph, verbatim, from the introduction:

"At this point it may not be undesirable to discuss these ideas, with reference both to the intuitions and speculations from which they were derived and to their final rigorous formulation.This may serve to bring vividly to mind the precise character of the contemporary conceptions of the derivative and the integral, and thus to make unambiguously clear the terminus ad quem of the whole development."

I admit that back in 1939, when this book was originally written, it was common for academics to express themselves in that sort of haughty, impenetrable prose.But that doesn't make it any easier to read today, and it doesn't really provide those people with an excuse for having written that way.Didn't it occur to them that their writing might be read by real human beings?There are plenty of mathematical writers today who can write in real English without sacrificing rigor or depth.

Secondly, I recommend that everyone read the review by the reader from Phoenix (February 7, 2001).In particular, I agree with the criticism that this book takes a backwards approach to the history of Calculus, interpreting each historical idea and contribution in terms of the way we think of those ideas today.As Boyer certainly should have known, the proper way to relate the history of ideas is to place each idea in the context of its own time.Instead, he writes this book as if each ancient mathematician had tried and failed to reach the level of understanding which we superior moderns are now gifted with.I think it is important for a reader to read this book with this defect clearly in mind.

Having got those two criticisms off my chest, however, I have to admit that there is a wealth of interesting material in this book, and I don't know of any other place where it is all gathered together in one volume.If you want a detailed, in-depth account of how mathematicians and philosophers (they used to be the same people!) eventually evolved the ideas and methods of calculus, then this book is probably the best place to find it.

(I just wish the publisher would hire someone to translate it into real English!) ... Read more

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Customer Reviews (16)

not good....
This book is poorly written. In fact, considering that its subject is most likely to be chosen by discriminating readers, it is so bad that I am surprised it made it into print. Among many other faults noted by other reviewers, most jarring to me is the way the author continually yanks the reader from the 17th century into the present by making reference to something that he'd recently seen or done. That may be the fault of the author, or of his editor, or both; regardless, it gives the book a wildly alternating tone and perspective. Both the author and the editor should feel embarrassed at having produced this shoddy work.

Please avoid this pomposity, at all costs!
If you've read the reviews that preceded this, you probably have an idea of how disastrously this book has been edited. I will add only that which hasn't been mentioned in other reviews, which is my two cents.

I must say that I only finished this book to give the author the benefit of doubt, after fuming over the many typos, disgustingly careless grammar, factual errors and irreverent first-person comments. I'm sorry to say it wasn't worth the effort.

Before sounding like a gripe, let me tell you what this book is good for. If you like reading your history as a smattering of tidbits within the confines a specific social context, in this case the lives of two prominent scientists at the turn of the 18th century, this is worth skimming over. At best, it is a slightly precocious commentary, and at worst it has the pretentions of being an analysis, with random, irrelevant and condescending first-person accounts thrown in. Worse still, in the epilogue, we are made to feel that Bardi is really modest as he claims to be embarassed by a friend's comments regarding his expertise on the subject.

There are questions that arise out of the subject matter, however, and relevant ones. The overarching one is whether the introvert inventor or the original but flambuoyant expositor gets the credit for an issue as thorny as the invention of Calculus? If this was the question Bardi set out to answer in his book, he should have realized that a chronological biographical sketch with some seemingly relevant characters thrown in would be insufficient.

There is no level of detail regarding the mathematics here. This is disdainful, and only shows how much regard even a science writer has for the subject, or was he perhaps muffled by his very competent publishers? I tend to lean away from the latter explanation because even the verbal treatment of the mathematics is shamefully cursory. A case in point is the description of the brachistochrone problem, infamous in the calculus of variations. How is one to understand the gravity (sic) of the problem if one doesn't quite follow what has led up to it? Merely mentioning that it was a Leibniz challenge is like conjuring a rabbit out of a hat.

It is one thing to avoid equations, lest the audience feel they are talked down to, but another thing altogether to use mathematical symbols for the purely decorative, as the equations in the illustratitive section have done. They have no explanations, no context whatsover, provide no insight to those who are unfamiliar with Calculus, and tautological to those who are. Instead of pulling out pages from text and rendering them unreadable in fine print even the briefest description of Newton's explanation of rainbows would have sufficed. Equations could have been in the body of the text, and where relevant, at the very least.

