Book Description
Scoring high on the AP Calculus AB & BC Exams is very different from earning straight A’s in school. We don’t try to teach you everything there is to know about calculus–only the strategies and information you’ll need to get your highest score. In Cracking the AP Calculus AB & BC Exams, we’ll teach you how to
·Use our preparation strategies and test-taking techniques to raise your score
·Focus on the topics most likely to appear on the test
·Test your knowledge with review questions for each calculus topic covered
This book includes 5 full-length practice AP Calculus AB & BC tests: 3 for AB and 2 for BC. All of our practice questions are just like those you’ll see on the actual exam, and we explain how to answer every question.
Customer Reviews:
ehh, it was all right.......2007-07-14
this book isnt the best to use if you're completely lost in calc and hoping to cram it at the last minute. i had a really good teacher for calc so did not have to rely on a prep book too much, but still i found this book helpful in just doing practice problems. for 2007, the practice frq they provide you in this book are nothing like the ones on the actual test. but i'd have to agree that this book is on the easy side, so beware.
A TREACHEROUS BOOK. Shame on you Princeton Review .......2007-06-15
Let me preface this by saying that I took the AP calculus test in the mid 1980's and now have helped my daughter with a self-study course on calculus in preparation for the 2007 test. After going through a total of 4 study guides, 2 textbooks, and the last 7 years of available free response questions from the actual AP test, I found this guide to be not only inadequate but also treacherous. It will instill a false confidence which will become glaringly obvious to you when taking the real test.
The AP calculus (AB or BC) has become considerably harder in the last 4 years. Like most other books, this book seems to have been developed for the test as administered in the 1990's. In order to pass, not only do you need to know your calculus - it is also mandatory that you know how to use your calculator in order to solve calculus problems. This book completely ignores this basic fact. Unlike other books (see my other reviews), there is no section on this important topic. The only reference is in the first pages when the book states that a calculator is allowed on certain parts of the test and that the Education Testing Service recommends a calculator. The fact is that a calculator and its proper usage are ABSOLUTELY ESSENTIAL in being able to solve some of the problems on the test (I also fault the testing service for not making it crystal clear that certain problems cannot be solved without the calculator). Princeton Review ought to know this simple fact which becomes obvious to anyone who has looked at the openly provided past free-response questions from the actual tests. For example, a question regarding volumes of revolution of an area between two curves has appeared on virtually every free-response section over the last 7 years. Each problem could not be solved without the use of a caculator in determing the points of intersection to use as your limits of integration. Rather than focusing on techniques of integration (which was a big deal for the earlier test in which calculators either weren't allowed or weren't capable), the emphasis has switched to integration via the calculator.
One last point of advice is that this book does not stress the concepts that are in turn stressed on the current tests - fundamental theorem of calculus, average value of a function by integration, and problems that depend on interpreting graphs and data points.
The book goes through each topic in calculus in a perfunctory manner that appears to have been adequate for the test I took in the 1980's, but not for the current exam.
When chosing a book, keep in mind that the test is no longer a simple can you integrate and take a derivative by hand type of exam. If you can solve the problems in this book, you may be prepared for the multiple choice non-calculator based parts, but you will NOT be prepared for the AP test as a whole.
absolutely fantastic.......2007-05-23
This book was amazing. I was really struggling in getting anything higher than a 3 on practice exams so I bought this book. It's true that the AB and BC materials are not separated, but it does include information noting which subjects are BC only. All you have to do is take note of that info and mark those sections BC yourself.
With the exception of two or three lessons, the lessons in the book were thorough and really helped me to understand the material better. The formatting was easy to follow as well and it didn't make me feel like I was doing a lot of work. I don't have my score back yet, but I can definitely say that this book helped. I'll definitely be using the rest of it for my BC exam next year.
Cracking the exams.......2007-05-16
I found this book to be helpful in some capacity. Although it covered all the necessary topics, I did not find it to be that in depth (it would probably help AB test takers more than BC). Some of the explanations made it more confusing than it was without the book. The practice tests were good, but did not provide explanations for the answers, which was a big downside. The essay questions provided in the practice section were so much easier than the actual test, so they didn't help either. Overall, a good basis for studying, but do NOT rely solely on this if you want to do well.
Dissapointing.......2007-05-12
This study book did not live up to the expectations set by other study books even by the same company. It was frought with grammatical, spelling, and factual errors. The explanations were confusing, and it offered little practical advice about how to actually take the exam well. If you need to study Calculus AB or BC for an AP exam, I strongly suggest that you try another company. This book was a dissapointment.
Customer Reviews:
Excellent!.......2000-04-08
This is a useful book for anyone involved in mathematics. This book has many practice problems as well as solutions. It also contains many problems that pertain to everyday life at home or office. This book is a must for any high school student wanting to get a head start on the college mathematics. This book reads very well, and contains excellent drawings to enhance the comprehension of the topics discussed.
