Reviews (38)

Not very useful
I have taken two semesters of calculus using this book, and am most disappointed and frustrated. It may be a good volume if you are coming into the class fresh from AP Calculus in high school (I was not), but if you have taken algebra and pre-calculus in college, and then proceed to this, as I did, the learning curve is very steep.

The exposition in Stewart's volume is of irregular quality. Sometimes clear, it is, at others, obtuse, and in some sections utterly fails to illuminate the topic.

The exercise sets seem well-designed for someone majoring in math, and whose experience includes high school algebra. For those students, this will be more review than new learning. In each set of exercises, the problems seem to be trying to force new epiphanies, with each new problem. For my part, a less steep curve would work far better, and I have found it necessary to acquire an alternate volume as a backup. My instructor has also observed that the exercises are overly complex, and that they rarely contain any problems suited for inclusion on an exam.

The software included is rather poor in quality, and will fail to work at all unless you accept the default installation path.

Finally, the binding is not up to the task of holding together a 1,200+ page book, and mine is falling apart, despite my having always carried it in a padded bag. At the price, that is unforgiveable.

As you will almost certainly be buying this for a college class, you have no choice -- the school will have selected for you. But be advised, you may need a second book to explain this one. Also note, the solutions guide often fails to enlighten, as too often they leave out steps that are the focus of the topic in the section to which the exercises relate. Further, the solutions guide covers only the first 11 chapters, so you will need to consider the multi-variable solutions guide as well, and that brings the solutions guide cost to over half the price of the book.

All in all, this is not a bargain, and not even a very good value.

Your undergrad calc bible
I've long since moved on to more advanced calculus since first cracking this book open, and I'll admit at first I didn't like it very much.But after using it for a couple of years, I have to say that it's the single most useful textbook I own.When you're first learning the concepts, it can be tough, but I blame that on calculus, not Stewart.As a refresher for different techniques, this book is a dream come true; examples are diverse and to the point, and the book covers many different techniques.For learning calc this book is good, and for someone who is already familiar it's wonderful.

Reviews (1)

Reviews (48)

Good, but a supplement is recommended
This is a good book on ordinary differential equations. Examples are very helpful to learn how to do problems. They are pretty much the best way to learn how to solve the equations. Also, there are answers to every problem in the textbook, so you can check your answer. However this book has some nuances which you should consider: Main important points on how to solve ODEs are not highlighted (only some are, and those are mostly the theorems). The important stuff IS in the chapters, but you gotta pick it out for yourself. For that reason I recommend getting some used ODE book for cheap, that has all the important concepts highlighted (Edwards/Penney comes to mind).

Great Book!
I personally liked this book. It's easy to read and study on your own without the aid of a teacher. Its weakness is perhaps the lack of demonstrations, but since I'm a physics major I wasn't extremely concerned with them.

Reviews (4)

no better than the first edition
It is always easy to add something to than to get rid of something from the book. I guess this is the case of the author when he prepares the second edition. However, I prefer the first edition because it is more readable, enjoyable, and most importantly, contains just enough information for the introduction to abstract algebra. There are huge number of textbooks on abstract algbra, and making another would not be the author's purpose of the revision, I hope, but it looks it is.
By adding more subjects in detail to the second edition, now it looks the same as any other, only to loose its expository and conversational style of writings, and became a reference-style textbook.

Boo
Before taking an abstract algebra course this semester I studied the material on my own using the introductory texts by Gallian and Hungerford.These books were very useful because they actually completed proofs instead of leaving them as exercises for the reader.Someone new to abstract algebra is also typically new to higher mathematics.This means a book should have clear and full explanations, not skip major points like Rotman does.Rotman commits another sin by failing to provide homework problems which correspond with the material he presents. One nice thing is that the book does provide a wide array of material (much more than most other introductory texts).This virtue soon turns astray however because by providing so much preliminary material on congruences, functions, divisibility, .... you'll be lucky if your teacher gets to groups by halfway through the semester.

Reviews (20)

Excellent!
This is probably the best book on linear algebra I have seen.

