Reviews (19)

Not really helpful
I tried to use this book as a supplement text for my multivariable calculus class. I found it to be very useless even as a supplement, let alone a main source to rely on. The main problem with this book is the fact that it is very short (Can I say way overpriced? Good thing I got it for free) and it doesn't explain the concepts properly. It is theoretical, but also in my opinion too far out there. I have nothing against theory, in fact I think its great to have theory in a math book. But in this case the material presented very tersely and unclearly. In my opinion books should explain concepts nicely and clearly with a proper use of examples. I do not wish to spend hours trying to understand what an author tried to say, especially when a concept is a really easy one. Another annoying thing about this book is the notation. Author uses "modern" notation for partial derivatives, but for some reason not many other people use it. It is found mostly in the 1950s era math books. This archaic approach to math is devastating to a student. Avoid at all costs.

Must be written by Spivak's evil twin
Spivak's other books are quite good, but don't let that fool you into getting this one. This is a horribly dry and terse text of the type which is convenient for authors and lecturers but hopeless to learn from. The object of Bourbakian worship is of course "the modern Stokes' Theorem", but, Spivak says in his preface, "Yet the proof of this theorem is, in the mathematician's sense, an utter triviality - a straight-forward computation. On the other hand, even the statement of this triviality cannot be understood without a horde of difficult definitions from Chapter 4. There are good reasons why the theorems should all be easy and the definitions hard." Perhaps these "good reasons" are that lazy authors can throw together unhelpful books where everything is "left to the reader".

Reviews (10)

Very thorough, but very dense
I'm currently taking an honors calculus sequence at the U of WI, and have used this book and the first volume for the past three semesters.Needless to say, you have to take Apostol with a grain of salt.Although the no-frills style and lack of worked examples is upsetting to many students who are used to pictures, thorough examples, and color, these volumes cover a lot of material in a small space.And also beware; my professor and others in the math department have found errors in definitions and theorems, and the archaic notation is off-setting at times.Basically, if you're looking for straighforward information (written by a mathematician, for a mathematician), you've found the perfect book.If you're looking for an easy-to-read and understand book, keep searching.

Weak
Few books in the mathematical literature have given me so much pain as this one. Freshman year, I took a heavily theoretical linear algebra class with Tommy II as the textbook, and then the next term I took multivariable calculus out of this book as well. In either case, this book was my first experience with the material, though as an "introductory" text it should have done the job. Suffice it to say that neither experience was terribly positive.

My problem is that Apostol never seems to try to motivate ideas well, and he uses cumbersome, nonstandard, and occasionally inconsistent notation. His proofs can be inelegant and opaque at times. He is far too sparing on geometrical intuition as a way to understand the material, preferring to talk in symbols rather than pictures. (This is especially true in the first five chapters on linear algebra. His multivariable chapters are well-illustrated, but calculus on R^n seems to be trivial once calculus on R is under your belt from a good introductory book like Larson/Hostetler/Edwards at a high-school pace. Thus, the motivation is needed least where it is used most.) As a result, I feel that I still don't intuitively understand how operators work on inner-product spaces, even after trying to remedy my deficiencies for a year and a half now.

I attributed my lack of understanding to my stupidity, but then I found myself learning exterior forms from Arnol'd's excellent mathematical mechanics book and groups from Dummit/Foote's superb abstract algebra text - and understanding the exposition perfectly. And I started to feel that this book is the thing at fault.

If a prospective reader is prepared for the terseness and difficulty of Apostol, I recommend that s/he go straight to the real math rather than settling for this obfuscated treatment of inroductory subjects. It is no harder to learn the rudiments of metric topology than it is to learn Apostol's open balls, and it seems no more inspired to take on Halmos' linear algebra classic, with its intimations of Hilbert space, than it is to struggle through Apostol's treatment. (The former seems to combine considerable difficulty with terse, but wonderful, motivation, but don't take my work on that: I'm only forty pages into it!) But the books are more inspired, and the math is far more general and beautiful.

My recommendation: learn your calculus (and potentially your first linear algebra) patiently but thoroughly from a prosaic, worked-example-ridden, 1000-page monster, then go straight to the upper undergraduate/early graduate classics for the real fun. Tommy II, caught somewhere in the middle, has no place in this plan.

Reviews (13)

The Long and Fluffy Intro to Differential Equations
I am an instructor teaching an introductory differential equations class using this book. Regrettably, the book is more of an extra weight to carry than a heplful tool.
Yet it is not so obvious to see why. A lot of the explonations are rather well done,
the examples are quite well chosen and constantly, th authors are trying to generate
a certain intuition in the reader.
I suppose the problem is that it is a full blooded ripoff textbook. It costs a whopping
$125 and therefore, it must have almost 800 pages, a shiny expensive looking
hardcover and a CD-ROM. The CD-ROM contains "Maple applet" like tools, that
come with huge drawbacks: often you can only choose the parameters in an equation in a very small interval and there is no normal way to print out any of the
graphics. You have to do a screen dump and then crop out the output screen of
these tools. Most freeware has more functionality.
To conclude, I suppose that my dislike for this book is mainly generated by the
fact that it has all the flaws of a textbook in todays perverted textbook market:

• overpriced
  
• comes with a semi-useless CD-rom
  
• explanations grotesquely drawn out, e.g. the basic theory of linear systems of
  differential takes about 80 pages
  
• core concepts and ideas are freely mixed with tangential remarks and colorful
  "faits divers" making no distinction between them whatsoever; when seeing diff. eq. for the first time you'll be as confused as humanly possible
  

The Perfect Soph/Junior level DE book
I used this book in a 2003 summer course in DE, and found it to be a wonderful introduction to the subject.I am not sure what some of the other people meant by saying it wasn't for math majors- I am one and found it wonderful.Not everything needs to be concise, (I gave Rudin's book five stars too BTW, so I AM a fan of some concise books).
It gave diverse examples of applications from all over--physics, EECS, ecology, biology, etc.The CD-Rom is a great learning tool.Ultimately analytic techniques are NOT what DE is about, and this book tries to show the student how to use qualitative and numerical methods early on.Anyone who wants to know DE must become familiar with numerics and the qualitative way of analyzing the equations.
This book will show you how to THINK about DE, and not how to mindlessly attack an equation based on its form.
This is the intro ODE book to which all others ought be compared.

If one wants an analytic reference just buy a cheap used copy of any of the countless DE cookbooks out there (I own a Shaums).

Reviews (21)

Wedderburn, Waring and Hamilton
Not necessarily in that order.President McCosh of Princeton
waxes eloquent in his Scottish Philosophy book somewhere on
the internet, re: Dugald Stewart, Kant and Hamilton.

Hamilton is a strong vice, but clearly represented in Herstein.

Good Introduction, useful for self study
I am an engineer by training and a sales man by profession, with a a strong liking for mathematics.
I found this book to be an very readable introduction to a subject (abstract algebra), I had never been exposed to during my engineering math - other than matirx theory, which was obviously taught extensively.
The proofs are generally easy to understand, but certainly not trivial.
A pleasure to read

Reviews (4)

Great Introduction
This is a text for Real Analysis at the Junior Level (American university level).It goes to extreme lengths to make analysis understandable to people who have no prior exposure.The organization is good.Completeness is introduced early as (the "piggy in the middle").Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument.It has good exercises making it an easy book to teach out of.Excellent for the absolute beginner.Good candidate for the classroom.

Basic Real Analysis unleashed
Bryant builds the basic concepts of a first course in mathematical analysis upon the notion of numerical sequences. This approach gives an unified vision and amazing insights. Infinite series, limits, derivatives, Riemann integral are studied in an integrated vision. Clear ideas, illustrations and humor are found across all its pages. Good and illuminating exercises, too. An excellent introduction to basic real analysis.

Exposes Mathematical Analysis Without Set Theory Background
Mathematical analysis is a refinement of calculus, and a pathway into further branches of mathematics, including topology and advanced topics in algebra. Analysis, however, may not seem to be at all related to calculus at its initial stages. An introductory course on analysis can render an unprepared student, even with experience in other branches of mathematics, perplexed and challenged to an extreme. Only later in the analysis course are even the most basic topics of calculus introduced.

One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic. Set theory, a branch of mathematical logic, is in fact the basis of calculus as well. Due to an emphasis upon computations, however, the highest grades in calculus are possible without understanding, or even knowing of, this underlying foundation.

This work is unique among those introducing analysis, in that it does not require a background in set theory. It in fact teaches numerous fundamental concepts of set theory, without stating that it is doing so. Examples provided are based on daily concrete experience, yet are altered for purposes of mathematical instruction. These descriptions are sufficiently general as to prepare the reader for when formal set theory is introduced in more rigorous textbooks.

In addition to being an extremely readable and accessible work,solutions and hints are provided for every review question for every section of the book. This is in stark contrast to textbooks on the subject, which, while costing several times more, are typically designed for a classroom setting, and so leave all questions unanswered. This self-testing of the understanding of each section is crucial for subject matter requiring such attention to detail and precision.

The numerous illustrations throughout the book are rendered clearly and with instructional purpose, yet are often drawn by hand, adding to the sense of familiarity with the author. All of the basic subject matter for a course on analysis is provided, yet has been specifically tailored for a reader in the stages of preparation, of review after completion, or one who is simply inquisitive as to what is required to comprehend analysis successfully.

The softcover edition is durable and portable, and the book remains in excellent condition through numerous readings, which it will almost certainly go through.

Reviews (5)

This is not a recipe book
I can see that this is not the book for you if you want to solve a particular differential equation.But in terms of understanding the field of dynamical systems, there is no rival.This book is a pleasure to read, for the first time I understood the importance and beauty of linear algebra.Academic Press says that this is their most successful mathematics text, and it is not hard to see why.I wish more texts were as clearly written and as beautiful to read.

A complete waste
This is not a book, it's a piece of trash!!! This so called book is a meaningless mess which wasn't even understandable for the person who had a PhD in math and was teaching our class. Do NOT bother with this nonsense. if you want to learn something just read Ordinary Differential Equations by V. I. Arnold.I would have given no star if I could!!!Just go with Arnold's and I'll be WAY better off.