Product Description
Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis. ... Read more

Customer Reviews (1)

Great Intro to Advanced Math
" Real Analysis and Applications" by Frank Morgan is probably one of the best introductory analysis books that I have come across. It gives a basic overview over real analysis without getting too hung up on a specific topic. Though it includes most important proofs, it stays away from too complex and lengthy ones. The book contains a very detailed explanation that goes with every proof. The author keeps complicated matter as simple as possible and approaches it somewhat with humor. It is a great introductory book, especially for people that haven't been exposed to the material before. If you are already an analysis professional you probably might want to stay away from this book, since this book is really primarily for the advanced calculus beginner. ... Read more

Product Description
Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems. In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples which are then tested in technically demanding situations. The author recognises the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the Differential, Integral and Geometric Calculus of Several Variables. ... Read more

Customer Reviews (2)

A neat book
This is not an elementary textbook, it is in fact aimed at higher level undergraduates. This means you shouldn't be afraid of theorems & their proofs, you should know some linear algebra, including some familiarity with n-dimensional euclidean space, as well as partial derivatives and elementary calculus. The author's Functions Of Two Variables could be profitably read before tackling the present book.

The book is about the differential and integral calculus of multivariable functions, including a very nice introduction to the classical elementary diffential geometry of curves & surfaces. A bent on differential geometry can be perceived all along.

The style is elegant and crisp and rather intuitive. All in all it is a very nice book. I didn't give it five stars because some of the stuff you'd expect to find in an advanced calculus book, such as series (including Taylor's series) and a careful discussion of differentiability, are missing.(This review is about the first 1998 edition).

Too Technical. Good for Students maybe...
But not for someone who wants to learn at his own pace.
It starts with the Matricial definition of derivatives and assumes
a complete knowledge of Matrix Theory.

This, at least for me, is neither intuitively nor psychologically
friendly. Other math books, which are not even targetted at
undergraduates are easier and more fun to follow
(e.g. Algebra by B.L. van der Waerden Algebra: Volume I)

Boring, maybe good for someone at college who has a teacher and
need to pass an exam.

If you are a math nerd who can follow books like:

Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
Corollary
Theorem
Proof
Corollary
...
[Some Explanatory Text]
...
Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
...
[Figure]
...

Then this is the book for you. ... Read more

Product Description
This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions. The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need. ... Read more

Customer Reviews (2)

A practical introduction not so practicle
I took this book hoping that it can help me learn fast the important concepts of stochastic calculus.I liked the fact that it has exercises with complete solutions, and the friendly presentation.However there are some aspects that I did not like about the book.First thing is that Durrett is not so precise in the proofs of the theorems.Here are several examples.

In Theorem (2.4) he proves that continuous local martingales localize to bounded martingales.I did not understand why it is important to have continuity, and the proof does not give any hints towards this.It is true that even in Rogers & Williams you do not see that.My guess is that the first exit time becomes a stopping time if the process is continuous.

Durrett also does not say in the proof of Theorem (2.4) why he can apply the Optimal Stopping Theorem (2.3) since he did not mention that the stopped martingale is uniformly integrable.

In Theorem (3.1) he defines the variance process of a continuous local martingale.I had troubles with the proof of uniqueness of Theorem (3.1).He does not say why the difference of the processes is of local bounded variation.This fact is crucial for the proof.

The book is good in combination with Rogers & Williams.

Written by the priesthood for the priesthood?
I bought this book after reading in the last chapter of Steele's "Stochastic Calculus" that this would be a good reference for constructing martingales via pdes for the case of x-dependent diffusion coefficients. An introduction, this book certainly is not, nor is it practical or even useful for nonspecialists. I can hardly imagine a worse divergence between reality and an author's stated belief of what the book really is. Richard Durrett states in his introduction that he intends to present coherently the material that would otherwise require understanding many other difficult books. He also complains that his former editor refused the ms, so he went to CRC. Like many other topics in the book, e.g., "Martingale" is not defined, the author simply refers to his other books! Steele's book is extremely difficult: I cannot follow many of his proofs but his examples are stimulating and can be worked out. The examples show how the theorems work, which is practical. Generally, one example is worth a thousand theorems. Durrett's book is 'practical' in that he does offer exercises, and apparently Steele took his execises from this book. I would have wished for better editing, all authors suffer from too little criticism.

