Product Description
We take great notes–and make learning a snap

When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts–from functions, limits, and derivatives to differentials, integration, and definite integrals– and get the best possible grade.

At CliffsNotes, we’re dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase– and zero in on the essential information you need to succeed.

Make the grade with CliffsQuickReviews

CliffsQuickReviews are available for more than 30 introductory level courses. See inside for a complete listing of these and other bestselling Cliffs titles. ... Read more

Customer Reviews (10)

Great primer, supplement, and refresher for calculus
Having completed the standard three semesters of calculus as a teenager, many years ago, I periodically need a refresher, and this book was perfect. However, it only reviews the basic calculus normally covered in the first semester of calculus, and part of the second semester. Topics, for example, which are not covered in this book include: sequences and series, parametric equations and polar coordinates, vectors and spatial geometry, partial derivatives, multiple integrals, and vector calculus. However, this book is a nice refresher that can be completed in a short period of time.

Because it covers the essentials, you don't have to spend more time covering topics than necessary to grasp the tools and concepts. I worked all the problems at the end of each chapter, and at the end of the book. I felt that the number of problems was just right: not too few and not too many. Answers are provided. There is an appendix that briefly revisits some examples given in the book, to show how your graphing calculator help you out with these problems. If you read all of the chapters in this book, I definitely recommend that you also read this review of graphing calculators in the appendix. The technology enhances one's study of mathematics tremendously.

For students entering calculus, I think this book is valuable as both a primer and a course supplement. If you only need the first semester of calculus, then this book covers all of the basics. However, you will need a textbook for thorough and in-depth coverage, as well as ample problem sets, to become proficient in the subject. After you've had one semester of calculus, then this book serves as a handy reference.

This book is not without some occasional errors, which are usually in the answers to problems. This is unfortunate for the new student unable to recognize these errors. There is no errata page published on the CliffsNotes website. Of the 42 review questions at the end of the book, the answers provided to six of these questions say, "Provide your own answer." Although these are critical thinking and proof questions, it is still annoying that an extra half-page, or less, wasn't included to provide solutions to these problems.

Good little book
I didn't purchase my Calculus text book, but I did get this. This is way cheaper and covered pretty much all the material I needed. I did find myself using online resources a little, but this book explains the concepts well and provides good practice problems. Well worth it. There's also a free version online at the Cliffs Notes website.

Useful only if you are reviewing for an examination of "plug and chug" differentiation and integration problems
Unless you are preparing to take a calculus exam consisting of a series of basic differentiation and integration problems, then I really don't see any use for this book. The reviews of what differentiation and integration really are have no depth to them, so those sections are of limited use in bringing you back up to speed in calculus.
This makes the book almost totally a collection of sections of the form:

Here is a type of mathematical expression and this is how we differentiate (integrate) it, with some examples.

One of my college math professors referred to these problems as "plug and chug", where you simply execute the rules without having any real understanding of the concept. Therefore, if you are trying to refresh your understanding of calculus, then this book will be of little value.

Unhelpful
I purchased this book because I had a good experience with both the Algebra and Algebra II Quick Review.This book, however has not helped me one bit.It's worse than using the textbook to learn!
The formulas it gives are too complicated and it doesn't even give you any shortcut techniques.I do not recommend this book to anyone who needs supplementary instruction in Calculus.

Great supplement for Calc!
I used this book as a supplement to Calculus I and II courses. Cliffs breaks down limits, derivatives and integration in a very simple way.You don't have to be a "math nerd" to grasp this book. During calculus lectures I would reference the book in class to make sure I understood the professor. There were even a few times when the professor asked to use my Cliffs in class because he knew the book had great examples. Needless to say I got an A in the course. Now as a senior electrical engineering student, I still use it if I need to reference stuff that I forgot.

Just a warning though, if you want to be good in calculus don't just read the Cliffs and your textbook. Dig into the text or cliffs and work a ton of problems (beyond just the assigned homework) and you will pass the course. ... Read more

Product Description
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students. ... Read more

Customer Reviews (20)

Does not include Wiley Plus
If you are looking for access to WileyPlus to be included with this book, do not purchase this item.
Even though the product description clearly states, "Readers will also gain access to WileyPLUS", they do not give you access.It does not say that Readers may also gain access for a fee.There is nothing in the listing of this book that says anything about purchasing WileyPlus separately.

Amazon will not stand by their product description.
In fairness to Amazon, they did offer to give me a refund.Since my son is at college now and needs the book, our options are limited and we will not be able to return it for a refund.

Since I can not count on Amazon to describe their products accurately, I have no other option than to look other places for products.

amazing
the quality was well beyond the price...and did I mention I got it like "new"?

the cover looks nice
I have a Ph.D. in math and teach at a college in California.I compared the Hughes-Hallett book with 7 other calculus books:Anton, Edwards, Larson, Rogawski, Smith, Stewart, Thomas.Here are some concerns with the Hughes-Hallett book.

This book is missing the following topics:reciprocal trigonometric functions (sec x, csc x, cot x), squeeze theorem, logarithmic differentiation, sketching graphs by hand by using derivatives, telescoping series, curvature, tangential and normal components of acceleration, line and surface integrals over scalar fields.All the other 7 books include these topics.

Six series tests are crammed into section 9.4.None of the other 7 books cram all six of these series tests into one section.

The Root Test for series is embedded into two homework problems.All of the other 7 books include the Root Test in a box within a section.

Planes (12.4) are discussed before talking about vectors (chapter 13).All the other 7 books discuss vectors first and then use vectors to develop planes.

Center of mass multiple integral formulas are embedded into the homework problems.All the other 7 books explain center of mass multiple integral formulas within a section.

The preface reads, "Students are expected to use their own judgment to determine where technology is useful."All the other 7 books make it clear when the students should use technology.

The preface reads, "There are very few examples in the text that are exactly like the homework problems.This means that you can't just look at a homework problem and search for a similar-looking `worked out' example."Many students learn calculus by seeing `worked out' examples.

Instructors:If you are considering adopting this book, then you've been warned.

Students:If you have to use this book, then go to class, do your homework, and good luck.

Hope this information helps.

Dr. Chuck

Calculus
The book does not give enough examples that a student can follow. Most likely the instructor has to do a good job of explaining steps.

good
ive hade 3 calculus books an this one is the worse, but the book did come in as ordered. ... Read more

Product Description
Contains carefully worked-out solutions to all the odd-numbered exercises in the text.Part One Corresponds to Chapters 1-11 of Thomas' Calculus, Early Transcendentals, Eleventh Edition. ... Read more

Customer Reviews (2)

Great product/seller
This book was in perfect condition no problems and fast shipment definitely would do business again

a good help for the serious student
solutions are a bit sketchy, but clear if you're willing to dig in and work with them.A valuable reference for serious students who want to excel in calculus.Also a helpful guide for tutors and instructors, to save preparation time and energy. ... Read more

Product Description

* Explains how to understand calculus in a more intuitive fashion
* Uses practical examples and real data
* Covers both differential and integral calculus ... Read more

Customer Reviews (23)

Learning calculus just got a lot harder with this book.
I was sorely disappointed with this book; it read like a Greek tragedy--symbols are not defined, though, some I did recognize from Algebra & Trig, others I had to look up. The steps to solve the equations are not clearly defined and are inadequate. I don't expect complete hand-holding, but for a so-called "self-teaching guide" I did expect to find thorough explanations written in plain English, not in scholarly academic speak. But this what one can expect from an author w/a PhD in Mathematics and who is entombed in an academic bubble. On a side bar, it should be noted that the author's most recent academic paper was entitled "The Schwarz lemma at the boundary" due to appear (if it hasn't already) in the next exciting issue of "Complex Variables and Elliptic Equations" available at a university library near you. Can we all say: "What the frell?" My point exactly.