Book Description
Updated to reflect the most recent Advanced Placement exams in Calculus, this manual presents four practice exams in Calculus AB and four more in Calculus BC, all with questions answered and explained. Extensive review sections offer brush-ups in functions and their graphs, derivatives and integrals, differential equations, and sequences and series. Additional features include test-taking tips and guidelines for using a graphing calculator. Review material includes multiple-choice questions, free-response questions, and many applications problems.
Customer Reviews:
AP Calculus.......2007-01-04
It's concise and clear for a review book. No use if you're LEARNING form it though, since it's designed to invoke and strengthen memory rather than to explain and teach. Great, challenging questions with good explanations.
good as a supplement to the class.......2005-09-10
This is a book that is best for final preparation for the exam. Last year, in BC Calculus, I was absent for the series and sequences lessons due to an illness and I came back for a test studying through the Barron's books and I had trouble understanding it. The tests are definitely a lot harder than the real thing. I studied my [...] off and got a 5 on the actual exam as well as a 5 on the AB subscore.
A Fair Book.......2005-07-16
This book is very comprehensive, too many details at times. The practice test is a little bit more difficult than the actual test. It is not very well organized or appealing to look. There aren't enough diagrams and pictures for visual learners.
Very helpful.......2004-10-01
I had several sources to help me do well in AP Calculus AB. One of them was this book.
Finney, Demana et al. "Calculus: Graphical, Numerical, Algebraic" just doesn't include enough problems. To boot, the presentation is pretty poor as too many images are bombarded at your eyes. Barron's includes a lot of extra problems for you to make sure you can apply what you know.
Provided that you work hard in class and outside, this book can help you get a five.
a bit harder than actual test.......2004-09-26
I bought two books, barrons' and Princeton's. The former was much harder to understand and contains more information than the latter. When I studied
Princeton's, I was relieved, but when I studied barrons I
became afraid that the test was really that hard. However,
when I took the real test, I found that the actual test
was more like Princeton's than Barrons'; and I got 5 on
the exam. I recommend you to buy this book for experiencing
the hardest questions that would be on the actual exam.
If you only use Princeton's, you may be frustrated to find
that there are some questions that aren't on the Princeton's
practice exams.
Book Description
This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text.
Customer Reviews:
needs complete student manual.......2007-09-28
could be better if included the solution manual for all the sections, not only for chapters 1-7
Very clear, great for learning and understanding quickly, a bit slow at times.......2006-06-16
This book is simply clearer than any other complex analysis book I've read, although it's not particularly advanced or concise.
This book is a great text for undergraduates studying complex analysis for the first time. It does not assume a strong background in rigorous analysis, making the material accessible to a wider audience.
At times I find that this book moves a bit slow for my personal taste, but what it loses in speed it makes up for in clarity. The explanations are always clear. I find that I never get stuck in a proof in this book. If there is a certain topic that I absolutely must understand, and I want to understand in a straightforward, useful way, as quick as possible, I turn to this book.
I would recommend this book for self-study as well as a textbook at the introductory level. It is not a particularly advanced book, and is not comprehensive as a reference for more advanced students, nor would it be a great choice for a graduate or advanced course.
If you like a well written, applied, operational kind book........2005-09-28
If you like mathematics but prefer an operational approach instead of the abstract approach, you will like this book.
An ideal complement to Calculus books (like Piskunov, Thomas Jr., etc.) that do not emphasize Complex Variables.
Clear explanations. Many examples. Relatively fast to read, that is, you will not stop the reading trying to demonstrate those boring "easy to show statements".
Pleased.......2005-07-05
The book was in great shape and I liked the math help websites included.
Excellent intro. to complex analysis!.......2004-06-19
This course was my first exposure to the mathematical field of analysis at the undergraduate level, and our school ditched Gamelin's book used two years ago in favor of this book. Just to give you an idea of the difference a book makes (it was the same teacher for both courses, mind you): when Gamelin was used, EVERYONE dropped out of the course; when Brown/Churchill was used, only one person dropped the course and half the class received A's!
Truly, this is a remarkable shift, and this book had a lot to do with it. I thought the organization was flawless (note: you will have to go through the book in order, as many examples depend on previous material), and starting from the beginning with the definition of a complex number was definitely the way to go, as about 1/3 of my class had never seen a complex number before. I loved the fact that there were many examples worked out (never explicitly showing people how to do the end-of-section exercises, but showing them the methods for where to go) and the major theorems were alloted many pages for clear proofs with diagrams and detailed explanations (an entire section was devoted to a proof of the Cauchy-Goursat theorem!). Also, the choices of problems were superb, with some routine exercises meant to get you thinking along the right tracks followed by some very difficult ones. Basically, enough to challenge even the ablest math student, but enough for the average one to get a grasp on the concepts as well.
The book also provides an advantage for the instructor as to what applications to teach. Granted, chapters 1-6 cover almost all the theory, but 7-12 are all applications (7 is "usually" considered theoretical as well, but it is called "applications of residues!") in physics, advanced calculus and geometry, and engineering. So, a professor could choose to emphasize only the theoretical parts and save the apps. for independent study (which my prof. did) or could teach the relevant theories coupled with some of the applications (conformal mapping with fluid flow and heat flow, for example). It truly is a versatile book.