Note added later (and I should have given 2 stars): Durrett's 1984 book "Brownian Motion and Martingales in Analysis" looks somewhat more readable and has some examples. In fact, the examples in Steel, as well as the Martingale discussion of his last chapter, may be motivated by or come from the 1984 book. It's often the case that an author's later books on a particular subject are not as good as his earlier ones. Warning: the 1984 book is also written in highly impenetrable mathematese.

Notes added after 3/2007:

1. 'Levy's theorem', pg. 111: take care not to conclude that martingales with variance linear in t are equivalent to a Wiener process, they generally are topologically inequivalent! E.g., for the exponential process with Hurst exponent H=1/2 one obtains E(x^2(t))=2t, and the factor of 2 makes all the difference, formally. More generally, consult Durrett's integration by parts formula (10.1) in part 2.10: since is generally not t, X^2(t)-t is generally not a martingale. Financial math texts tend to advertise falsely that all martingales are Wiener processes.

2. Instructive derivation of the Coulomb Green function from the martingale defined by the Poisson eqn.

3. The Girsanov factor for Ornstien-Uhlenbeck given on pg. 204 is wrong, see my revierw of the 1984 book for the correct factor. Better yet, work it out for yourself.

4. A statement on pg. 212 is wrong on acount of violating the warning of 1. above: an arbitray martingale is topoligically inequivalnt to a Wiener process!

5. Part 6.4. Very nice, and related to the Coulomb construction: or a class of odes the Green function is given by a martingale constructed from the corresponding Ito process. Sorely and sadly missing: explanation how the boundary terms vanish (to create the desired martingale) at the stopping time. Even worse, the Ito process is sidesteped in favor of a standard construction from odes which hides the role of the stopping time andhow one can handle it! Note that the 7th eqn. on pg. 223 is wrong, the correct one is the 3rd eqn. The two are not equivalent unless the underlying Ito process is Wiener, and it generally is not. ... Read more

Product Description

With Bob Miller at your side, you never have to be clueless about math again!

Algebra and calculus are tough on high school students like you. Professor Bob Miller, with more than 30 years' teaching experience, is a master at making the complex simple, and his now-classic series of Clueless study aids has helped tens of thousands understand the tough subjects.

Calculus-with its integrals and derivatives-is famous for tripping up even the quickest minds. Now Bob Miller-with his 30-plus years' experience teaching it-presents high school calculus in a clear, humorous, and engaging way.

Product Description
Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis. ... Read more

Customer Reviews (3)

Very Good Bridge between Calc and Analysis
This book is a proof-based calculus and a first Analysis.I've had experience with a few Analysis books and this is much more approachable while still containing rigorous definitions and proofs.The author takes care to give intuitive examples and motivation.That being said, it would be difficult (but not impossible) for someone who wasn't familiar with writing and closely reading proofs.If you intend to attempt this book without having had some sort of math reasoning course or background you should pick up an introduction to proofs book - I suggest Eccles "Intro to math reasoning":
An Introduction to Mathematical Reasoning

hard to understand if you've never done proofs
this is a good book in a sense that if you've already done rigorous proofs before. This book targets undergrads who've taken single variable calculus up to multivariable calculus. This book ismeant to be taught in two semesters. I've never really done proofs except for simple proofs like trig or so. This book is really rigorous and i would not recommend it for those that have not taken a proof class. The author assumes you know the basics of proofs already and starts off with sequences and limits of sequences and introduces the the completeness axiom. One frustration i had with this book was trying to understand half of his definitions. I could not find a solutions manual so I don't even know if most of my solutions are correct. So if you've never done proofs, stay away from this book until you're comfortable and want a challenge. The only reason i have this book is the class i'm taking requires this book. If you're really good at proofs then this might be your favorite book. IF your weak at proofs then try looking for an easier book that spoon feed you cause you'll pull out all your hair out before you even get halfway. But don't get me wrong, this isn't a bad book; its more rigorous.