I agree with the reviewer, Thomas P. Connolly, I seriously thought I was getting denser with age and had become inept. It was poorly written math books like this that kept me away from learning Calculus in the first place. The authors may be holders of PhD in Mathematics and experts, but their ability to write an engaging non-academic tome is non-existent. Learning math shouldn't be a frustratingly painful process. I stopped reading this book about a third of the way through Chapter Three, "Applications of Derivatives". The author only succeeded in confusing and frustrating me even further.

On a brighter note, I did find other helpful resources that succinctly explained limits, derivatives and other calculus topics, and continue to use them. Salman Khan of khanacademy.org offers some excellent and free video tutorials and Jason Gibson of MathTutorDVD.com sells a Calculus 1 & 2 DVD for less than $40. I also found that W. Michael Kelley's book "The Humongous Book of Calculus Problems" to be very helpful.

Avoid Krantz's book at all costs! It will only succeed in mystifying you even further and make calculus a lot harder to learn.

Demystify what?
It does NOT demystify anything for me.It introduces new notation, new concepts and DOES NOT explain them.eg, it introduces the Derivative in 1 line without any explanation - somehow Lim x-> 0 (f(c+h)-f(c))/h relates to f(x)=x^2+x because in 2 lines it shows that because a limit can be calculated for the former at a value means that a derivative of the latter can be found with the same value.Sorry, not demystified here - how does the former even relate to the latter?An explanation of that would demystify.

Calculating Success for Teacher Texts
Purchasing this item was simple and nicely priced.There were no challenges in the process and I was pleased with the quality and "newness" of the book even though the listing stated that it was only "like new."Without hesitation, I would be likely to purchase from this vendor again.

Skip it. You'll thank yourself later.
I'll keep this short. Skip this book. I picked it up on a whim without reading reviews, and I regret it immensely.

If you've already gotten through calculus recently, then you'll be fine here. However, terms, concepts, and variables are thrown at you without any definition at all.

The "you try it" problems of course have no answers, so you get no help there. The examples are of the most basic, useless variety, while the "you try it" problems and the exercises often are far, far more complicated than anything the examples have shown you. It's the equivalent of showing you how to buckle a seat belt and what the throttle, yolk, and rudder pedals are for in an airplane, and then expecting you to fly a jumbo jet as your first "practice run". Through, say, O'Hare international. The day before Thanksgiving.

And this is called a "self-teaching" text.

The author strikes me as a typical bad math teacher. He's gotten through it, he understands it, and he expects you to have that same understanding, a priori, and to have similar intuitive leaps of ability that took genius minds years to achieve.

I've been looking for an overview of calculus before I go back to college to work on a degree, and I can honestly say that this book is worse for understanding concepts than the laughably bad demo clip of a DVD of strippers explaining calculus while they grind and get naked.

Avoid this book
I think all you need to know about this book is the intro to limits.Why not use a simple continuous function with a single definition to introduce the idea?What can possibly come from using a function that has different definitions depending on the range of x, except adding an unnecessary detail for the reader to weed through?It almost seems that the author is intentionally making it sound complicated to convice the reader that he (the author) is so brilliant that he (the author) can't understand how the reader isn't able to connect the dots, which he (the author) has made unnecessarily difficult to connect.

Examples of this unnecessary obfuscation is found in spades in this book.


... Read more

Product Description
A focused review to help you score high and earn college credit. This hard-hitting guide features:

• Helpful test-taking strategies
• Focus sections on specific topic areas, including precalculus, limits and continuity, derivatives, and integrals
• Sample multiple choice and free-response questions
• A discussion of calculators to use during the exam, including which are the best types

Customer Reviews (9)

Poor Practice Exams
The practice tests don't mimick the actual AP exam.After looking at some questions on their practice test, I had to turn back and look at the cover of the book--I thought that I was looking at some sort of pre-calculus book.

For example, one multiple-choice question (on the practice exam) asks you to complete the double-angle formula for sine(2x).How ridiculous!Such a question would never be on the AP exam.

Another multiple-choice question asks for the interval over which ln(x+3) is nonnegative;Again, another question which is highly unlikely to appear on the AP exam because it's a simple pre-calculus question.

okay
basically what most of the other reviewers said. this calc prep book is too easy for the ap tests that are now being administered. there are quite a few typos which makes everything a little more confusing. the lessons are okay, but only if you want to review or clear up a fuzzy area. i dont think you can learn calc from this book. what's helpful though is that in the back there are these english-to-calculus translations that are great to memorize and help tremendously for the test. but other than that, look elsewhere for an outstanding calc book.

Fallsshort of the mark ...
Let me preface this by saying that I spent the last year helping my daughter self-study for the AP Calculus Exam given in May 2007.I bought 4 AP Calculus review guides, 2 textbooks, and looked up the openly available free response questions from the actual tests for the last 7 years. Unfortunately, I agree with the more recent reviews that this guide is inadequate.My overall impression was that Cliffs wanted to expand into other "study" areas besides their well-known CLiffs Notes in literature booklets and put this book together for such a purpose.

The book is filled with typographical errors which are annoying.More over, the book is just too easy.Anyone who has looked at the actual free response questions given on either the AB or BC tests will quickly realize the inadequacy of this book.

The AP test is no longer one in which simple differentiation and integration will carry the day.You need to knowhow to use your calculator to solve problems, clearly understand the Fundamental Theorem of Calculus and its applications, be able to read graphs and determine their properties as they relate to calculus, and be able to use data tables in solving problems.This book does none of these adequately.

Not at all reliable
I used this book both for Calculus BC and AB, last year, mostly to review for the AP tests.The sections explaining various concepts were marginally helpful but not especially easy to follow.However, the most severe disappointment was the practice problems and tests - what for me should have been the real purpose of the study guide.Both the questions and answers were FULL of typos, so much so that I don't know how this book got published, and I could never tell if I was actually doing the right thing because the book would be wrong.Also, the practice tests were way too easy, and mostly different types of questions than are on the real AP (which I took this morning).You'd do much better off looking at past AP tests, which are accessible online for free.

In response to one of the reviews.
One of the review said that Calculus is "Algebra 1" of Advanced Mathematics, which is blatantly incorrect. Calculus and Algebra are two distinctly seperate branches of mathematics although they may involve the use of each other. Also it is rather correct to call calculus a baby Analysis; more correct way to call high school AP Calculus is Calculus without proofs - calculus without substance. ... Read more

Product Description
This ingenious, user-friendly introduction to calculus recounts adventures that take place in the mythical land of Carmorra. As the story's narrator meets Carmorra's citizens, they confront a series of practical problems, and their method of working out solutions employs calculus. As readers follow their adventures, they are introduced to calculating derivatives; finding maximum and minimum points with derivatives; determining derivatives of trigonometric functions; discovering and using integrals; working with logarithms, exponential functions, vectors, and Taylor series; using differential equations; and much more. This introduction to calculus presents exercises at the end of each chapter and gives their answers at the back of the book. Step-by-step worksheets with answers are included in the chapters. Computers are used for numerical integration andother tasks. The book also includes graphs, charts, and whimsical line illustrations. Barron's Easy Way books introduce a variety of academic and practical subjects to students and general readers in clear, understandable language. Ideal as self-teaching manuals for readers interested in learning a new career-related skill, these books have also found widespread classroom use as supplementary texts and brush-up test-preparation guides. Subject heads and key phrases that need to be learned are set in a second color. ... Read more

Customer Reviews (30)

Calculus if you already know calculus
If you need to learn Calculus form scratch don't buy this book. It is fun reading but there is too little explanation and hardly any examples of the problems they assign at the end of the chapters. If you have already had a couple of courses in Calculus this would be a great review book. But it just doesn't live up to it's name.