I noticed a complaint on here about not having enough examples or worked-out proofs. Well, to that individual (and any others who might be having the same problem), this book is meant for an upper-level undergraduate course, which means that there are going to be less examples worked out in great detail, the proofs may just be thumbnail sketches, and the problems will not have a quick reference page in the chapter for a formula or method like in calculus, for example; even though the book is versatile, a lot of the learning still falls on the student's shoulders.
My one and only gripe is that the book didn't take a lot of time to spell out how to perform a delta-epsilon proof for limits, which is one of the basic proofs in analysis. But, luckily, I had a very patient instructor who was willing to walk it through with me (most of the rest of the class had already had real analysis, so they didn't need to go over it). But, still, it's not enough to take it down a star, in my opinion.
They say this book is among the canon of undergraduate mathematics, and I can certainly see why. What a great introduction to complex analysis! This book will definitely be accompanying me to grad school!
Book Description
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Customer Reviews:
The Pinacle of Introductory Analysis.......2007-03-12
Walter Rudin's book barely needs introduction at this point. It has gained a reputation as the best text anywhere for an introduction to real analysis, and is the gold standard for many first year graduate courses in the subject. Rudin's work is a masterpiece of style and form, and his presentation is second to none. Care has been taken with every proof to make it as elegant as possible. The selection of problems typically ranges from those requiring a few minutes thought, to the fantastically difficult.
Therein does lie one of the two problems with this book, however. Occasionally Rudin relegates an important--and useful--result to the exercises where it could be overlooked by the unwary. There are some sections where more examples aimed at getting a student to practice applying fundamental concepts would be useful, instead of making them bend over backwards to find an answer.
The only other problem, which is often brought up as a criticism of the book, is that Rudin is often perhaps a bit too terse in his exposition between proofs. There isn't always a strong motivation given for a topic, which makes this book a difficult one to learn from without a good instructor.
Overall, it would be hard to do better than the so-called "baby" Rudin book. The price tag is a little steep for something so slender, but the content inside can easily outshine any other 3 similar texts in the area. This is an absolute must own for any aspiring analyst.
Solid and elegant.......2007-01-02
This book is well known for being terse. I will not refute this, but I will say that it is certainly not the tersest math book I have read (that honor might go to Samuel's algebraic number theory text). I am a graduate student in computer science, and I found this book to be enjoyable, well-structured, easy-to-read, and with excellent exercises. I probably would not attempt to use it for independent reading, though. The book develops calculus from the beginning, wasting no time, and giving almost no examples (unless you take the time to work through all the exercises). It is thus important to have a good instructor who can fill in the gaps as you go along.
The price, however, is ridiculous.
Simply the best ... .......2006-06-23
If you didn't use this classic in your first pass at elementary
analysis, you owe it to yourself to find a copy and work
through as many exercises as possible ... especially if you
plan to go further to graduate level work in mathematics.
Other books that are increasingly used for this subject still
leave readers with a 'maturity/sophistication' gap relative to
more advanced texts in real analysis, etc.
A course at MIT based on this text is presented at the link
below, with suggested coverage, exercises, solutions, etc. -
[...]
Analysis 101.......2006-05-13
Principles of Mathematical Analysis by Walter Rudin can rightly be called "the Bible of classical analysis". I have seen it cited in more books than I can count. And after a full year of working through the book in graduate school, I can see why. As many other reviewers here have pointed out, this book requires more than a little of that magical quality called "mathematical maturity". Simply defined, "mathematical maturity" is the ability to read between the lines and fill in the gaps in a given mathematical text.
While Rudin certainly provides an encyclopedic account of basic analysis in metric spaces, he does leave some gaps (many are intentional) in his proofs. So be alert when you read this book, and if anything in his super short, slick proofs is not 100% clear, be prepared to fill in the details yourself. Also, remember that Rudin's way of presenting proofs is not always the most instructive when first learning the material. There is an implicit challenge to the reader to see if he or she can provide a more expository proof. Although I can say that when the classical proof suffices, Rudin usually does not deviate from it.
Some of the highlights/weaknesses of the book are the following:
Chapter 1: The material in this chapter is of course standard. However, Rudin supplements the chapter with an appendix on the construction of the real field from the field of rationals via the notion of Dedekind cuts. After reading many, many analysis books, I can tell you that it is difficult to find an explicit construction of the reals in books on an elementary level. Thus, while certainly not required to appreciate the rest of the text, I do recommend at least a casual perusal of the appendix just to see that "it can be done".
Chapter 2: Rudin may seem to go a little overboard in his presentation on basic topology, but trust me, it will *all* be used later. So do not gloss over anything in this chapter. In particular, note how the notion of compactness is not defined a priori by any metric space ideas. However, in metric spaces, compactness does imply certain useful properties. One that is used again and again is the equivalence of compactness and sequential compactness in metric spaces. Thus, after moving on to Chapter 3 and beyond, I advise you to look back at Chapter 2 often.