A readable analysis text (esp. chapters on vector function)
This is a very good book. I recommend this book for anyone who wants to learn calculus on a rigorous level.
This text is very readable. Unlike most analysis texts out there that focus on rigor without any intuition, Fitzpatrick strikes the perfect balance. The topics are well spaced (via the sections) and exercises are accessible.
I also recommend this for non-math grad students like econ, stat, and engineering.
The section on Multivariate calculus is the best I have seen out there.
If you went through an analysis course in undergrad and did okay but never really grasped the concepts and
how they all fit, then this is the book for you. But just that you know this is not a book on the level of Royden.
To some extent its a little bit on the level of Rudin. (maybe a little bit lower)
This is my first time writing a recommendation for a book review, but I felt obligated to mention how useful
this book has been to me.
I will repeat If you have a strong analysis background you may want a different book with less intuition and examples. But if you are in the middle and you feel like you want a comprehensive, cohesive and readable real analaysis text thenthis is the right book for you. ... Read more

Product Description
Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities.It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems.Throughout the text, calculus is treated as a problem solving science of immense capability. ... Read more

Customer Reviews (23)

Calculus with Analytic Geometry
I am a Chemistry and Mathematics major at Marian University.This book is the most readable way to learn calculus on your own.The author makes the information in calculus fun and exciting by adding in interesting scenarios by way of examples as well as history.This is a great book and I highly recommend anyone who is trying to learn calculus formally or informally.Absolutely the best reading math textbook I have ever encountered.

Perfect Review for Graduate Study
I am using this book to review calculus in preparation for graduate study in physics after several years out of academic study.Simmons is not only easy to follow, but also sufficiently rigorous for all but the most esoteric purposes.I have really been enjoying the brief but fascinating notes on some of the important figures in the history of calculus (Newton, Leibniz, Riemann, Fermat etc.), whom every science student should be familiar with.

The problems at the end of each section range from easy to difficult, and cover all newly introduced material as well as tying in previously covered material.I recommend buying the solutions manual which gives step-by-step solutions to all the odd-numbered problems.

Precise, Accurate, Elegant and Flowing
I own all of Professor Simmons' books not only for their mathematical clarity and incredible instructiveness, but because his books are, in addition, the most interesting books I have read from a literary viewpoint. They are a complete joy to own and to read over and over.

With reference to his Calculus text, it is clearly the best on the market. If you are in search of a deep understanding of the principles and applicability of this subject, then Dr. Simmons' text is the book to buy and own.
Bottom line.

Pathos.Tension.
This book will have you on the edge of your seat, from the first linear approximation to the last double integral.It's better than sex (well... maybe not)

change your life with this book
I originally learned calculus at OU with james stewart 4th edition, but came to this book through the MIT open courseware readings.I love this book and can't understand why math departments everywhere aren't using this as their text.Simmons' strategy for writing about calculus is unique, and in my opinion the best.He gives quite a bit of history and ties it into physics and the other sciences giving the reader a broad perspective on why the hell it matters and how it came to be.At most state unis, calculus is probably more plug and chug, but if you want a better source of material to supplement your class, buy this book. ... Read more

Product Description
Clearly written text for advanced student covers: Necessary Conditions for an Extremum; Sufficient Conditions for an Extremum; Variations and Hamilton’s Principle; the Nonparametric Problem of Bolza; Parametric Problems; Direction Methods; Measure, Integrals and Derivatives; Variation Theory in Terms of Lebesque, more. 1969 ed.
... Read more

Customer Reviews (2)

Admirable, but hard to learn from
This book has one previous Amazon customer review, with 5 stars and a glowing review. I do not dispute that reviewer's assessment; rather I'll observe that his familiarity with calculus of variations is much deeper than mine. I find this book almost impossible to learn from, although there is much in it that I would like to learn. But I confess that I have difficulty with calculus of variations, and always have had.