It approaches linear algebra from a theoretical point of view (i.e. linear maps instead of matrices), it is not "watered-down", and yet it is accessible to undergrads. The key reason for this is because Dr. Axler has kept the book well-focused, has put in only the necessary results needed, and has tied these elements together clearly. I obtained the book, because like the author, I never liked some of the more standard proofs of "classical" theorems. However, even the material at the beginning is superbly organized and well thought out, and a joy to read. His use of a single lemma in chapter 2 for example, (the so-called "linear dependence lemma") makes many of the results given later on in the chapter (and the book), trivial to prove. One of the reasons Axler can use this lemma so effectively, is because he is careful about his notation, and uses ordered tuples instead of sets of vectors. This is just one example of where his care in such matters pays off immensely for the reader.

I agree with one of the earlier reveiwer that his use of side-comments, though uncommon in texts, is very helpful and enjoyable.

Also, even though the book is not application oriented, Axler does give a lot of examples of abstract defintions, which for someone learning linear algebra, is essential to have. He ties new abstract notions, like say linear maps, to things that an undergrad with modest math background would understand (like derivatives, etc). These examples I think are also crucial to a good abstract math book. Too often, an abstract math book will go from theorem to theorem. In this book, I felt like I was pacing myself. There were a lot of theorems that followed sequentially, but there were also "breather sections", where Axler will stop and take a look at what he is doing. This, I think, gives the student time to stop, reflect on what he is doing, and get a better, deeper, fuller understanding of the material.

If you can purchase one book on linear algebra, this is the one book I would suggest!

Elegant theoretical presentation of linear algebra
This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent.The student has perhaps taken a linear algebra course designed for engineers and scientists.Such a student is comfortable reading mathematics and writing proofs.It is meant to be read and re-read until the ideas are absorbed.The exercises are relatively easy and no answers are provided.With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.

Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra.

The price is right.This could be a very useful purchase even if it's not assigned as a text.

Reviews (10)

Excellent introduction to analysis
Of the many analysis books I have seen, I think this is one of the best for the student approaching the subject for the first time.

It is mathematically rigourous, yet develops the major concepts of analysis in a leisurely (in the good sense of the word) way with interesting and sometimes unusual examples.

Beginners will especially appreciate the quality exercises and the solution guide in the back.

The style of this book is a bit similar to Spivak's *Calculus* in that the author is a bit wordy.I find Ross' presentation more direct and less pretentious than Spivak--and far less intimidating.

This is definitely the best introductory analysis book I know of for self-study.A student who masters the material in this book will be well prepared to tackle Rudin and other classic works in real analysis.

Entirely mediocre
A solid, if limited, textbook. The author provides an entry level approach to analysis without much use of more abstract topological concepts like metric spaces. A decent book for the reader who desires this type limited approach. Even in that light it is hardly spectacular as the author's logic often does not flow as clearly as in alternate texts

This book might be better viewed as an auxiliary text beside a classic like Rudin or the very good Real Mathematical Analysis by Charles Pugh.

Reviews (22)

Excellent intro. to complex analysis!
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!

excellent! (as an intro)
This book would be really good for a physics or engineering student, or for a math student as an intro since it isn't as theoretical as other books. Everything is explained very clearly, with lots of examples but still with some hard/interesting problems also. The first 7 chapters cover all the theory, which is the usual stuff like complex numbers, differentiability & Cauchy-Riemann equations, integration & Cauchy integral forumla/theorem, series, Taylor series, Laurent series, residues, poles, solving real integrals with residues, etc etc. Chapters 8-12 cover applications which I admit I don't know a lot about, but if the 1st half of the book is any indication, they are good also. The text covers everything in a CONCRETE way, as opposed to an abstract way using concepts from topology like connectedness, compactness, open/closed sets, star-shaped sets, etc. For that stuff I used GJO Jameson's Complex Functions text & I also like the one by Ahlfors & the one by Jerrold Marsden. I think every scientist or engineer would find this Brown/Churchill book very helpful. :-)

Wonderful intro to complex analysis.
I used this text for an undergrad course, and I thoroughly enjoyed it.The book, as the title suggests, is ideal for physicists, engineers, and applied mathematicians, in that it hits the important and powerful features of complex analysis which are tremendously useful for applied work.What's more, it succeeds in doing so without sacrificing mathematical rigor, and without getting bogged down on stodgy formalism.

As for the scope of the book, I believe it can be fairly stated that just about everything in the book should be studied and mastered by readers doing applied work.From my own experience, everything covered in the book has turned out to be relevant at one point or another.It can be said without exaggeration that this book is a gold mine.