Chapter 3: One notable feature is that Rudin does not attempt to discuss limits per se before discussing numerical sequences and series. This may make you a little uncomfortable at first, but it turns out that this approach works best. Again, everything in this chapter is essential to the rest of the book. My only gripe with this chapter is the material on "upper and lower limits", better known as lim sup and lim inf. I feel that he should have expanded the discussion in this section a little more. In particular, his Theorem 3.19 should have had a proof supplied in the text. One of the reasons I feel this way is because the Root and Ratio tests for convergence of infinite series of numbers use lim sup heavily.
Chapter 4: Limits are finally introduced as the reader remembers them from basic calculus. The only difference is that Rudin works with arbitrary metric spaces, which turns out to be very useful later. Take note of Theorem 4.2. Reformulating the existence of a limit of a function in terms of limits of sequences is a handy theoretical tool that makes a lot of proofs (Rudin's included) much easier to understand. That said, there are no real surprises until Theorem 4.8. You can probably omit the subsection "Discontinuities" with no loss. I say this even though some of the theorems in "Monotonic Functions" use that material in their proofs. Theorem 4.30 in particular (monotone functions on open intervals have at most a countable number of discontinuities) has a much better proof than that Rudin provides. So try and look elsewhere for the proofs of those theorems.
Chapter 5: All the derivative proofs are just like you remember from advanced calculus. The only one that merits special attention is L'Hospital's Rule. Work through it very carefully, it is more subtle than it appears.
Chapter 6: The Riemann-Stieltjes integral can be obtained by only slightly more effort, so Rudin wisely decides to base all of his proofs (through Theorem 6.19) on it. Just be aware that some of the material covered, such as the Fundamental Theorem of Calculus and integration by parts is only discussed for the original Riemann integral. Theorem 6.25 (based on the Cauchy-Schwarz inequality) acquires a special significance in the following chapters, so memorize it!
Chapter 7: By far, this is the most crucial chapter in the book. This is probably the material that you may have had limited or no exposure to in the past. The famous Weierstrass Approximation Theorem (and its generalization by Marshall Stone) is given here. Read this chapter front to back at least four times. Yes, it is that important. Otherwise, the Fourier Theory presented in Chapter 8 will seem like gibberish.
Chapter 8: Expansion of analytic functions via power series is presented here. A brisk, but complete development of the exponential, sine and cosine functions is also featured here. Problem 6 in the exercises at the end of the chapter is worth special consideration. Work it out after you read about the exponential function. The Fourier material is relatively straightforward, although awkward when divorced from measure theory. As Rudin himself notes, the hypothesis that f be Riemann integrable is often unnecessary, so you may want to peek ahead at Chapter 11 while reading many of the proofs, especially Parseval's Theorem. The material on the gamma function is cute, but not really needed.
Chapter 9: The standard treatment of multivariable functions. Rudin's coverage of linear algebra is succinct. Also, the linear algebra has more important uses than merely providing a pathway to "multivariable calculus". The theory of linear operators sketched in Theorems 9.5 to 9.8 will lead you directly to the more abstract theory of Banach spaces. The Banach spaces take a very central role in advanced analysis as can be seen by reading Royden's "Real Analysis". I also recommend supplementary reading for this chapter. A good book to look at is Charles Pugh's "Real Mathematical Analysis" which has an extensive treatment of multivariable functions. Also, you might skim over George Simmon's "Introduction to Topology and Modern Analysis", a great introduction to the abstract theory of operators. This material is only hinted at in Rudin, but comes to its full fruition in Simmons.
Chapter 10: This is Rudin's introduction to differential geometry. I honestly have not given this chapter a thorough reading, but on the surface it looks ok. Most of the deeper theorems from multivariable calculus (excepting the Implicit Function Theorem, discussed in Chapter 9) are treated here, such as the trifecta known as Stoke's, Green's, and the Divergence Theorems, respectively. This chapter is important to anyone going into fields such as partial differential equations.
Chapter 11: This chapter seems to be the one that most people criticize in the book. Rudin gives a perfunctory outline of Lebesgue theory that seems to rob the reader of much needed detail. Indeed, this chapter is a little too lean for my tastes. But in Rudin's defense, he warns the reader at the outset that "proofs are only sketched in some cases, and some of the easier propositions are stated without proof". Hence, I recommend just giving this chapter a light read, then go to another book (such as Royden) for the real proofs. As expected, Rudin discusses some of the seminal results of Lebesgue theory, including, but not limited to: the Monotone Convergence Theorem, the Dominated Convergence Theorem, and the correspondence of the Lebesgue integral with the ordinary Riemann integral (whenever the latter exists). The Riesz-Fischer Theorem from Fourier analysis appears here. Lebesgue's Dominated Convergence Theorem (Theorem 11.32) is worth a careful reading. Afterwards, look at Exercise 12 in Chapter 7 for a simpler version of the DCT using the familiar Riemann integral. The proof is not that difficult.
It goes without saying that the exercises are extremely important and should all be attempted. Unless you are brilliant, odds are that at least a few will elude you. Nonetheless, many important results and counterexamples are listed in the exercises, so you will benefit from working them. Be warned though that Rudin will intermingle easy with very difficult problems.