For me, calculus of variations breaks neatly into two eras, before Weierstrass and after Weierstrass. Before Weierstrass there was no rigor in the subject, and practitioners from Bernoulli to Lagrange used whatever methods they could devise to solve particular problems, or classes of problems, that attracted their attention and that seemed to be tractable. Weierstrass turned the subject into a rigorous one, and was followed by a number of creative theoreticians, some of whom could also solve practical problems: Bolza, Hilbert, Bliss, McShane (whom I knew) and various others. They created mathematical theory that would have been incomprehensible to Euler, but which eliminates the slop in the subject.

When I look for literature on calculus of variations I seem to find the literature also divided into "before Weierstrass" and "after Weierstrass". I have no trouble with the "before Weierstrass" sort, but I would like to go further. And the trouble I have with this book is that despite the promise of a jacket blurb, it doesn't show how the subject developed from an intuitive art into rigorous mathematics; it determinedly sticks to the "modern" viewpoint. I note with amusement, for example, that Lagrange is mentioned only in one slightly pejorative paragraph on page 109, with no indication of how Lagrange actually solved variational problems.

So this book will sit in my personal collection of math books until I get tired of seeing it around and get rid of it (which is what happened to my copy of Bliss many years ago). Is there some text on calculus of variations that will permit a reader like me, with reasonable knowledge of measure theory, modern algebra and topology, and classical analysis, to learn how the calculus of variations has progressed in the last hundred years? This isn't it.

Very deep and detailed
I have had this gem of a book for ten years, and I'm still enjoying it. Actually, it turns out that the text itself was written some time ago, but don't let you be put off by that - this book is very scholarly and you really will be enlightened by it.

Now, where do you begin? Usually at University, I guess, this subject is treated in a way that makes most folks think that just about all "Calculus of Variations" problems can be solved with the Euler Lagrange equation, and from there on, you just have to solve the resulting differential equation. And I guess that's sometimes possible. But in the real world, sometimes you end up with that equation simply not working, and your problem is more messy and not expressible using "nice" functions. Now, this is where this book begins. We start by looking at "sufficient" and "necessary" conditions for solutions - and these are not the same things! This at least allows you to work out whether a solution is there, for goodness sake, before you waste time trying to find it.

Ewing does better in later chapters. He showcases a whole slew of problems which deserve special consideration, and this gets at times really exciting, covering all sorts of ideas about what we mean by optimum values for integrals, and how to specify systems of equations when one method doesn't really work too well.

One question which he digs into, which is very entertaining, is the problem of what an integral of a function really means. For example, we all know about the Riemann integral - the limit of a sum - but had you ever heard about the Weierstrass integral - or the Lebesgue integral?

Mr Ewing serves up these exotic and flavorsome new varieties in a most satisfactory fashion, with lots of examples to help.

The text never gets too far away from real problems. How easy that would have been! This book is so amazingly practical and also deeply committed to a really thorough treatment. He also gives excellent commentary on the history of this subject.

Overall I would say that this book is not one which belongs on the shelf with the numerical methods books, or the operational research section (thats what numerical optimisation is called over here in Britain), but I would get this now anyway before it goes out of print (if Dover are so crazy as to do that). ... Read more

Product Description
Perfect for those afraid of calculus, this book offers an innovative, three-step process for solving almost any kind of basic calculus problem. By unifying coverage and emphasizing similarities across a spectrum of calculus problems, it succeeds in simplifying the subject by providing a conceptual framework. Learning takes place in a comprehensive way, not in unrelated fragments. Numerous illustrations and examples further simplify and illuminate the concepts. ... Read more

Customer Reviews (6)

Schaum's Outline of Understanding Calculus Concepts
Item was sent as described and is a most useful overview of the ideas, good for someone getting back into such a topic after many years away from it.