Improved AP Calculus Score
I came across this book in high school.In my senior year I had a rather serious case of mono that kept me home for months.The district sent a "homebound" teacher to keep me current with my classes, but she was not able to help with my AP calculus class.So, my mom got this book for me and it was very engaging.I finally understood real-world applications for calculus and understood the reasons behind the formulas.When it was time for the test, I received a greater score than my classmates.It took me longer to take the test because I didn't know the formulas from memory as well.However, I was able to reconstruct them because I had an understanding of the why and how behind the formulas.Few books have made me smile when I think of them many years later, but I still have a fondness for this one.

Very good but
This is a pretty good Calculus book.Most but not all of the problems have good explananations.I have found several glaring mistakes with the answers in the back and also in the exercises where the problem has been printed incorrectly for example a plus sign where a minus sign should have been.I have had to go on the internet several times to find how an answer was derived because the book especially in the back where the answers are seemed to skip major steps.I dont see how working with this book while taking a course could help because it is pretty labor intensive.Make sure your trig and algebra and precalc skills are pretty well honed before starting in this book.

Having said that this book has helped me out a lot.The new concepts are pretty well explained.Has lots of diagrams to help out.

It Is Calculus The Easy Way
After taking calculus 18 years ago I needed a refresher. Boy do I wish that this had been my calculus book back then. It was so easy to read, the examples were great and the problems even better. It is story based, which makes it more interesting to follow. Before the end of the chapter problems there is a worksheet page that starts with very basic problems and gets the brain juices flowing to make it easier to answer the tougher exercises at the end of the chapter.

Know what you're buying...
After being very impressed by Barron's Organic Chemistry book, which I used to help me study for the PCAT, I bought this Calculus book without looking inside.It's nothing like the other book I bought.It's written like a novel, with ponderous medieval settings and dialogue used to explain calculus concepts that should really be straightforward.

I hated it.Maybe if you have no practical need for learning calculus, or if you have infinite time on your hands to do so, you'll like it.But for me, it made it 1000 times more difficult to learn.I had to dig through mountains of foolishness to find what was really a simple rule.It's not like it balances the "fun" with a clear presentation of concepts--it's all fun, and the concepts themselves are hidden like Easter eggs.Calculus the hard way, if you ask me.I'd rather have a regular calculus textbook any day, if they weren't so darn expensive. ... Read more

Product Description
Success in your calculus course starts here! James Stewart?s CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course! ... Read more

Customer Reviews (32)

Book
This was a required text for a college course. The book came as described in terms of condition and came fairly promptly.

Good
Item is a little worn, and written in, but nothing that i didn't expect really.

ehhh
got the book within a week. the condition of the book was reasonable, but i dont think the price matched the way the book was.

Perfect!
Received this item within days. Minor binding issue but still in tact. Can't beat this quality at this price!

Disaster
First time taking calculus - this book made it a disaster.I'll give the author one thing, he is a smart guy.However it seems as though Stewart has forgotten how difficult it is to learn this material.Explanations are wordy and overcomplicated, and example problems are constantly missing important steps.In addition, homework problems are almost undoable.My first assignment for calculus 2 (using the second half of the book) took six hours to complete with two other friends because we just couldn't wrap our brains around the concepts.The only reason this review has two stars instead of one is because of the useful integral table in the back and an attractive cover design.Beyond that, prepare to be lost. ... Read more

Product Description
A traditional and accessible calculus book with a strong conceptual and geometric slant that assumes a background in single-variable calculus. It uses the language and notation of vectors and matrices to clarify issues in multivariable calculus, and combines a clear and expansive writing style with an interesting selection of material.Chapter topics cover vectors, differentiation in several variables, vector-valued functions, maxima and minima in several variables, multiple integration, line integrals, surface integrals and vector analysis, and vector analysis in higher dimensions.For individuals interested in math and calculus. ... Read more

Customer Reviews (27)

Three stars mean look for a better alternative
As strange as it sound, I used this book and the solutions manual for self study.It was totally unappropriated for that purpose.I did my due diligence in finding a good textbook but endured the 6 chapters to study this. the solutions manual wasn't anymore helpful that the plain answers at the back of the book.

I have maintained that when a math textbook claims it is rigorous, it most definitely means inelegant and this is true for "Vector Calculus".The content is not arranged in a meaningful way and the content that is covered is covered to satisfy a checklist.Furthermore, there is very little relationship between the chapters.In order to do the exercises I used Mathematica to check and understand my answers and I think that "Vector Calculus" uses it instead of Matlab or Maple which other authors prefer.

I would have preferred to see it integrated with more linear algebra, that which is not anymore demanding.

Not Helpful
This solutions manual is not helpful at all. It doesn't have answers for even questions or most of the odd questions. Any tough problems just aren't included. The problems I actually need help with aren't in the solutions manual, making it totally useless.

Disorganized book
I've read Courant (Vol II), Apostol, Kaplan, and less so, Widder, Marsden & Trombda, and come under the impression that any of these books will better cover the material than Colley's Vector Calculus.

This book was used for the final of my college's calculus sequence, and I only used it for the exercises.

What I didn't like most was the way it was organized. Let's see, I flip to a random page - parametrized curves and Kepler's Laws. It goes, wham, definition, definition, example, theorem, proposition, theorem, definition, proposition, step 1, step 2, step 3, theorem... Very disorganized. No proofs. No mathematical motivations. It feels like an outline.

Only worse, because no indication or motivation is given to lead in to important concepts. The index looks nearly the same as any advanced calculus textbook - yet when you flip to any entry, you'll realize it's just in boldface, lying on the tangent to some example or exercise question.

The content is not very extensive. In Kaplan, Apostol, a chapter is dedicated to linear algebra, whereas Colley only discusses vector algebra - this comes back say in the extrema of functions, in the discussion of quadratic forms. The content starts with multivariable calculus, differential operators, multiple integrals, and ends off at Stokes' theorem etc. before a discussion on series.

I don't understand the purpose of this book. It has an applied slant - you can go through all of the exercises just plugging into the 'propositions/definitions' - but is heavy on notation (not rigor), because you can finish these exercises without actually appreciating any one of the theorems/definitions/propositions in a way that will teach you how to formulate a proof.

Tries to really go Deep but fails
This book tries to do a great thing, but fails at it.

I can list several examples where this book really goes into detail, but unless you have another source, you wont understand this.

Simply put, this book is like a list of directions for me. Not every book I have seen (I have a few from older classmates) covers everything thats in this book.

I see that I have to learn, for example, the Hessian Criterion for Constrained Extrema, but I will go to another source to do it.

If I didnt have this book, I wouldn't know about the Hessian Criterion (unless someone told me or I found it), but I wont really learn from the book.