An obvious problem is the outrageous price. Unfortunately, this book is essential reading, so you'll just have to cough up the dough or look for it cheap elsewhere. It is a good book to learn from and a fantastic reference. I don't know if I would call it the "best analysis book ever". But its current edition was released 30 years ago, so that says something about its popularity.
P.S. Once you've finished Rudin, the book by Pugh referenced above is a good read to "pull it all together". There are some well-thought out problems that will both challenge and inspire you to learn more at the same time.
Highly recommended.
Pretty Good.......2006-05-13
I want to start by listing some of my complaints. First of all, I do not think it is entirely appropriate for a student's first exposure to analysis. The majority of students would be better off taking a an honors calculus or advanced calculus course first, so they can learn how to prove things about the continuity of specific functions or convergence of series before they start proving things and functions and series in general (a look at, say, Bartle's book over summer break would probably work just as well, but my point remains the same). Second of all, the exercises are, for the most part, extremely challenging. While this is not a bad thing by any means, the book would probably benefit by having a few extra, easier problems. Third, it could use some pictures, not that many, but they would certainly help illustrate some of the ideas. Fourth, a few of the proofs are very difficult to understand because they are perhaps too concise (for example, the Cauchy-Schwarz inequality in the first Chapter). Finally, $140 is prohibitively expensive.
That having been said, PMA is considered the classic of its genre, and for good reason. It is extremely well-written, if a bit concise, and forces the reader to do a lot of thinking. While the problems are challenging, they are very non-trivial, and again, force the reader to do a lot of thinking. You may be noticing a theme here. This is an excellent book if the student has enough experience with mathematical thought, however, many others will be lost.
Personally, I prefer Pugh's book, which I think addresses all the shortcomings I listed above, but I certainly see why many would want to stick with the tried-and-true PMA.
Book Description
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.
Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Customer Reviews:
The exercises are not very good.......2007-09-11
I used this book in a first year graduate course. I found the exposition not very clear, and the exercises particularly uninteresting. If you have the choice, I definitely recommend Gamelin's Complex Analysis instead.
bad book.......2006-05-03
This book is not helpful. There are no answers to problems. Symbols used in the problems are not explained. It is difficult to learn unless you have someone explaining the concepts for you. I would not buy this book now.
Beautifully written !.......2006-04-16
This is a very beautifully written book on complex analysis. It is not very easy to read though, especially if you've never been exposed to the subject before. Most proofs are clearly presented, and can be easily understood by the mature reader. Other proofs require filling in the gaps to get the whole picture. As far as problems go, there's a list of relatively easy exercises at the end of each chapter. Following the exercises is a list of problems which require some head scratching. Overall, I had a fun time reading and learning from this book.
A Gem.......2006-01-20
In reviewing a textbook, one should consider the background of the book's audience. I believe that this text by Stein and Shakarchi on complex analysis is outstanding, and is appropriate for a student who has the background of a course in real analysis at the level of Rudin's "Principles of Mathematical Analysis".
The text has a number of strengths. Some of these are the following:
1. The choice of material and the order of presentation are superb. Just to give you a sample, within the first 100 pages, the authors cover Runge's Theorem, the Schwarz Reflection Principle, Riemann's Theorem on Removable Singularities, the Casorati-Weierstrass Theorem, Rouche's Theorem, and the homotopy version of Cauchy's Integral Theorem. The novice is thus treated to some beautiful mathematics very quickly.
2. The statements of theorems and definitions are simple and clear. The authors carefully avoid unnecessary technicalities that would only tend to confuse the beginner and obfuscate the essential concepts.
3. The proofs are very clear and elegant. The main ideas are emphasized, and just enough details are given so that a diligent student with the background stated above will be able to grasp the arguments.
4. The examples are nontrivial, and worked out in detail. Some may prefer a greater number and variety of examples, but I found that there were enough to illustrate the theory.
5. The authors pay considerable attention to motivating the development of ideas. It seems to me that the authors were keen to enhance the reader's intuition for the subject and to impart an appreciation for the inherent beauty of complex function theory.
6. The book is very well edited. There are very few typos, none of which should cause difficulty for a beginner.
For these reasons and others, I highly recommend this book to anyone who desires to learn complex analysis, or who simply desires to learn some beautiful mathematics, and who has the suggested background. Stein and Shakarchi have written a book which is a joy to read!
very good indeed.......2005-05-01
The two authors are indeed very good writers. This book presents the elements of complex analysis at the graduate level (so the assumption is that the reader has gone through undergraduate real and complex analysis). All the topics covered are covered well (I especially like their treatment of the Prime Number Theorem and Elliptic Functions). Note: theorems of Picard and Mittag-Leffler are not proved in the textbook - they are actually assigned as exercises for the reader to prove). If you need the proofs of these theorems, look them up elsewhere. Overall, a very solid book.