A discussion about Calculus necessiates a discussion about the tools and the formalism, and even if Bardi wished to avoid excessive technicality, he could have done what most good science journalists do, which is to collate and quote opinions from folks who are well-versed in the mathematical subtleties.

There are a few instances when Bardi stoops from his pedestal to do just this, and those are the few slivers of salvation this book offers. At one point (page 130), he quotes a balanced review of the Pricipia, and mentions how it lauds Newton's geometry but not his physics, since Newton is to have famously declared that 'I do not invent hypothesis' [for gravity]. At another (page 207), Bardi quotes Johann Bernuolli's defense of Liebniz when he mentions that Newton didn't quite demonstrate his method of fluxions in the Principia when he had ample chance to do so, but dogmatically stuck to the geometrical style of his predecessors.

The first case was interesting because it echoes something of Edwin Hubble's attitude regarding his data for receding galaxies. He apparently refused to interpret what his data implied, even if it favoured something like the Big Bang. From a philosophical standpoint such extreme empericism must have indeed looked bizzare and rattled Leibniz in his time, as it did contemporary astronomers.

The other instance, involving Bernuolli's commentary, is somewhat more illuminating of Newton's character. It is an irony that Newton avoided his method of fluxions (perhaps embittered by Hooke's criticism) in the Principia so it would be widely understood, and Leibniz introduced the formalism of Calculus so that it would be widely used to solve a broad class of problems. While Newton's approach was to introduce his concepts of motion and gravitation using existing geometrical tools, looking backward, Leibniz's was to introduce a generic technique of solving infinitesimal problems, complete with a set of tools and it associated new symbols, moving forward. As testimony to the latters vision, we still use his symbols today. In this sense, contrary to the review of the Principia from long ago, Newton was really original in his physical insight about gravitation while Leibniz had the vision to understand that the scope of Calculus was much wider, and not just restricted to gravitation.

The redemption factors are not able to salvage the book, alas. It remains balanced but shallow, and goes to show that however well a book may be researched, an interesting narrative is one where the assimilation is almost invisible, and in a way that inspires meaningful questions. To this end, even an exhaustive bibliography still remains a means, not an end.

Just okay, borrow from library
The author presents a less technical account of the development of the calculus and the acrimony between Newton and Leibniz later in their lives.Other reviewers here have noted many of the deficiencies of this book editorially; I completed the entire book, and have the following additional criticisms.The "warring" part of the book is only about the last 20%.While the author has done his research, in his presentation I detect only a superficial scholarship that suggests a post-modern, blasé approach to describing the topic. (A reader might get a slightly more engaging account of Newton and Leibniz in Neal Stephenson's "Quicksilver", but there again you have to slog through hundreds and hundreds of pages of post-modern writing).

Beyond the vast amount of editorial mistakes, in one instance the author also seems to have confused the Balkan peninsula, the Iberian peninsula, diplomacy, politics and wars in these areas, etc. with his mention of "France would indeed eventually invade Egypt under Napoleon, who grasped the value of the peninsula..."Finally, there are serious instances where the author's personal opinion has no place in the text.

Overall, it is an okay effort, but more serious readers might best go elsewhere.

Heavy on Biography, Light on the Origins of Calculus
Students of mathematics at the calculus level and beyond are usually made vaguely aware that, despite some minor historical contention, Isaac Newton is credited for the discovery of calculus. Fewer in number are those who learn the name Gottfried Wilhelm Liebniz as Newton's rival claimant for that honor, and still fewer are those who are informed that Newton's methods of fluxions and fluents were almost immediately abandoned in favor of Liebniz's differentials and his superior mathematical notation (essentially that still in use today).