This textbook tells you what you should learn, and you go and learn it.

The reason for the poor instruction is the lack of explanations, and sometimes repeated usage of the same variables, which, as one might guess, in multi-variable calculus, is EXTREMELY confusing and shouldn't be allowed.

If your required to get this book, expect that you'll see what Calculus 3 is about, but dont expect to learn it.

Good introduction.
This book is a good introduction to calculus in higher dimensions, but thats all it is, an introduction. It lacks a bit in terms of theory, and mostly focuses on chug and plug type methods, which is fine for an introduction, but if your curious about learning more then look elsewhere. ... Read more

Product Description

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 elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Additional topics include black holes, gravitational waves, and a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume's appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. 1982 ed.
... Read more

Customer Reviews (6)

Tensors and Relativity for high-functioning amateurs
As a writer and philosopher I have tried to get a genuine scientific understanding of topics like quantum physics and relativity. Treatments tend to be either over-simplified (no math) or presume you are very competent at graduate-level math. My past efforts have raised my math competence to the point where this book, for me, is at a near-perfect level. I found the explanation and use of tensors tied to physics in a way that helped me with both subjects.

I was also pleased with the treatment of general relativity. Many books give good accounts of special relativity, but this is the best presentation of general relativity that includes the mathematics involved.

I would recommend this to anyone who is willing to do the math. But without at least a basic understanding of vectors and partial derivatives, you will not be able to follow the text.

Good but dated, only for beginners
This book provides a good introduction to the basics of both the special and the general Theory of Relativity. I do not, however, like its style entirely. It is a little dated, too. For example, for the special part of the theory, the author sticks to Cartesian tensors only, which is advantageous only from the vintage of a student interested in... Special Relativity! This wastes time; moreover, I regard the choice of x_4 = ict unfortunate. Finally, despite the book being only 205 pages long and covering a reasonable amount of basic stuff, the style is wordy.

Study elsewhere (the book by D'Inverno is OK, the ones by Schutz and Wald rock), and if you feel the need for practice with some elementary point, go for the exercises in this book.

A reasonable introduction, but outdated and superceded
I bought this work years ago as an undergraduate and worked through most of it. It does a decent job of presenting the basics, though generally in an old-fashioned approach to the subject. I have never found occasion to return to it (except to write this review). There are quite a few texts that do a better job. For example, at the undergraduate level there is Hartle's excellent text and for the more serious student Carroll's and Wald's books are the solid standard texts. In short, I advise bypassing this little volume, despite its tempting price.

Excellent book for self learners
I'm really impressed with the clarity of the material.
I've worked through 21 problems in chapter 2, and the answers to the exercies do not have a single mistake in them yet.

The publisher will also email you a .pdf file of all of the chapter problems worked out in detail. I've found the solutions to the problems to be a good supplement to the text itself.

I would buy other titles from this author and publisher.

Good introduction to the topic
This book is very good for those seeking an introduction to Tensor Calculus, Relativity and Cosmology. Nothing more than a basic and fundamental know-how of physics is required, atleast for the first few chapters. If you're comfortable with the simple basics of linear algebra, classical mechanics, electromagnetics and calculus, you should have no problem with this book.

The book starts out with a basic review of classical physics and very quickly progresses to the Lorentz Transformation, and then to Cartesian Tensors and Special Relativity. Lawden handles the flow quite well, and covers the basic Special Relativity mechanics & electrodynamics as well as general Tensor Calculus & Riemann Spaces. Finally, he proceeds to discuss the General Theory of Relativity with a strong focus on Black Holes & Gravitational waves and analyzes elements of Cosmology in the light of the General Theory of Relativity.

However, I would not recommend this book in and of itself for learning Tensor Calculus. Unfortunately, Lawden does not have any relevant references to Quantum Mechanics, either, which would have proven to be immensely useful to the novice reader. You'd also do well to brush up on your physics fundamentals before jumping head-on.

This book primarily acts as a very basic introduction to those that are not familiar with some aspects of elementary modern physics such as Tensor Calculus and Relativity, and does an extremely good job of that.

Personally, I'd highly recommend this book if you're looking to read up on Relativity & related areas. ... Read more

Product Description
This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too. ... Read more

Customer Reviews (19)

Tensor calculus
One of the best books you'll find covering the tensor analysis. Full of exercises, theory well explained and curious theory applications. Good purchase.

Excellent book
I used to feel that tensor is difficult to study because of lousy tensor textbooks. However, since I used this book, I could easily make a smooth progress every day without painfulness. As a branch of mathematics, to practice as many as possible execises is extremely important. Without practicing enough exercises with detailed explaination, one can never completely understand and proficiently master tensor. This book is the best in this sense. The explaination and statement are very clear. A typically classic tensor textbook!

The Standard Schaum Fare
This is the normal Schaum Outline fare: long on mechanics and solved problems, but short on heuristics and anything approaching robust explanations. I believe tensor Calculus is one area where more than just a minimal overview is needed. Although it was very helpful in the introduction for the author to have thrown in (almost as an after thought) that the key use of tensors is in situations where a "change of coordinates" is in order, at least another paragraph of this sort would have been maximally useful. Why be so skimpy on critically needed explanations?

While it is understandable that a great deal of time can be saved with more cryptic notation, here it almost reaches the outer limits and the breaking point of understandability - not that I have a better solution, nor have I seen better ones in other texts, given the circumstances of the substance. Yet, for the novice, the continuing compounding makes for exceedingly difficult trudging. The mental bookkeeping gets mind-boggling. Even so, I am happy the author elected to take the more conventional component approach, grounded more in Linear Algebra, Vector Analysis and Vector Calculus - all areas where I have at least had some minimal preparation. I shutter to think what learning this subject would have been like taking whatever the alternative route is.

As a final nitpick, with the newer photo print technology, one would have expected by now that Schaum would have updated its graphics and pictorials, especially in a subject where doing so could add an important new dimension of understanding. I get it that the cover has changed, but what about the graphics? (Hint, hint)

With these complaints made, one certainly cannot fault the excellent examples of the use of tensors exhibited here, both as they apply to the theory of electromagnetism and to Relativity theory - less so for aerodynamics and fluid mechanics. Even with the daunting notational hurdle to overcome in the beginning, it brings into clear focus the real need for both Riemann Geometry and Tensor Calculus for solving problems of higher physics. Four Stars

Great book
This is a very usefull book for those one who want to learn tensor calculus with a lot of applications of Relativity.

I enjoy it. An of course Amazon.com rules!!!!!

Claro y contundente
Este libro te lleva de la mano, como cualquiera de la serie, para un mejor entendimiento del calculo tensorial, no lo recomendaría para se el texto principal de un curso, sino un apoyo para ejercitar y repasar, es bastante claro y de gran ayuda, ya que sus ejemplos y desarrollo son de utilidad para poder desarrollar habilidad en el manejo de la notaciòn tensorial. Puede ser de gran ayuda para un curso de metodos matemàticos de la fisica. ... Read more

Product Description
The author of this imaginative self-teaching book tells an entertaining story about travels in the fictional land of Carmorra. In the process he introduces a series of problems and solves them by applying principles of calculus. Readers are introduced to derivatives, natural logarithms, exponential functions, differential equations, and much more. Skill-building exercises are presented at the end of every chapter. Books in Barron's new E-Z series are enhanced and updated editions of Barron's older, highly popular Easy Way books.New cover designs reflect the brand-new interior layouts, which feature extensive two-color treatment, a fresh, modern typeface, and more graphic material than ever. Charts, graphs, diagrams, line illustrations, and where appropriate, amusing cartoons help make learning E-Z in a variety of subjects. Barron's E-Z books are self-teaching manuals focused to improve students' grades in skill levels that range between senior high school and college-101 standards. ... Read more

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Customer Reviews (2)

Get this and Mulitivariable
The solutions manual was a great purchase.This book breaks down the problem and shows step-by-step on how to complete the problem.