Average customer rating:
- Professors Should Choose Another Book
- Another excellent Real Analysis Text
|
Introduction to Real Analysis (2nd Edition)
Manfred Stoll
Manufacturer: Addison Wesley
ProductGroup: Book
Binding: Paperback
 General
| Science
| Subjects
| Books
Calculus
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Science
| Subjects
| Books
Calculus
| Pure Mathematics
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Calculus
| Mathematics
| Sciences
| New & Used Textbooks
| Stores
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
jp-unknown1
| Specialty Stores
| Books
Similar Items:
-
Complex Analysis
-
Elementary Probability
-
Abstract Algebra: An Introduction
-
Applied Combinatorics
-
Cracking the GRE Math Test, 3rd Edition (Graduate Test Prep)
ASIN: 0321046250 |
Customer Reviews:
Professors Should Choose Another Book.......2006-06-01
This was my undergraduate textbook for Advanced Calculus I and II (as they were called at my school). I am returning to school to start my master's degree this next term and am going through the book to refresh my memory.
Wow, it is just the way I remember it. Frankly, I can't believe the other reviewers ratings. So, I thought I'd balance the average rating a bit with a review of my own.
When I was in college, this was my most dreaded reading material. It is a difficult subject to master, sure, but the author does not help matters by using failing to use a clear structure with emphasis on key points. Instead, there is barely any structure at all. Headings consist of unenlightening phrases such as "Theorem." Pragraphs are downplayed by the typesetting style as well, making each section almost an undifferentiated block of information. (The author has not even used an end-of-proof symbol!)
And not only is this book unfriendly, it is dry. The author tends to use strictly symbolic language when explaining in words would be so much clearer. In fact, he frequently skips the explanatory material altogether and moves straight to the examples. What is the context or object for these examples? The reader is mystified.
If you are a professor, please do not choose this book for your analysis class. I have a feeling it is only comprehensible to those who already thouroughly understand the material.
If you are a student who has come here to buy this book, you have my sympathy.
Another excellent Real Analysis Text.......2002-03-10
The style of this book is a bit like Robert Bartle's Introduction to Real Analysis. It is detailed and rigorous. It is an excellent book for those who want to learn Real Analysis.
Book Description
Be Prepared for the AP Calculus Exam is your indispensable guide to scoring well on either the AB or BC AP Calculus. This book features an outstanding team of authors and practice exam contributors: veteran AP Calculus teachers who have served on the AP Calculus Test Development Committee and are College Board consultants, exam grading leaders, and AP award recipients. The book expands Skylight's Be Prepared series, and it is crafted with the same care, attention to detail, and respect for the student as our Be Prepared for the AP Computer Science Exam, which has helped many thousands of students get a good grade on AP exams in that subject.
A serious introductory chapter describes the exam format and requirements and offers important tips for successful exam taking. Eight review chapters thoroughly cover all of the AB and BC material. Embedded in these chapters are 200+ multiple choice and free response questions with solutions that show you effective strategies and shortcuts. Five complete practice exams with answers and solutions (three AB and two BC exams) will give you plenty of practice material and help you decide whether to take the AB or BC exam. This book's companion web site contains annotated solutions to free-response questions from past AP exams.
Whether you sit in the front row, the back row, or anywhere in between, Be Prepared will help you focus on the AP Calculus exam requirements, review the material, and fill the gaps in your knowledge. Review, practice, and take the AP Calculus exam with confidence, knowing that you are well prepared.
Customer Reviews:
One of the best study guides for AP Calculus.......2007-06-15
Let me preface this by saying that I took the AP calculus test in the mid 1980's and now have helped my daughter with a self-study course on calculus in preparation for the 2007 test. After going through a total of 4 study guides, 2 textbooks, and the last 7 years of available free response questions from the actual AP test, I found this guide to be one of the best AP calculus preparation books.
The AP calculus (AB or BC) has become considerably harder in the last 4 years. Most other books seem to have been developed for the test as administered in the 1990's. In order to pass, not only do you need to know your calculus - it is also mandatory that you know how to use your calculator in order to solve calculus problems. Most other books, completely ignore this point (see my other reviews). Rather than focusing on techniques of integration (which was a big deal for the earlier test in which calculators either weren't allowed or weren't capable), the emphasis has switched to integration via the calculator.
This book addresses the issue clearly.
One last point of advice is that this book does stress the concepts that are in turn stressed on the current tests - fundamental theorem of calculus, average value of a function by integration, and problems that depend on interpreting graphs and data points.
When chosing a book, keep in mind that the test is no longer a simple can you integrate and take a derivative by hand type of exam. If you can solve the problems in this book, you indeed will be prepared for the AP test.
Best AP calculus review book!.......2007-06-13
After having read the rave reviews online and wanting something different from the typical princeton review/barron's books, I ordered this off Amazon because my local Borders/Barnes & Noble did not have any. It is as good as people say it is! Filled with tons of practice problems and concise notes. Unfortunately, the 2007 AP Calculus was unusually hard nation-wide in both the multiple choice and free-response so I'm not going to say I will get a 5... but, this review is the only thing that got me through the exam so I highly recommend it!
good review, bad practices.......2007-05-13
good reviews, you can probably even take it as a textbook, however, the practices have no thorough explanations, but to say that one of the practice exam is extremely hard
Everything You Could Want in a Review Book.......2006-08-20
Trust me on this. I have gone through about every AB book out there, and this one is your best bet. Unlike the others, it is actually very up to date, and it contains the most recent changes to the AB curriculum such as slope fields.