Author Jason Bardi aims to correct that knowledge shortfall in THE CALCULUS WARS: NEWTON, LIEBNIZ, AND THE GREATEST MATHEMATICAL CLASH OF ALL TIME. The use of the word "wars" and the hyperbolic phrasing "greatest clash of all time" set the expectations stage for an epic battle of intellectual giants as potentially juicy as 20-year-old Evariste Galois's fatally romantic duel with pistols. The historical facts are rather less sensational, however, consisting largely of letters and journal articles (most submitted anonymously at the time) hurling nationalistic accusations, often petty or unfounded, from one side of the English Channel to the other. As a result, Mr. Bardi struggles to deliver the implicit drama: there is no critical face-off between the principals, no momentous debate (even the British Royal Society largely shrugs it off thanks to Newton's presidency of that august body), no climactic moment when the truth is laid bare.

Perhaps more disconcerting, the vast majority of Bardi's book is not about calculus at all, not about the battle over its discovery, its historical underpinnings, or its subsequent development along the lines of Liebniz's work. We never see a comparative representation of the Newtonian and Liebnizian models, their notational differences, or their intellectual geneses from the mathematical work of their predecessors (Archimedes' famous method of exhaustion, for example, receives just one passing mention). Instead, the author falls back on the more conventional approach of chronological biography, trailing the two men's parallel lives from 1642 to 1728. It could certainly be argued that their respective biographies give important background to their personalities and professional status when the "calculus wars" finally broke out in 1699 (175 pages into Bardi's 250-page book). However, Bardi writes extensively on Liebniz's silver mining schemes, invention of a leather folding chair and a new type of windmill, promotion of binary numbers, theories of planetary motion and theology, political machinations, court genealogical work, and studies of China, to name a few. Similarly with Newton, it is his optics, theories of universal gravitation, stewardship of the British Mint, dabblings in alchemy, psychological mood swings, even his sexual orientation.

In the end, Bardi sides with Liebniz as the more aggrieved party, clearly innocent of the charges of plagiarism. Newton is clearly the loser in this "war," both for hoarding his great discovery to the detriment of fellow scientists and mathematicians and for treating his Continental contemporaries with such disdain. Sadly, the entire affair did nothing to polish the honor of either man.

Bardi's storytelling prose is fluid and well suited to his task, with one significant exception. In a tale of dueling mathematical, scientific, and intellectual giants, one inserts oneself at the greatest of risks. Perhaps a Stephen Hawking could merit an occasional authorial "I" in this story, but decidedly not a Jason Bardi (despite his ostentatiously displayed middle name, Socrates, that ironically only emphasizes the disparity). Author Bardi is given to repeated, utterly trivial, and mostly parenthetical insertions of his own opinions that are presumptuous, irrelevant, and distracting: "When I was in London, I noticed..." , "...an event I like to call..." , "I get this picture when I think about it..." ,"...as I recall from my encounter..." , "For my part, I can't help but wish..." , "a docent told me..." , "I examined..." , "...I have read..." , "I examined... [again]" , culminating with the irrepressible "I'm not surprised, really" and the exquisite "For me, what's really interesting... " Every one of these first person insertions should have been removed by a more exacting editorial pencil.

I approached this book hoping to discover a comparative treatment of the origins and development of Newton's and Liebniz's twin lines of calculus development, to learn how two intellectual giants of the 18th Century each separately made a conceptual mathematical leap nearly on a par with Einstein's leap to relativity. The similarities and differences in their developmental threads would surely be part and parcel of the historical argument over rights of discovery and accusations of plagiarism. Regrettably, I found instead seemingly endless pages of biographical minutiae about everything else in these two great men's lives.

Proofreading Errors Are Too Distracting
When I received the book, I began reading the section "Bibliographical Essay" and encountered ten proofreading errors in nine pages.I found this too distracting to continue, and I lost trust in whatever scholarship was used in the preparation of this book.There is no excuse for such carelessness.If I were the publisher, I would be embarrassed. ... Read more

Product Description
Shortly after the invention of differential and integral calculus, the calculus of variations was developed. The new calculus looks for functions that minimize or maximize some quantity, such as the brachistochrone problem, which was solved by Johann Bernoulli, Leibniz, Newton, Jacob Bernoulli and l'Hopital and is sometimes considered as the starting point of the calculus of variations. In Woodhouse's book, first published in 1810, he has interwoven the historical progress with the scientific development of the subject. The reader will have the opportunity to see how calculus, during its first one hundred years, developed by seemingly tiny increments to become the highly polished subject that we know today. Here, Woodhouse's interweaving of history and science gives his special point of view on the mathematics. As he states in his preface: ``Indeed the authors who write near the beginnings of science are, in general, the most instructive; they take the reader more along with them, show him the real difficulties and, which is the main point, teach him the subject, the way they themselves learned it.'' ... Read more

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Customer Reviews (14)

It is by Dunham ...
... and it is about calculus. I think no more needs to be said. Again for people interested in math - Dunham is one of the best writers. For parents of young children - read these books before you start teaching them. They will help you be better teachers.