Nice for what it has, but a little light on content
For what it includes, this book is pretty good. Unfortunately, it misses more than it contains, so it's more a summary than a real reference.

A great book
This is a wonderful book. I enjoyed reading it even though I have learned calculus more than a decade ago. I just regret that I did not read it during my college time. Absolutely helpful for those who are studying and will study calculus.

Boring
This book won't make you want to learn calculus because it's more boring than most textbooks. Extra explanations of concepts are always helpful, but you get explanations with every calculus book, so don't think that this book is something special.

Quickly guide to understand Calculus
Understanding Calculus is a esay and quick way to review and learn the hard topics in that course.The author uses a simply manner to explain the exercises and the theorems discuss. ... Read more

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Customer Reviews (2)

A mathematical view of selfishness and altruism
The calculus of selfishness begins with a calculated approach towards the daily incidents an individual can experience. Completely devoid of any mathematical intricacies, borrowing heavily from real life, the first chapter summarizes and justifies the calculations, which are seen in the rest of the book. This draws the reader deeply into the plot making more curious about how mathematics can encapsulate such complex scenarios? This is exactly is what is answered in the second chapter which essentially describes the foundations of evolutionary game theory and explores its roots in traditional game theory and the concepts and terminologies are made clear.
The chapters after that make clear the title of the book. Exploring the effects (or the cause?) of direct and indirect reciprocity, models involving reputation, rewards and punishment are analyzed for the evolution and maintenance of cooperation. Lastly how collective actions are sustained and maintained is theorized, again involving the above-mentioned subjects. The role of structured populations is touched upon briefly but not without presenting the important results which have been popularized until now.
In a nutshell, Karl Sigmund shows us again what makes him an authority in the field of evolutionary game dynamics and puts together the most important concepts which have been developed in this field since its inception. His earlier book "Games of Life" generated interest in many a physicists and mathematicians in biology and made biologists look towards biology through the looking glass of the mathematics of dynamical systems creating a generation of evolutionary dynamicists. It wouldn't be surprising if this one did the same and more.

A great book!
In "The calculus of selfishness", Karl Sigmund provides an excellent overview on recent research on the evolution of cooperation. The first chapters are non-technical and written in the brilliant and refreshing style of the popular science book "Games of life" by the same author. The transition to the more mathematical parts is very smooth and all calculations are transparent enough to allow the reader to repeat them. Most importantly, no results are left uncommented. Whenever Karl Sigmund calculates something, he tells us why and what the result means. This book is is a great way to introduce someone to this field and to get a comprehensive overview on recent developments. I will certainly recommend it to my students and collaborators! ... Read more

Product Description
The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance. ... Read more

Product Description
Building off the success of Zill and Dewar's popular Precalculus with Calculus Previews, Fourth Edition, the new Expanded Volume includes all the outstanding features and learning tools found in the original text while incorporating additional coverage that some courses may require. With a continued aim to keep the text complete, yet concise, the authors added three additional chapters making the text a clear choice for many mainstream courses. New chapters include: Triangle Trigonometry, Systems of Equations and Inequalities, and Sequences and Series.This student-friendly, four-color text offers numerous exercise sets and examples to aid in students' learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. ... Read more

Customer Reviews (2)

Quick and Easy Transaction
I had ordered a book, which I received in mint (LIKE NEW) condition. The shipping was fast and I recieved the book with extra care taken, in the packaging for the item. I recommend this seller for future transactions. The item I received was exactly how it was discribed and am very happy for the great trasaction.

Happy Customer
I ordered this item through Amazon from one of their used book sellers, Book Depository.The book was new as described and arrived timely.I never ordered used books, but as with all of us I am trying to save a dollar where possible.Thanks, Amazon for providing other options for ordering textbooks through your site.If you are a little apprehensive about ordering used, the price indicated on Amazon's ($125.00) site is a good price for this book.I have shared this information with other parents and they were happy to save a dollar as well.I would defitnely order from Amazon and when possible order from their provided list of sellers. ... Read more

Product Description
Everything you need to know-basic essential concepts-about calculus

For anyone looking for a readable alternative to the usual unwieldy calculus text, here's a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.

Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition's comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green's theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.

If the dry "theorem-and-proof" approach just doesn't work, and the traditional twenty pound calculus textbook is just too much, this book is for you. ... Read more

Customer Reviews (4)

ideal first calculus text, especially for for non-math majors
I still remember my freshman year 25+ years ago as an undergraduate student and the 1300 page phone book that passed as a calculus text.Thinking back to this time, I recall how
much I hated the approach taken to teaching calculus to a large (200-300 people) diverse
class at a major university. Basically, neither the theory or the important ideas and insights were very well described by the mathematics professor or the textbook. At best, an engineering or physics student could learn the techniques of calculus in order to use them in further classes. Many math professors operate under the fallacy (in my opinion at least) that a first college level
calc class is a major failure
if it does not impart to all students the eps/delta scaffolding that the theory of the derivative and integral are based on.I would argue, that although this is a noble goal to achieve, in the end almost everyone in the
class winds up disappointed for various reasons. In my experience at least, most students resist the
rigor. ( For good reasonas the ideas are very intricate and took some of the best minds after Newton/Leibniz to refine).

A first course in calculus should teach techniques and discuss ideas and concepts. Those students who need further analysis will be taught the rigor later. However, most people in a freshman calculus
class simply have no need for abstract analysis. Prof. Bear knows this full well and his book is his way of
addressing the problems just discussed. This book is short, well-written, and to the point.The
essentials of calculus are taught in the way one human being would teach another, not like the usual phone book size calculus book which tries to meet the needs of every student present and future.
This book is like a set of typed lecture notes for a real class. In any case, I would have
liked this book far better than the one I used 20+ years ago.

Why only 4 stars then?The discussion of limits needs to be a bit longer than the few sentences provided in the text.
Without going into eps/delta too far, the idea of limit should have been fleshed out a bit more.
After all, the limiting process is what distinguishescalculus from all math that comes before.However, in the real world, it is the techniques of calculus that should be
mastered first.Those who need the refinements will go seek them if and when the time is right.

Depends what you want ...
Both previous reviewers are correct.

If you are a mathematician, this book is not for you. For a more rigorous, yet brief, alternative try "Short Calculus" by Serge Lang.

If, on the other hand, you are an applied scientist or engineer, this book does what it says on the tin, providing brief introductions to almost all calculus concepts you are likely to need for applied problem solving. Some previous exposure would be beneficial as the book is highly concise.

Good for review, bad for teaching fundamentals
Like all skills, your ability to do calculus fades over time. When you reach the point where your skills need to be refreshed, then this book will work for you. All of the material covered in the standard three or four semester calculus sequence is explained in a very brief manner, followed by a short set of problems. If you knew it at one time, it is an excellent way to be reminded about all of the fundamentals of differential and integral calculus. Brief solutions to the problems are included.
However, I strongly disagree with the premise that this book can be used to learn calculus. To believe otherwise is to adopt the position that it is possible to learn calculus without understanding the fundamental proofs. For example, the concept of continuity is almost completely ignored, which limits the coverage as well as the understanding of this important principle. The end result will most likely be a student who can run through the basic problems by following the rules without really understanding why they work. The solutions to the problems are too brief to provide any explanation of how the answer was derived.
I completely disagree with the blurb on the back cover, "If the dry `theorem-and-proof' approach just doesn't work, . . .this book is for you." Like it or not, mathematics is theorem-and-proof, and it is up to all educators to reinforce that this is the way it is. I would never consider this book as a textbook for my introductory calculus classes, as the `theorem-and-proof' approach does work for me and it prepares the students for their advanced math classes.

Highly Recommended
This book is exactly as described--it's clear, concise, and has very good example problems.This book is the perfect companion to your Calculus 1 textbook.It's well worth the cost. ... Read more