If you're only planning on taking (Calculus 1 up to Calculus 3) then this book is all you need.But if you're going to take Calculus 4 (Multi-variable Calculus) then you should get the second book.

Very Helpful!
I'm taking an online Calculus 1 course and I wouldn't have been able to get through the many homework assignments without this solutions manual! It provides step-by-step solutions that are easily understood by even the most mathematically challenged. I would definitely suggest purchasing this manual to accompany the actual textbook. ... Read more

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Customer Reviews (47)

Not the best text for learning Multivar for the first time
I'm a freshman taking Multivariate at University with a distinguished math reputation, and I dropped my multivariate course because of this book. The writing style is not unified and incoherent at best, and so the proofs and discussions of theory meander quite a bit. If this is your first exposure to vector calculus, as it was mine, this can be quite discouraging.

The problems are very difficult, and often involve proving theorems that are only tangentially related to the topics being studied. While this book does go much further in depth than a standard multivariate calculus textbook, the cost is a deeper working understanding of the material. This book is really only worth it if you already know multivar or vector calculus and are seeking harder problems. the examples and lessons are simply insufficient.

My new course uses Thomas' Calculus, which is a textbook lightyears head of this one in overall quality of instruction. Stay away from this book.

Horrible exercises
I rarely ever find myself making reviews for any textbook of any sort unless I truly think that the textbook is horrible. Now while I do like the cover art the example diagrams and the historical aspect integrated into the book there is one huge drawback that I would like to mention.

The exercises are horrible!!

I find myself coming up on answers that are such ugly fractions with ugly algebra integrated into them that you spend most of your time juggling the algebra rather than doing what you're supposed to be doing in vector calculus course which is of course learning calculus. I have taken the full entirety of vector calculus and I had to retake the second semester again with this book (seeing as how UC's don't give you credit for the second semester.) After the first three homework sections I am convinced that this book has problems that were not very well chosen whatsoever. My previous book (early transcendentals stewart 6e) was brilliant compared to this one. When you find that even your own graphing calculator does not have the power to create a fraction for a sum of really horrible looking fraction you realize how terrible this book is. That being said I don't recommend this book to learn unless you only set up the integrals without integrating. Rarely am I dissatisfied with mathematics (for such a beautiful language it is) to the point where I write a review. Look elsewhere my fellow mathematicians, engineers, and physical science students.

horrible horrible horrible
This book is horrible.The example problems don't match with the practice problems, and the way they were written was simply hard to understand.

It might be a good book for those who have plenty of experience in vector calc, but not for people, such as myself, who are relatively new to this field.

are you using this book in multivariable calculus?
as the topic says, "are you using this book in multi-variable calculus?". I've heard heavy complaint from those who have. Myself on the other hand used it for a 400 level "Advanced Calculus" course whose prerequisites is multi-variable calculus. We finished the entire book in 15 weeks.

Since this book introduces Vectors from scratch, we ended up re-learning vectors, gradients, double integral, triple integral, path integral, line intergral, stokes, divergence...essentially most of what we learned in multi-variable.

One would think this would be piece of cake. Well not exactly. Despite having previous knowledge on most stuff in the book, we found it hard to follow (by 'we' i mean my classmates and myself). Not only that the exercise were terrible. Some of them were over-stretchy in terms of calculations while most ended up being straight forward questions.

---

I bought Vector Calculus Study Guide & Solutions Manual to accompany this book. The solution manual summarizes each sections and provides solutions to selected (those that numbered in red in the book) problems. It isn't great but you'll benefit from it for sure.

Another thing that you'll benefit from is an easy to understand multivariable book. I've used Calculus (you can just get the multivariable part Multivariable Calculus (Paper)). It is from the same publisher, goes over pretty much the same stuff...and it 10x easier to understand. I would recommend it. I'll also throw out Stewart's name, i haven't used his Calculus book but from what i've heard of it's decent.

Poorly written
Book isn't very well written, but pretty. Doesn't explain vector calculus very well, but unfortunately it was required for my course. I would recommend buying a different book if you have an option, I have heard that Multivariable Calculus (Stewart's Calculus Series) or Multivariable Calculus: Early Transcendentals (Stewart's Calculus Series) is really good. Not sure what the difference is between the two though... ... Read more

Product Description
This book is designed as a text for graduate courses instochastic processes. It is written for readers familiar withmeasure-theoretic probability and discrete-time processes who wish toexplore stochastic processes in continuous time. The vehicle chosenfor this exposition is Brownian motion, which is presented as thecanonical example of both a martingale and a Markov process withcontinuous paths. In this context, the theory of stochasticintegration and stochastic calculus is developed. The power of thiscalculus is illustrated by results concerning representations ofmartingales and change of measure on Wiener space, and these in turnpermit a presentation of recent advances in financial economics(option pricing and consumption/investment optimization). This bookcontains a detailed discussion of weak and strong solutions ofstochastic differential equations and a study of local time forsemimartingales, with special emphasis on the theory of Brownian localtime. The text is complemented by a large number of problems andexercises. ... Read more

Customer Reviews (7)

Excelent
This is a great book. By far, the best I have red about stochastic analysis

A Superb Book
I found this book to be an excellent introduction into the subject matter. A good background in measure theoretic probability theory definitely helps, but even without much background, it is possible to understand all, but the finest measure theoretic points (I am a hobby mathematician with an engineering background, and I simply used the book "Probability Theory" by Laha & Rohatgi to learn what was needed about measure theory).
It is amazing, how the authors motivate, what they are doing using very few, but the right, words.

The pace of the book is just right, not too brisk and not too leasurely.

The only negative point is the following:
It takes some getting used to, that many important results are presented in the form of "problems".The solutions are generally given at the end of each chapter, so one has to thumb back an forth through the text.

Last but not least, the book contains virtually no misprints! For someone, who uses this book for self study, this is a very important point!

Massive Exercise to the Reader
This book isn't really the place to start learning about stochastic calculus. Get Oskendal's Stochastic Differential Equations: An Introduction with Applications for this.

Even to the prepared reader, this book is exasperating. It is as if the authors came up with an excellent outline for an advanced treatment of this topic. Then they realized that to do all of the material justice, they'd need to have not one, but two 400 page volumes. Their publisher must have balked at that idea, so their solution was to leave out half the detail, forcing each of our poor readers to re-generate the missing 400 pages of needed detail on his/her own. In the opinion of this reviewer, that is exactly what they have done with this text.

Fortunately for us all, there exists a nice two volume (800 page total pages) treatment of this material. Rogers & Williams Diffusions, Markov Processes, and Martingales: Volume 1, Foundations and Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus provide a thorough, accessible exposition with all the needed rigor, generality and detail.

