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.
Customer Reviews:
Well written for the beginner.......2007-07-19
This book is great for the person new to Calculus as I was at the time I went through an earlier version. The examples are well written, with the steps easy to follow. Interim steps to the result are not skipped as has been the case with other Calculus books I've read. The book begins very simply, so someone with just algebra can follow. I can not overstate the importance of working through the problems though, that was the only way I came to appreciate Calculus. What I liked most about this book was that it had alot of applications to real life, using economic, business and science examples. I learn best when I can apply the information directly to my work, and this text did a good job of allowing me to do that.
I would also like to state that the way some of the word problems are stated can be misleading. Section 7.6, problem 17, for example is a maximizing problem and if one applies the approach suggested in the book, then area is not maximized, because more area can be derived by applying the circumference to a circle.
Calculus and Its Applications, Eighth Edition.......2005-09-30
Probably I did not read the description of this book carefully, that is why not what I expected. Anyway, the transaction was very pleasant!!!
Very good for a beginner taking calculus.......1998-07-20
Its examples and explanations are very good. It contains the essentials of Calculus and good applications in many fields, e.g. biology, economics, etc.
Average customer rating:
- Perfect book for its purpose
- Good explainations.
- Great book
- Great text on discrete mathematics especially for non-math majors
- Great Introductory Book
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Discrete Mathematics with Applications
Susanna S. Epp
Manufacturer: Brooks Cole
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ASIN: 0534359450 |
Book Description
Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.
Customer Reviews:
Perfect book for its purpose.......2007-09-16
This book serves as a terrific introduction to concepts which are of paramount importance in upper-level math courses, most notably Probability Theory, Real Analysis, and Abstract Algebra. Moreover, it provides a solid basis for computer science majors who wish to write more logically sound and efficient programs. I regularly referred back to this in my Real Analysis and Probability courses, and I imagine others would do the same. Also, Dr. Epp's clear, conversational style doesn't hurt the student's confidence later in more rigorous academic enterprises, as well as a concise layout and reasonable pace. Highly recommended.
Good explainations........2007-08-15
This book explained concepts very well. The chapters were easy reads and I even referrred to this text for a Math Reasoning class. If you are a math genius and hate explainations then don't get this book. But if you like to fully understand what you are doing then I would suggest this book.
Great book.......2007-01-03
Wow, this is a great book. I bought this book as a secondary helper book to a really bad math textbook and this book helped me tons. It only seemed to help during the first half of the semester because by the end it wasn't covering the same material as the class was. But it covered the material that it did really really well.
It also has really good problems with good solutions that explain what's going on. Something that so many other math books seem to lack on Discrete math. Just a great book.
Great text on discrete mathematics especially for non-math majors.......2006-08-09
I used an earlier edition of this textbook in a discrete mathematics class that was required for those of us with a non-CS background enrolled in a MSCS program at Virginia Tech, and I found this to be an excellent and complete book on the subject. If you find yourself enrolled in a class using this book, you can be sure of two things - your instructor knows how to select good textbooks and also it won't matter if your instructor is a good teacher since this book does all of the work for him/her.
If you are enrolled in a class on discrete math and this textbook is not assigned, might I suggest you get a used copy of the previous edition. It is just as good as this current edition and used copies can easily be found dirt cheap. If you buy a copy of a previous edition the topics you'd be missing that are new to this edition would be expected value, conditional probability, Bayes' theorem, modular arithmetic, Fermat's little theorem and the Chinese remainder theorem, and RSA cryptography.
The author has included illuminating examples of all concepts throughout the textbook, defined all terms, and makes sure that each new concept introduced builds on previously explained material. Subjects covered include the logic of computation, including the predicate logic that is necessary for fully understanding artificial intelligence, methods of proof including the method of induction and also the terminology of sequences, number theory and combinatorics, O-notation and the calculation of the efficiency of algorithms, graph theory and discrete structures, and an introduction to concepts from the theory of computation. There are many exercises included, with the solutions to selected exercises in the back of the book.
This book only assumes mathematical maturity at the level of precalculus, excluding trigonometry. I highly recommend this text especially to students who are transitioning to computer science from some other discipline and need a firm foundation in the basics of that field. You'll find it useful as a foundational text for studying artificial intelligence, the theory of algorithms, mathematical models of computation, and the theory of computation. Another useful book on this subject is the "Schaum's Outline of Discrete Mathematics".