Dunham's book is a winner!
Some authors try to explain calculus to the literati with the hope of enlightening them a bit.They apologize at the inclusion of an equation, and wave hands like magicians.That's OK, for the innumerate.But the result is invariably like reading Julia Child's recipes and not cooking any of her meals.Not so William Dunham.The only way to appreciate the masterpiece that calculus really is, is to know your basic mathematics, and then plunge into such a book as his.
This is a great book for students of mathematics.By following the counterexamples that mathematicians themselves create in order to test their own inventions (such as the Riemann integral), Dunham does better than most in showing us how tough the trek is to understanding.We feel the sense of humility that this handful of men develop in the face of the utterly unknown.
And he gives us the sense of how unknown the frontier truly is in mathematics, because Cantor, for instance, cannot just build a better telescope and discover a new theorem.It's all done in the mind, many times in response to the needs of the sciences (e.g., Fourier), but ultimately, it's in the minds of these incredible men.
Thus, well done, William Dunham!But if all you can read is Dickinson and Joyce, then you cannot appreciate this book.

William Dunham in his elemens!!!
If you have read William's Dunham's " Journey through Genius ", "Euler,The Master of Us All", there is no need to add anymore praise to this book,just buy it and enjoy it!!!

Calculus is Good but Hard!
Well worth the effort!The beginning is easy (but very informative) if you've had college level differential and integral calculus.Then there's Cantor and Lebesgue!!Tough going, but very satisfying!

Pete

Another masterpeice by William Dunham
If you enjoyed "Journey through Genius" by the same author, you will also enjoy the present volume. It requires more math knowledge (at least a working knowledge of calculus), but the level is aimed at a bright high school AP student, or a college undergraduate I would recommend it for even serious mathematicians who would like to know more about how the present state of knowledge of analysis came about. I would especially recommend it for teachers and students of calculus. Too often, ideas which took literally centuries to mature are presented in finished form, as if some mathematician sat down one day and wrote out finished, rigorous theorems. Seeing how even venerable mathematicians like Newton and Cauchy got results without the rigour which we see as necessary today is an eye-opener, and should be an encouragement to experiment and "learn by doing", and not to be afraid to go boldly forth, even if you haven't dotted all the "i" and crossed all the "t". ... Read more

Product Description
This is a lucid account of the highlights in the historical development of the calculus from ancient to modern times from the beginnings of geometry in antiquity to the nonstandard analysis of the twentieth century. It emphasizes the genesis and evolution of both fundamental concepts and computational techniques. The intended audience includes not only students of the history of mathematics, but also the wider mathematical community, specifically those who study, teach and use calculus. Among the distinctive features of this exposition are historically motivated exercises and carefully chosen illustrative examples. Numerous sections of the book are suitable for use in courses in introductory and advanced calculus as well as the general history of mathematics. ... Read more

Customer Reviews (1)

Useful resource, but dry and incomplete
The historical path is often more sensible than modern textbooks, as we see here in numerous cases: the logarithm should be understood as the area under the hyperbola y=1/x, Taylor series should be understood in terms of the Gregory-Newton interpolation formula, etc. But if there is one lesson history should teach calculus textbook authors it is this: power series. Power series were always indispensable and inseparable from the calculus at every stage of the development. Modern authors shoot themselves (and their students) in the foot by postponing power series as far as possible. Euler, in his Introductio, beautifully derives the derivatives of the elementary functions by power series methods, which is neat and systematic and makes use of concepts of great power and scope. By contrast, modern authors, suffering from rigour hiccups, insists that these derivatives must be deduced from "the definition" of the derivative, using horrendously ad hoc limit-manipulation tricks. This book is useful and certainly much better than Boyer's awful book, but it is still very far from being a satisfactory history of the calculus. In particular there is no physics, which is of course utterly absurd if it is to be a true history of the calculus. Also, it treats only the very basics of the calculus, essentially ignoring differential equations, several variables, the calculus of variations, etc. ... Read more