Karatzas & Shreve's treatment of early foundational material is less than helpful to the student. Consider a pair of key results on martingales early on in the text: the optional sampling theorem and the optional stopping theorem. The authors "prove" the optional sampling theorem by appealing to the discrete time results in Chung's A Course in Probability Theory and then applying limiting arguments to bootstrap to the continuous time case. Since all of the real "ideas" are in the discrete time case, it's not clear how much of a service the authors' treatment really is. Worse yet, the optional stopping theorem isn't even called out as a theorem, but instead buried as problem.

It is curious to see which topics inspire the authors to spill ink. For example in Chapter 2, we get not one, but 3, yes three different constructions of Brownian motion: convolved heat kernels, Haar interpolation and random walks/Wiener measure.Of course, only the last construction is used going forward and the first two constructions are not brimming over with detail. This is a curious indulgence in a text that is purposefully being stingy with detail. Our poor reader has to pay the price for this indulgence with an extremely terse treatment of the strong Markov property and reflection principle, the Blumenthal Zero-One Law, and other foundational properties of Brownian motion.

Chapter 3 represents the core of the text and develops all the of "greatest hits" including the Ito Integral, Ito's rule, Levy's characterization of Brownian motion, the martingale representation theorem, the Girsanov Theorem and an introduction of Brownian local time. (Brownian local time is further developed in Chapter 6). The development of the Ito Integral is shamelessly sketchy. All the theorems are correctly stated, but the "proofs" offered aren't detailed enough to explain why all of the stated assumptions are needed. When the reader gets to the development of Ito's rule, he/she finds a rude 3 sentence introduction to semi-martingales, a topic which hadn't been explored and never gets more than a passing mention in the authors' text.

Assuming that you've understood everything going on in the text up to this point, Chapter 4 is quite nice. It gives a very intuitive introduction in the role of the Mean Value Theorem as a hook connecting stochastic integrals with classical PDE's. The section on Harmonic functions and the Dirichlet problem is quite nice. The material on the heat equation requires properties of Brownian motion most easily derived from the convolved heat kernels construction. The chapter winds up with a nice treatment of the Feynman-Kac formulas.

After the PDE's material, the reader might develop a sense of hope that the remainder of the exposition will be readily accessible. This is not the case and with the SDE's in Chapter 5, the authors return to their now too familiar terse style as they study strong and weak solutions to stochastic differential equations. At one point, the authors decide to approach the problem by generalizing from functions to functionals without even so much as defining their notion of a functional.

Really, the only good role for this text is as base material for a do-it-yourself "Moore Method" class on stochastic calculus, like they used to do for general topology at the University of Texas. If you completed a Moore-style class this way and wrote up all of your work, you'd have a very fine text covering diffusions, Markov processes, and martingales.

A Must
If you want to learn about stochastic calculus, this is the gold standard. Certainly a challenge, but if you can answer all the questions posed in the book you will have a very thorough knowledge of BM, stochastic integration with respect to BM, SDE's, and the SDE/PDE relationship.

While this is a great book, I do have a couple complaints. First of all there a points in the book where overly complicated notation can obscure the point being made. Secondly, since the book does not cover semimartingale integration, topics like the quadratic variation process (which are still important for things like representing a martingale as a time-changed BM) are spread throughout the book and can be difficult to find.

I recommend reading Rogers&Williams "Diffusions, Makov Processes, and Martingales" Vols I&II in addition to this book. Not only does it give a second (and sometimes easier) point of view on the somewhat difficult topic of stochastic analysis, but also covers some topics in greater generality including integration wrt a general semimartingale.

Finally, a warning to those who have interest but are not proper mathematics students. This book presupposes a fair amount of mathematical maturity - if you don't have a good understanding of real analysis and measure-theoretic probability you probably won't understand anything.

The best introduction
The theory of Brownian motion is ubiquitous in physics and mathematics, and has recently become very important in mathematical finance and network modeling. The observation of the irregular movement of pollen suspended in water by Robert Brown in 1828 led Albert Einstein to formulate a theory for Brownian motion. In this book the authors outline rigorously the theory of Browian motion. Their logic is impeccable, and the content is fascinating reading, even to those very experienced in the subject.

The authors begin in chapter 1 with the task of defining martingales and filtrations, with the notion of a stochastic process being adapted to a filtration taking on particular importance. They omit the proof that a process is progressively measurable if and only if it is measurable and adapted, because of the difficulty of the proof, but give a reference where the proof can be found. Continuous-time martingales are defined, with (compensated) Poisson processes given as an example. The Doob-Meyer decomposition and square-integrable martingales are discussed, and the chapter if full of exercises, with solutions provided to some of these at the end of the chapter. Brownian motion is formally defined in the next chapter, with its existence proven using Wiener measure on the space of continuous functions on the positive half line. The discussion in this chapter has to rank as one of the best in print, due to the meticulous and precise manner in which the material is presented. The Markov property of Brownian motion is proven, along with a good presentation of the Levi modulus of continuity. Readers working in constructive quantum field theory will see their usual construction of Wiener measure in the second exercise of the chapter. Those working in that area are used to seeing (conditional) Wiener measure defined on a collection of cylinder sets, which is then extended to the Borel subsets . Such a construction is done in this book, but the approach is somewhat different than what physicists normally see in quantum field theory.

The theory of stochastic integration is presented in Chapter 3, and it is superbly written. The authors are careful to distinguish the theory of integration for stochastic processes from the ordinary one with emphasis on the actual computation of stochastic integrals. The reader is first asked to explore the Stratonovitch and Ito integrals in an exercise., and then a thorough treatment is given by the authors later in the chapter. The authors point out the differences between the Ito and Stratonovich integrals, with the latter being defined for a smaller class of functions than the former. The important Ito rule for changing variables is discussed, and then used to give the Kunita-Watanabe martingale characterization of Brownian motion. Physicists involved in constructive quantum field theory will appreciate the discussion of the Trotter existence theorem in this chapter.

The connection of Brownian motion with partial differential equations, so familiar to physicists via the heat equation, is the subject of the next chapter. These equations give the transition probabilities of the stochastic process, and are studied here first in the context of harmonic analysis, namely the classical Dirichlet problem. This is followed by a beautiful treatment of the one-dimensional heat equation and the Feynman-Kac formulas. Those readers working in constructive quantum field theory will see the Green's function lurking in the background.

The very important topic of stochastic differential equations is outlined in chapter 5, with emphasis placed on the study of diffusive processes. The solutions of these equations have an immense literature, and the authors do not of course overview all of it, but do give a useful introduction. Both strong and weak solutions are discussed, with the Girsanov and Yamada-Watanabe techniques used throughout. Explicit solutions are given for linear stochastic differential equations, such as the Ornstein-Uhlenbeck process governing the Brownian motion of a particle with friction. Financial engineers will appreciate the discussion of the applications of this formalism to option pricing and the Merton consumption theory in this chapter. Options pricing is cast in martingale terms, and then the usual Black-Scholes equation is derived from this. The notorious Hamilton-Jacobi-Bellman equation is discussed in the consumption/investment problem, and the authors show how to employ techniques for solving this problem instead of solving this difficult nonlinear equation. The authors give a hint of the important Malliavin calculus in the Appendix and give references for the reader.

The last chapter of the book is more specialized than the rest and deals with the Levy theory of Brownian local time. This theory does have a connection with the theory of jump processes, which are currently very important in financial and network modeling. The authors do a fine job of explaining how Poisson random measures permit the event bookkeeping in these jump processes. Their discussion is applied to the computing of the transition probabilities for a Brownian motion with two-valued drift. ... Read more

Product Description
Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. ... Read more

Customer Reviews (21)

great deal
This book was like brand new, and arrived quickly.Saved a lot of money over the used book price in the school bookstore.