The table of contents are as follows:
1. The Logic of Compound Statements
2. The Logic of Quantified Statements
3. Elementary Number Theory and Methods of Proof
4. Sequences and Mathematical Induction
5. Set Theory
6. Counting
7. Functions
8. Recursion
9. O-Notation and the Efficiency of Algorithms
10. Relations
11. Graphs and Trees
12. Finite State Automata and Applications
Great Introductory Book.......2006-01-13
For a subject which has so much potential to be conveyed in complicated and esoteric ways, this book actually manages to present every single chapter in a clear and accessible way, even for those unfamiliar with formal logic.
It doesn't cover every single theorem you might come across in a first year class, but it comes close. I'd thoroughly recommend this book, even for self-study. I've used a couple of texts for this subject and while none of them are actually bad, this one is streets ahead for understandability and clarity.
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
Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.
Customer Reviews:
Great book!.......2007-10-08
I've used the third edition in conjunction with Professor Strang's excellent video lectures on the MIT OCW site. The combination of the two is absolutely superb. If you do the exercises at the end of each section you will learn linear algebra even if you never intended to!
Unsurpassed clarity - and this book just got better!.......2007-09-15
Professor Strang has taught Linear Algebra for many years to legions of one of the United States' top institution. So give him some credit, for starters...
This book is inimitable in its clarity and in how it yields so much insight. I have many books on Linear Algebra and I think this book is worth its weight in gold. I know of no other book that teaches the fundamental subspaces so well.
The book covers standard material in Linear Algebra (and then some) and has a strong matrix-oriented flavor (as opposed to a book giving an algebraic treatment - look for Valenza if you want that).
I don't understand what some of the complaining is about by some reviewers. The book is not abstract enough, not formal enough? No first treatment in Linear Algebra is or should be - that is Linear Algebra 2. Besides, matrices are pervasive in all fields of engineering, physics, applied math and other disciplines and later on the student will advance to even more complex issues (such as numerical linear algebra) and they simply cannot afford not to have seen the standard matrix treatment. In fact, that would be the reason it's so widely taught - because it's so useful. It's no use delving into abstract treatment if one doesn't understand the most basic facts about why it is that you can solve a system of linear equations.
Best of all, his lectures now can be seen on MIT's Open Courseware site.
I have used this book since the second edition. I believe this 4th edition is the best edition yet. Unlike some other books on the market, this new edition is a fully thought-through new edition (Strang has been restructuring his book throughout all editions, ever making this more clear and insightful). Not bloat at all. I wholeheartedly recommend it. In fact, I believe you might get hurt using some other books that are on the market that do a very lousy job on teaching this subject (such as Lay). This book is the gold standard.
Non Fiction.......2007-09-03
A somewhat dry but good text on the subject. An introduction to vector spaces, among other things. I just looked at fishpond and the price for a new hardcover is $300. Is this delivered by a strip-o-gram, or what? Unbelievable.
Anyway, it is good, but no way it is worth that sort of money given the subject and its age.
Excellent book.......2007-05-28
I stumbled across this book a few years ago when I was visiting someone in Pittsburgh. I woke up early, and having nothing else to do, I picked up Prof. Strang's book to read and I could not put it down. I am a mechanical engineer with an aversion towards mathematics - but Prof. Strang's conversation style completely won me over ( I refer to 2nd and 3rd editions of his book). Since then I have purchased three other books authored by him, and I have watched many of his videos on MIT's OCW website, and I have never felt let down.
No author can write a book that will be acceptable to every reader, and I find some of the criticism of his books exceedingly harsh. If you do not know how to multiply matrices, then this is not the book you want to start with, but once you know a little linear algebra, his video lectures and this book will give you a completely new perspective.
A solid explanation of linear algebra.......2007-02-21
First off, this book is not well-suited for students who have never seen a matrix and have not yet mastered the basic calculations of how to multiply and add matrices, or for those who have never seen Gaussian elimination. There are many other textbooks that do nothing but provide you with exercise after exercise of manual computations of inverses and determinants that are better suited to that purpose.
That said, for anyone taking a course in linear algebra who actually wants to know more than the rote mechanics of matrix multiplication and Gaussian elimination, this book provides a succint explanation of what matrices actually represent. And I've held onto the book as a reference now for many years (referring to the 3rd edition).
I came across it as a graduate student studying for doctoral qualifying examinations. Someone suggested that I check out Strang's book from the library as a supplement to my utterly confounding graduate school text. It was a godsend! I pored over Strang's book, doing computations on occasion, and taking copious notes of his thorough explanations of concepts like null space, row space, column space, and eigenvalues. After that, I had no problem passing my qualifying exam in linear algebra!