Product Description
This book describes the development of what we would now regard as a class of statistical fitting procedures between 1750 and 1900. The book contains detailed algebraic descriptions of the fitting of linear relationships by the method of least squares and the closely related least absolute deviations and minimax absolute deviations procedures. The prerequisite is a basic course in mathematical statistics. The primary audience for this book will be statisticians concerned with the fitting of linear models. However, it will also be of interest to engineers and scientists concerned with the empirical determination of linear relationships. ... Read more

Product Description
Webster's bibliographic and event-based timelines are comprehensive in scope, covering virtually all topics, geographic locations and people. They do so from a linguistic point of view, and in the case of this book, the focus is on "Calculus," including when used in literature (e.g. all authors that might have Calculus in their name). As such, this book represents the largest compilation of timeline events associated with Calculus when it is used in proper noun form. Webster's timelines cover bibliographic citations, patented inventions, as well as non-conventional and alternative meanings which capture ambiguities in usage. These furthermore cover all parts of speech (possessive, institutional usage, geographic usage) and contexts, including pop culture, the arts, social sciences (linguistics, history, geography, economics, sociology, political science), business, computer science, literature, law, medicine, psychology, mathematics, chemistry, physics, biology and other physical sciences. This "data dump" results in a comprehensive set of entries for a bibliographic and/or event-based timeline on the proper name Calculus, since editorial decisions to include or exclude events is purely a linguistic process. The resulting entries are used under license or with permission, used under "fair use" conditions, used in agreement with the original authors, or are in the public domain. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
Webster's bibliographic and event-based timelines are comprehensive in scope, covering virtually all topics, geographic locations and people. They do so from a linguistic point of view, and in the case of this book, the focus is on "Calculus," including when used in literature (e.g. all authors that might have Calculus in their name). As such, this book represents the largest compilation of timeline events associated with Calculus when it is used in proper noun form. Webster's timelines cover bibliographic citations, patented inventions, as well as non-conventional and alternative meanings which capture ambiguities in usage. These furthermore cover all parts of speech (possessive, institutional usage, geographic usage) and contexts, including pop culture, the arts, social sciences (linguistics, history, geography, economics, sociology, political science), business, computer science, literature, law, medicine, psychology, mathematics, chemistry, physics, biology and other physical sciences. This "data dump" results in a comprehensive set of entries for a bibliographic and/or event-based timeline on the proper name Calculus, since editorial decisions to include or exclude events is purely a linguistic process. The resulting entries are used under license or with permission, used under "fair use" conditions, used in agreement with the original authors, or are in the public domain. ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Product Description
This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame. The book develops calculus, as well as the necessary trigonometry and analytic geometry, from witin the relevant historical context, and yet it is not a textbook in the history of mathematics as such.The notation is modern, and the material is selected to cover the basics of the subject.Special emphasis is placed on pedagogy throughout. Whhile emphasizing the broad applications of the subject, emphasis is placed on the mathematical content of the subject. ... Read more

Customer Reviews (13)

Severely lacking in practicality...
I agreely wholeheartedly with the reviewer who called this a "Calculus Appreciation" textbook.It includes lengthy histories of the theories and processes highlighted in the chapters, but completely fails to elaborate on them or provide thorough proofs or adequate examples and explanations.There are also absolutely no answers whatsoever to the practice problems; it's impossible to check/verify one's understanding of the material with this book.For all practical purposes... useless, in my opinion.

A Website for Hahn's Basic Calculus
Basic Calculus: From Archimedes to Newton to Its Role in Science
is a beautifully done text.It is very clearly written and
logically organized, tracing the development of calculus with
many interesting examples from the physical world and man's
quest to understand the physical world.The text is concise
and so readily understood as to be elegant.Finally, all of the
solutions to the exercises are given at Professor Hahn's internet
site.Its address is www.nd.edu/~hahn/One way to remember the
website is that the letters "nd" are for Notre Dame, where Dr. Hahn teaches.