Low quality calculus text
Calculus texts seem to have lost its rigorous approach to mathematics. The best book on the market to actually learn Real calculus is Calculus Volume I by Tom M. Apostol. James Sewert's book lacks proofs and examples. I think if you're going to pay top dollar for a math book it should have at least tons of examples as well as tons of problems to solve that will actually help the student in his/her studies in more advanced topics in math or science.My Calculus II professor even hated this book due to its lack of quality. I think publishers should try to publish higher quality books over time rather than pretty pictures of the same material to just force the schools to change over and collect the money. I would pick up Apostol's book to accompany this book in the studies of mathematics.

Thanks!
Thanks for this purchase. Im sorry I forgot to write you a review. As you can see I ordered a Calculus book, so that takes a lot of my time on top of taking 22 credit hours. Wish me luck!

great service.fast shipping and product as described
great service.fast shipping and product as described.Except one of the disks doesn't work.But that might be my computer.

good book for high schoolAP calculas
My child's high school uses this book as their AP calculas text book. I bought this one as a backup. It is a very good book and explain everything clearly with a lot of examples, execises. ... Read more

Product Description

The acclaimed Calculus: Concepts and Applications is now available in a new edition, revised to reflect important changes in the Advanced Placement curriculum, and updated to incorporate feedback from instructors throughout the U.S.

Customer Reviews (4)

Good for what it is
The title says it all. This book is designed to be a "textbook" for the AP Calculus AB/BC exams. I think in that respect it succeeds immensely!

My teacher chose this text for our AP Calculus AB class and found it a delight to work with. The concepts were explained clearly, there were enough example problems to get the point across. I did find an occasional "skipped" step which would basically force me to try to fill in the gap, but hey, that helps get the calculus juices flowing, right?

The problems in the book -- which are the cornerstone of any textbook -- are really well designed for what an AP Calculus student should be able to do. There are several kinds of problems. The "quick reviews" are useful for beginning of class warmups (you know, 10 minutes to drill the basics) and the actual problems can vary from easy to challenging (but all within the scope of AP difficulty).

So if you're an AP Calc teacher looking for a class text or a student who wants to self study calculus specifically for the AP exam, then this is, by all means, the text to use. I suggest pairing this with Princeton Review's AP Calculus prep book if you want a 5.

pretty good
This was the main textbook used for my Calculus AB class. Its explanations are clear, though sometimes difficult steps in algebraic manipulation are skipped (which may initially confuse but can be figured out after some additional work). The text progresses within each chapter, relying initially on an exploratory section where concepts are not directly stated but figured out through a little guidance with the questions. This first section introduces the readers to the concept being studied in each respective chapter. Then, the information is given in ensuing sections of the chapter. The best part of this text is the "green boxes" which sum up concepts learned, definitions, formulas, etc., which make reviewing for a final exam a much simpler task. It has a simple presentation with few colors, sticking mainly to a light olive green and gray for the pictures and other illustrations. This textbook is a very good tool for calculus students, relying on varied methods of learning and some self-discovery of the subject matter.

Great Book
This is a great book, I used it in my Pre-Cal and BC Cal class. It's very easy to understand, and easy to get into Calculus class!

An excellent book from an excellent teacher.
This book made a difficult subject (calculus) easy to understand through its effective use of diagrams, examples, and word problems.Iwould not have been able to survive Calculus BC AP without it. ... Read more

Product Description

Customer Reviews (31)

newspaper quality
I'm giving this review not so much to discuss the contents of the book, which I think is very good and would give*****, but the production quality of this edition which is truly appalling.As an undergraduate I used the first edition (OK, I admit I'm retired) which was on nice semi-glossy paper with crisp printing and figures.This edition from Westview Press looks like it was faxed onto newsprint.The earlier edition is virtually impossible to find so you are probably stuck with this one.If however you can get the earlier one, it is worth paying extra to buy a book and not something that looks like a newspaper flyer.

Great book.If you're prepared that is.
In the preface Spivak says that this book is accessible to anyone that has had good courses in calculus and linear algebra.While this is true, the term "good" needs a little clarification.If you've taken a two semester calculus sequence using the "cook book" approach, you will be grossly under-prepared for Spivak.Ideally you'd have taken one of the many theoretical calculus with honors courses offered at good universities or a nice undergraduate analysis course.I'd suggest preparing by means of Spivak's own book, Calculus, barring that you'll do well with Introduction to Analysis by Maxwell Rosenlicht, Understanding Analysis by Stephen Abbott, or, if you want to be old school, the first seven chapters of Principles of Mathematical Analysis by Walter Rudin.All the aforementioned books (except for Spivak's Calculus) cover topology and continuous functions at a more leisurely pace than Spivak.For the linear algebra I'd suggest one of Finite Dimensional Vector Spaces by Paul Halmos, Linear Algebra Done Right by Axler, or Linear Algebra by Peter Lax.The book by Lax is a wee bit more advanced and may require more maturity.Also the book by Axler downplays the role of matrices, focusing instead on linear maps as separate entities that can be expressed by means of a matrix given a basis.While this is a good approach, I'd suggest making an effort learn how to play with matrices.A lot of properties of differentiable functions from R^m to R^n can be handled with matrix tricksIf you work through one of the three calculus books and one of the three analysis books I've recommended you'll be in great shape for Spivak.It must be said that the exercises in Spivak are challenging and many are proofs of nontrivial theorems.It's hard work and requires significant creativity on the part of the reader.Of course, this makes the book ideal for training up new mathematicians.That's what the book is for and it is excellent at that; which is why I've given it five stars.

More Advanced Than It Claims
Be warned:Spivak is speaking a different language from any I was taught.I have spent hundreds of hours on this book, and have filled three binders with notes on the first three chapters.If you are using it in the right manner, it is a fantastic book;otherwise, it is a nightmarish exercise in frustration.Expect to rewrite the textbook in your efforts to understand it;for some, this is a plus.It is an excellent book for inspiring effort and creativity, but it is dreadful if you do not have outside support.It is NOT a primary text by any stretch of the imagination.

The first blow against the book is its claim that "only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course" are required.This is enormously demoralizing to the student who has these prerequisites and yet finds Spivak incredibly obscure;but it IS obscure.The problem here is partly one of miscommunication:it turns out that Spivak has written his own "Calculus" textbook, based on his own notions of what such a course should contain.Having examined and read part of that text, I would describe Spivak's "Calculus" as a challenging introductory analysis textbook with a deep review of calculus.It is absolutely not a book to learn calculus from in the first place, unless one is prepared to spend five times as much time as it should take, and then to relearn the entire subject in order to be able to communicate with everyone else.

The second blow against it is the notation:Spivak has invented his own.Despite having had calculus, and being a successful calculus tutor, I found it nearly impossible to recognize the basic rules of differentiation in his encryption.The situation was bad enough that I felt compelled to devise my own hybrid notation to translate back and forth between the style used in Spivak and the style I have seen everywhere else in my studies, and to add clarity at a few crucial confusing points.

The third blow is that there is no clear indication of what tools are expected to be available to the student.I ended up taking breaks to devise and prove large sets of lemmas and theorems in topology and analysis just to make the problems more feasible.I suspect that that was the intent--but one might have said so.