Many books out there are much too easy, such as the book published by Princeton. Easy does not necessarily equal good preparation for the test! This "Be Prepared" book will challenge you and actually get you to see the level you will see on the actual AP exam. Plus, this book gives great hints at far as successfully using the calculator. This book has everything you could want in a review book, and I recommend it over all the other AB titles.
very helpful :).......2005-09-23
This review text really helped me do well on the exam (along with my other AP's this should help a lot with college apps!). Obviously this isn't the kind of reading for a day at the beach, but it got the job done, so no complaints!
Customer Reviews:
Intersting indeed. Indeed........2007-10-03
Hi, so I was looking for a book on auto manifolds and here I am. This all seems pretty out there to me, but the cover looks pretty nice, so 5 stars it is. Great work Mr. Spivak
Not very satisfying or rigorous.......2007-06-23
A key thing about this book: it's basically typed up lecture notes. Especially as it gets further along, it displays a notable lack of rigour. Some of the problems are not necessarily provable using information from the book. Furthermore, theorems don't clearly state the assumptions under which they operate. In chapter 5, the author resorts to basically presenting a laundry list of facts about differential forms on manifolds, so it's hard to get much beyond a basic idea of what's going on.
I believe this book may be good for a course where the instructor can answer student's questions about ideas that aren't addressed rigorously. For self-study, it could be, at best, a supplement to another book. I'm actually a little baffled about why it seems to be so well-reviewed.
Good, but not great........2007-03-12
Spivak's book came with high praise, and for the first 3/4 of the book I certainly agreed. Spivak has a style that is at once conversational and precise. He doesn't skimp on the details, but strives to make the content as understandable as possible. His proofs aren't always as slick and polished as those you may find in Rudin, but they are well thought out, and the exercises complement them very well.
There are, however, two problems with Spivak's book. The first being that for the most part, it is rather easy. The level of most of the exercises is rather low compared to the material he is presenting, and as the book goes on, they help you adjust to the material less well. Similarly, Spivak's readability falls apart eventually. He introduces complicated notation and concepts without sufficient explanation which serves to make the last (crucial) part of the book nearly incomprehensible compared to the earlier chapters. It reads as if the end was put together in a rush, or at least by a different person. This puts a large dent in the enjoyment to be had from the book, and relegates it from the place of essential reference, to merely a good read.
A Must Read Book.......2007-01-19
Many years ago, when I was a freshman in a Physics class, my Calculus teacher gave me this small book. It changed the way I viewed mathematics. Spellbound, I turned page after page enjoying the beauty of the theorems and the logic of the whole construction. This books explains the reason behind Stokes and Gauss theorems and introduces many useful concepts. It is a must read book for anybody seriously interested in the modern Calculus. It does not require exotic mathematical background, and any reader having some classes in classical Calculus can read it.
I recently reread this book and was happy to recall the magic of this great introduction to the real mathematics.
One reviewer said :"by carefully developing only what is essential." which is best thing to say about this book.......2006-01-20
So far Im at chapter 2 (just finished it). So Im going to update this once im done with the book.
Let me say first this is not a book to read while you are lying on bed, You absolutely need a pen, a paper, and write down the theorems, and then rewrite all the proofs, and write on your own the skipped steps. Note the author says more than one time "clearly", and those "clearly" are kinda clear, however proving them will take space, and I think they need to be proven anyway, to get a better grasp on material.! (sometimes if you think the clearly is not near clear, then maybe your thinking wrong, rethink about the problem).
Anyway, whats BEST about this book, is that it "is carefully developing only what is essential" to get to manifolds (which I never studied b4). But comparing this book to other books, Other books introduce LOTS and LOTS of material, that you really might not need to know ALL of it to get to manifolds. I am not saying all those extra material are not important, but to simply study the subject of manifolds, you really do not "need" them.
this book is five chapters:
1)Functions on Euclidean Spaces
2) differentiation
3) Integration
4) Integration on chains
5) Integration on Manifolds
IT might sound trivial for grad math books, but this book does NOT have solution to the exercices at end of book, however, some of the excerices have hints just right after the statement of the problem, and I think they are kinda solvable.
True, not so many examples provided in the book, however, if you sit and write and prove theorems, then you should be able to create your own example, and more like discover things!
Simply, if you love studying Math, (some say torture urself with Math), then that's the right book for you.
I can not but give 5 stars for this book. Overpriced, not many examples, WHATEVER, The name of the book is calculus on Manifolds (not advanced calc 2 or real analysis 2), and thats what you will absolutely find in the book.
*** Update ***
now that I'm done with the book. It has been a great experience, especially it's my first exposure to manifolds (also differentials). However, I think this book really lacks examples. If I was not studying this book as independent study with a professor, I would have learned some wrong concepts on my own (especially in the section about n-cubes, examples by the author were REALLY needed there to clear any confusion). The way I studied this book is that I read it, try to rewrite all the proofs on my own rigorously including all the left-out details, then go to my professor, he will give more intuition, and I try to come up with examples in his office. It's been great, I learned a lot. I still think lack of examples is a problem. Though wud not want to change my 5 stars.