A Wonderful Introduction to Calculus
What this book is not is a traditional calculus text. It covers a lot of traditional topics, but not in a familiar way. It is not terribly rigorous, nor does it need to be. It is designed to fill the first two semesters of calculus. There are a LOT of books that do this in the traditional way, that is they scare the life out of the student :-). It is my belief that this book will take a lot of the mystery out of calculus, since it develops the subject in the context of applications. I also think that most students will find the approach engaging. There are plenty of practice problems at the ends of the chapters, and some are quite challenging.

The focus of this book is not to present calculus as a theory, a thing which most students are simply not prepared for at this level. Rather it is to present calculus as the pragmatic development of methods to solve certain classes of problems. In this regard it does a fantastic job. Along the way the students's algebraic, geometric, and trigonometric skills are all tested and firmed up.

The notion of the limit, such a mystery to most freshmen (and, truth-be-told, to many upper-level undergrads) is given a strong intuitive thrust right from the beginning.

If you want more problems, get the Schaum's outline book and read them side-by-side.

My students enjoy "The Story of Calculus".
How can we say that introductory courses in calculus at universities are meaningful if the students are never involved in math as professionals? What motivation can we offer them for studying it? This textbook, by Alexander J. Hahn, provides an outstanding answer to the question backed up by the author's precious teaching experience at the University of Notre Dame.

After reading the text, the reader will start to see calculus as a gift by our ancestors that helps us to analyze practical daily problems: calculus as a culture to be passed on to the next generation. Firstly, as the author says, "this text could as well have the title The Story of Calculus." As we read it, we find ourselves reliving history with the great persons like Archimedes, Descartes, Leibniz and Newton. We feel the activity and wisdom of the characters close-up, and we even experience their joys and sorrows as if they were our own. In a way, this book is a historical novel. It shows what calculus looks like as a critical tool that has helped to clear up the mysteries of the universe. Secondly, "the purpose of this text is to demonstrate its broad and formidable informative power." As the author explains, calculus enables us to designing telescopes, to read nuclear clocks, to design suspension bridges, and to understand the interior ballistics of rifles, the rocket equation, gravity, and the expanding universe. Economic subjects, such as banking, CPI, market mechanisms, cost analysis are also covered with full explanations. Books with such range and depth are rare indeed. It is easy to understand why the author received an award for teaching excellence.

Of course, "the emphasis is always on the careful development of the mathematics and information that it provides", and most of the topics of first-year calculus courses (including differential equations) are covered (but partial differentials and double/triple integrals are not). The exercise section of each chapter contains advanced explanations of historical, scientific, and mathematical topics, and is organically integrated with the text. The total number of the problems in all the 15 chapters is close to 700. With its many figures and illustrations, as well as full derivations of the equations, this text is also suitable as a supplementary or a self-study manual.

I strongly recommend Basic Calculus to those who have doubts about "the usual math training" which sometimes makes us feel like machines (not humans), as a rare and engaging view of mathematics from a different angle. I have found the contents of Hahn's textbook ideal for my students in general physics and calculus courses at Hosei University, Tokyo, and I am now completing a translation of this book into Japanese in collaboration with my colleague Professor Ichimura.

Basic Calculus
This splendid book aims to develop calculus from within its richhistorical context and to demonstrate its power across a range ofdisciplines.The author succeeds admirably.Two hundred pages devoted tokey ideas in the history of mathematics and science lead smoothly intocalculus as we know it today.The remaining three hundred plus pages coverthe usual topics, but with attention given to an extraordinary spread ofinteresting problems in science and business.The explanations of conceptsand notation are as lucid as any I have encountered in a basic calculusbook.