The fourth problem is also part of its appeal:it is incredibly concise.This means that there are next to no examples, and huge amounts of detail have been skipped.Far too much has been skipped in places.The Implicit Function Theorem proof in particular was a nightmare;I had to completely rewrite it.

This book is most properly used as a challenge problem set for fairly advanced mathematics students, with guidance, to inspire huge amounts of work and creativity.It is least properly used as a primary text, an introduction, or a means to learn anything rapidly.

disappointing
What a bunch of hype on this book.It's format is so concise as to be practically useless. It seems to be a bunch of class notes cobbled together.Mulitvariable calculus in a book that is only 5 inches across?What a dis-service to the subject.It can barely contain the full definitions for tensor products. Just silly.Lacking examples or much of anything for the reader to bridge the gap his terse prose leaves. A Font so small that indices are lost on some equations. It is no Differential Geometry. The difficulty is not within the subject matter, but with it's meager presentation.Not at all the quality you would expect from this author.God, I hope this isn't "The" book on calculus on manifolds. Not to mention the typos.I never knew that f(a)= f(a)+ f'(a)*h...oh wait it isn't, but f(a+h) is!Iguess it was tough proof reading a hundred pages with 10 sentences on each page.Get the cheapest version you can.

Tip of the iceberg...
This book would serve well as a self-study introduction to smooth manifolds for a student just finishing a high school calculus course. For those serious about the subject, pick up John M. Lee's "Introduction to smooth manifolds." ... Read more

Product Description
Here is the first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities. With mathematical precision and in a style tailored for market practioners, the authors describe key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model. Starting from discrete-time hedging on binary trees, the authors develop continuous-time stock models (including the Black-Scholes method). They stress practicalities including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. The authors provide a full glossary of probabilistic and financial terms. ... Read more

Customer Reviews (33)

This book sucks!
Someone recommended me this book, claiming it was one of the best introductory books in derivative pricing in the market. As soon as I opened it, I knew I was going to have trouble with it, and my fears were confirmed when I read the first paragraph. I come from an engineering background, with little knowledge of stochastic calculus, so that had to play a role in my difficulties. However, I picked a book in advanced stochastic calculus from 1962, and its a whole new world altogether, it is at least readable. So, here are my comments:

1) it is NOT an introductory book, as it claims to be, if you want an introductory book, I recommend Hull (btw, very effective)
2) presents equations without identifying their variables
3) sometimes introduces 2 symbols for the same variable
4) other times gives several definitions for the same symbol (such as in f, right at the beginning)
5) sometimes gives the variables definitions 10 paragraphs ahead (as in the stock price log-normal distribution)
6) introduces equations without giving any reasons for assuming them (as in q-martingale probability) as if it was some sort of magic trick, when in fact they have a meaning in statistics the author knows all about from the very beginning
7) concepts are given in illogical order
8) too many and complex equations in the middle of wording, which makes the reading almost impossible
9) misses too many steps in between equations...

And the list goes on. I think the authors were high/low on drugs when they wrote this. I do not recommend this book to anyone, especially if you are one of those rare people interested in understanding what you are reading.

Financial Calculus: An Into to Derivative Pricing
This book has a good coverage of Financial Calculus and Stochastic Calculus, however, there should be more mathematical steps involved in solving problems and creating theorems in their examples.

Modern And Up-To-Date
"Martin Baxter
Works at Nomura International in London.
He was a Fellow for four years at Pembroke College, Cambridge, has held a one-year visiting position at the University of British Columbia, and has been an invited speaker to both academic and financial audiences in Europe and North America.

Andrew Rennie
Studied mathematics at Cambridge.
He is presently Head of Financial Engineering at Rabo Bank in London, a position he reached via philosophy, chemistry and graphic design."
[from the book of the front flap]

"The book is the First published 1996
Reprinted with corrections 1997
Reprinted 1998 (twice), 2000 (twice), 2001 (twice)
Printed in the United Kingdom at the University Press, Cambridge."
[from the book]

".....This unique, MODERN AND UP-TO-DATE book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world."
[from the book of the back jacket]

Excellent introduction
I think this is one of the best introductions to mathematical finance around. Unfortunately, the book was out of print when I taught the subject, so I never got to test it as a textbook.

In particular I really like chapter 2, where the authors introduce the key concepts in discrete time binomial processes. This allow them to introduce deep concepts like information and filtration in an understandable manner, while few students really understand measurability. (If you think that is a trivial idea from stochastic analysis, you may want to go for another textbook.) The binomial representation theorem is almost trivial, but show what the general version, the martingale representation theorem is all about, and why it is so useful. Similarly, the Cameron Martin Girsanov is heavy stuff in continuous time, but the idea is simple for binomial processes. I guess a lot of students will understand what the theorem i all about for the first time when they se the binomial version.

The book then goes on to generalize all these ideas to continuous time and space, but with somewhat less mathematical formalism than many other books.

Second edition please !!!
This is a great book, no doubt about it...

The basic ideas and tools of mathematical finance (Arbitrage Pricing Theory, Stochastic Calculus, Martingale Measure) are presented in a VERY conceptual way, allowing one to gain solid intuition in a field often obscured by abstraction and formalism. The description of the impact of change of measure on Brownian Motion, among others, is a little gem!

Although the level of mathematics is not overly complex, some sections still require a fair amount of "fiddling" with pen and paper to fill in the gaps and make sure the concepts are clearly grasped. That definitely demands a little mathematical maturity and assertiveness. The section on the Binomial Representation Theorem, for example, could be expended a little, with more concrete examples. But if one spends the time, goes through the book over and over looking at everything in ever finer details (...it is only 200 pages and a pretty quick read), it is immensely rewarding and provides a solid basis to tackle more complex monographs.

The only reservation is about the quick and much rougher presentation of Interest Rates Models. While the first sections on the Black-Scholes framework, Arbitrage Pricing and replication strategies for Vanilla options are very detailed, the Heat-Jarrow-Morton model could definitely be expanded (some of the results presented are not easy to derive given the material presented) and LIBOR models should be covered.

Given the success of the book, one however wonders why a second edition polishing a few sections (see Martin Baxter's website for extra material) and addressing newer developments has not been issued... ... Read more

Product Description
Stewart's CALCULUS: CONCEPTS AND CONTEXTS, THIRD EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because it has successfully brought peace to departments that were split between reform and traditional approaches to teaching calculus. Not only does the text help reconcile the two schools of thought by skillfully merging the best of traditional calculus with the best of the reform movement, it does so with innovation and meticulous accuracy. ... Read more

Customer Reviews (15)

Calculus: James Stewart 3rd Editon
This is a calculus textbook for college classes Math 151, 152 and 153. The most current edition is the 4th, but the material is the same. Unfortunately, the homework problems are often different. The 4th edition is far more pricey, but helpful if you need to complete homework assignments.

Fair price and good condition
The product, Calculus Concepts and Contexts 3, was described correctly and listed at a fair price. The seller is great and shipped the book quickly. *Five Stars*

It's A Book
It isn't the nicest book I've gotten. Heavily used, but it's a book and it has the cd's and codes still, so I am satisfied.

Overall Review of Book
Not actually the book I wanted. I needed a different edition of the book. NO idea whether I can trade it in for the newest one or not.

Awesome quality, slow delivery
The book was in excellent condition,and at a great prize, but took a while to get shipped and delivered. ... Read more