Now I think studying this book as second (at least not first) exposure to the material would be a lot better, That's if you are studying it on your own! However, IF you have extra time and IF you can discuss the material with a professor everytime you read a section, and He can direct you to develop the right examples, then this book is GREAT (and I think can be covered in one semester)!
Amazon.com
Very useful CD-ROM for all numerically inclined scientists and engineers. Produces TeX source code for selected formulas. Multiplatform-ROM for Mac, Windows, and UNIX.
Book Description
The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.
- Fully searchable CD that puts information at your
fingertips included with text
- Most up to date listing of integrals, series and
products
- Provides accuracy and efficiency in work
Customer Reviews:
Excellent.......2007-07-20
Doesn't replace every other reference--but is pretty darn complete. I love that this 7th edition comes with the CD containing the complete searchable text for no extra charge.
7th Edition book includes the CD-ROM.......2007-03-07
After a 7 year wait, the 7th Edition of Gradshteyn & Ryzhik has finally been released! Other reviews speak to the tremendous utility of this classic. It is worth noting that the latest edition now INCLUDES a fully-searchable CD-ROM version of the book. However, I did notice a bug when using this on Windows XP SP2 with FireFox 2.0.0.2. (The CD-ROM is optimized for the Netscape browser and CANNOT be used with Internet Explorer.) Although I am able to click on the "Contents" button and navigate through the sections; and although I am able to go back to the title page by clicking on "Home"; when I click on the "Book Contents" button in the middle, FireFox freezes on me and I have to terminate the browser process.
Comments on an earlier edition.......2007-01-30
My copy of this book is the 4th edition, 1965. I still vividly
remember going to a bookstore in Berkeley, CA in 1971 and buying this
book for $10 (I also bought the "Feynman Lectures in Physics" on this
trip for $7.45 per volume). I also remember eating lunch at an
outdoor restaurant in Berkeley and having a fantastic view of the San
Francisco Bay Area, as it was an absolutely clear day. As a piece of
useless trivia, I had a liverwurst sandwich on a dark pumpernickel;
this is the first time I ever had liverwurst and fell in love with it!
This book is compendium of mostly integrals. What made it stand out
back then was its organization, making it relatively easy to look
up a particular integral. Most of the formulas come with a reference
to where the formula came from, should one desire to research things
a bit more. While it's not a panacea for dealing with all integrals,
you're likely to find something in here to aid in attacking most
problems.
Before using any of these integrals in an important problem, I'd
recommend you verify the formula first. Fortunately, this isn't
hard to do numerically with modern scripting languages like python,
accompanied by something like scipy, or a computer algebra system
such as Mathematica or Maple.
Integrals Series and Products review.......2007-01-04
I have found the book to be very useful and informative.
A gem.......2007-01-04
Let's keep this short and sweet. The book is probably THE best in what it claims to be, i.e. a compendium of mainly integrals, but all sorts of interesting stuff also manages to find its way in. Why some former reviewers exhaust their artillery in complaining about the CD is beyond me. This is a reference BOOK an as such unsurpassed. Buy it for sheer pleasure if for nothing else. While you're at it, you might want to take a look at Handbook of Mathematics by I. N. Bronshtein et al. which I ordered from Amazon in Germany a moment ago. That one also comes with a CD and I'm getting curious about how it will turn out to be. But Gradshteyn and Ryzhik - the BOOK - are a must.
Books:
- Data Structures and Algorithms in C++
- Deformations of Algebraic Schemes (Grundlehren der mathematischen Wissenschaften)
- Differential Equations (2nd Edition)
- Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
- Discrete Event Simulation: A Practical Approach (Cre Press Computer Engineering Series)
- Division Algebras:: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics (Mathematics and Its Applications)
- Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
- Dynamical Systems with Applications using MATLAB
- Einstein: His Life and Universe
- Estimation with Applications to Tracking and Navigation
Books Index
Books Home
Recommended Books
- Falling Through the Earth: A Memoir
- Bread: A Baker's Book of Techniques and Recipes
- Two Novels: The Captain and the Colonel / Two Years, or, The Way We Lived Then
- Think and Grow Rich!: The Original Version, Restored and Revised
- Who Killed Albus Dumbledore
- An Introduction to Quantum Field Theory
- A Voice in the Wilderness: Conversations with Terry Tempest Williams
- Holding the Center: Memoirs of a Life in Higher Education
- The Making of United States International Economic Policy: Principles, Problems, and Proposals for R
- The Radical Lives of Helen Keller
Cracking the AP Physics B and C Exams, 2006-2007 Edition (College Test Prep)
Cracking the AP Chemistry Exam, 2006-2007 Edition (College Test Prep)
Cracking the AP English Literature Exam, 2006-2007 Edition (College Test Prep)
Cracking the AP U.S. History Exam, 2006-2007 Edition (College Test Prep)
Cracking the AP Biology Exam, 2006-2007 Edition (College Test Prep)