Because one of the distinguishing features of Basic Calculus fromArchimedes to Newton to its Role in Science is its historical dimension,something should be said about the criticism of one reviewer that the bookoversimplifies the history by using modern notation.Yes, Hahn does tidythings up.(Very nicely, I might add.) But what else can anyone really do? As Hahn notes, Leibniz's cryptic first work on calculus - Nova methoduspro maximis et minimis, itemque tangentibus...calculi genus - bewildered evenhis friends, the brothers Bernoulli.These famous mathematicians foundLeibniz's article "an enigma rather than an explication."Hahn could tryto unriddle the Nova methodus for us, explaining in detail all the fuzzyconcepts and strange notation that baffled the Bernoullis.But that hardlyseems the thing to do in a basic calculus book.Better to do just whatHahn does - seize on the essential ideas and use everything now at amathematician's command to bring them into a clear light.Hahn has anexcellent sense of just how far to go.The result is a truly extraordinarybook that will amply reward readers looking for something special. ... Read more

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This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. Various examples of problems, with their typical solution methods, are analyzed, and sometimes translated completely. Indeed, it is another aim of this book to ease the reader's access to modern editions of old mathematical texts, or even to the original texts; to this end, some of the problems discussed in the text have been reproduced in the appendices in their original language (Greek, Latin, Arabic, Hebrew, French, German, Provençal, and Italian) with explicative notes. ... Read more

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This inexpensive paperback uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues.Topics include: Oh So Mysterious Egyptian Mathematics; Mesopotamia Here We Come; Those Incredible Greeks; Greeks Bearing Gifts; Must All Good Things Come to an End?; Europe Smells the Coffee; Mathematics Marches On; A Few Good Men; A Most Amazing Century of Mathematical Marvels!; The Age of Euler; A Century of Surprises; Ones and Zeros; Some More Math Before You Go. ... Read more

Customer Reviews (5)

I loved Dr. LeWinter's class, and I love his book
I graduated from SUNY Purchase in 2001. Dr. LeWinter's History of Mathematics was one of the last classes I took before graduating. Because I have dyscalculia, I wasn't able to pass an actual math course, so my advisor suggested this speciality class. It was amazing. Marty LeWinter brought his guitar in every day, recited poetry, and had us create math-related poems for homework. His class was geared toward students who were doing badly in math but needed a math class to pass. Thanks to Dr. LeWinter's teaching -- and his textbook, now sold on Amazon -- I had so much fun learing math, without the headaches.

easy read, but be wary of the "history" of civilizations
I enjoyed reading this book until I got to Chapter 5 which I found to be inaccurate about Islamic history, not to mention extremely offensive.It would be different if the statements were true, but they're untrue and unneccesarily harsh.Other than that, this book is easy to understand and is quite humorous.I would recommend it for people who would like to learn the history of math, but I feel there are better resources out there to learn about the history of civilizations.

I finally understand math
I never appreciated my math courses in school. As a returning adult, I really found this book easily explains the concepts it is trying to get across. I especially liked the Chinese numbers. It is nice to learn about math fromother cultures. I now want to learn more math. Thank You, Lewinter and Widulski, I hope you guys write more math books.

An Excellent Book!!!!
This book covers Egyptian mathematics through to todays computers. It takes you on a journey through "mathematics" time. But the best part is even I understood it which says quite alot. I especially enjoyed the humor (Yes, a math book with humor) and the historical tidbits. I love this book!!

math affects everything!
fun to read; full of history; math was easy to follow; showed
impact of math on science, music, art, navigation, computers and philosophy; every parent should read this for when their kid says, "i hate math"...i loved the picture proof that the first n
odd numbers add up to n squared (like 1 + 3 + 5 + 7 = 16 which is 4 squared)...i envy the authors' students! ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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PREFACE. In 1810 a work was published in Cambridge under the following title-A Treatise on Isoperirnctrical Problems and. the Calculus of Variations. By Robert Wood/toiise, A.M., F.E.S., Fellow of Cuius College, Cambridge. This work details the history of the Calculus of Variations from its origin until the close of the eighteenth century, and has obtained a high reputation for accuracy and clearness, During the present century some of the most eminent mathematicians have endeavoured to enlarge the boundaries of the subject, and it seemed probable that a survey of what had been accomplished would not be destitute of interest and value. Accordingly the present work has been undertaken, and a short account will now be given of its plan. As the early history of the Calculus of Variations had been already so ably written, it was unnecessary to go over it again; but it seemed convenient to commence with a short account of two works of Lagrange and a work of Lacroix, because they

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for free at www.forgottenbooks.org ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more