Customer Reviews:
Great Teaching Substitute.......2006-06-09
My teacher for calculus was so bad and couldn't teach. The only way I understood the concepts for the class was through this book. I was expecting a confusing book from what the reviews said, but this is one of the best math books I've used.
Fine book.......2006-05-09
This book explains concepts well. My college professor was Russian and I never understood anything he taught.. this book saved my grade in that course.
Absolutely Unintelligible.......2005-06-29
I am currently taking a math course where this book is used. It is useless and expensive! While I don't consider my instructor particularly adept at teaching, he is a valuable resource in understanding many key points in the book. Whatever language the author writes in, it's not the language of math nor the English language. Any points the author tries to emphasize get lost in a garbled mess of words. All of the assumptions made by the author are unfair to students who have simply tested out of other math courses and are unfortunately stuck taking this one. This text is awful, and even worse for someone trying their best to study this stuff and do well. I'm stuck...
Worse than useless........2004-09-07
I'm an engineer. Although I'm not a mathematition, for twenty years, I have used math in my work. This semester, my wife enrolled in a class at the university in which this was the assigned text. I was totally astonished how this author could take the simplest concept "the function" and make it utterly uninteligible. This is not new material. We honestly don't need a new book for it. The book my father used back in 1940-something would be better than this mush - and far cheaper too. This textbook is worse than useless.
Stupid author.......2004-01-02
Indeed, the author doesn't show much examples for most of the
problems. The author assumes students know how to solve the problems, therefore, she skips most of the details. This type of math is not very useful in today's society. It's really stupid!
This is also an expensive book and it certainly not worth leaning when the author didn't show much details especially for the more difficult problems. She is a stupid, lazy author!
Average customer rating:
- Excellent if it si still as good as the edition from 20 years ago
- A totally ineffective method of teaching Calculus
- Brilliant method
- excellent for basic calculus ....
- The worst math book ever
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Calculus and Analytic Geometry
Sherman K. Stein , and
Anthony Barcellos
Manufacturer: McGraw-Hill Science/Engineering/Math
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ASIN: 0070611750 |
Book Description
A revision of McGraw-Hill's leading calculus text for the 3-semester sequence taken primarily by math, engineering, and science majors. The revision is substantial and has been influenced by students, instructors in physics, engineering, and mathematics, and participants in the national debate on the future of calculus. Revision focused on these key areas: Upgrading graphics and design, expanding range of problem sets, increasing motivation, strengthening multi-variable chapters, and building a stronger support package.
Customer Reviews:
Excellent if it si still as good as the edition from 20 years ago.......2005-09-20
I can only review an edition of this book dated at least 20 years ago. I bought it when I was in high school (in 10th grade actually) and used it by myself to learn calculus.
When I got to the actual class, I knew basicaly everything and I mean everything that the teacher taught us in 12th grade. I didn't even need anything for my first 2 university level courses in calculus, just took the notes in the class and that was enought to get A+ in both, differential and integral calculus (course 1) and Vetor calculus.
The explanation of derivatives was great and my teache just enhanced my knowledge there. The book was specially great when teaching integration. There was a chapter devoted to that. I skept the section about using tables for integration and only learned a few basic formulas. The book taught the methods and still now, after 20 years, I can integrate pretty much anyhing without any difficulty at all.
If the current edition is as good as it was 20 years ago, then this book is definitely a winner.
A totally ineffective method of teaching Calculus.......2005-02-25
I am a student at CSUSB and I have had to use this book for 3 quarters of Calculus. At the school all the professors say the book is horrible and can't wait until the department changes. In 2005 they finally changed the book to Caculus by Larson, Hostetler, Edwards. It is ironic in desperation I asked a fellow student how he was handing the problems of this book. He said that he borrowed a book from his friend who said the book was excellent. It turned out that it was the book written by Larson, Hostetler, and Edwards. I then obtained a copy for myself and found the book to be excellent.
Stein's and Barcellos's book has very poor explanations in the chapters and very few examples to explain to you the concepts. Whereas Larson's book has excellent explanation of concepts and follows it up with good examples that make the concepts easy to understand. At the present we are studying the disk and washer methods of finding volume. Stein covers these topics in approximately 3-4 pages of very poor explantions. The Larson book had 2 chapters on the subject and 9 pages just on the 2 methods. I currently have an A in the last quarter of Calculus and I attribute that to using the book by Larson.
As you can see I can not say enough bad about the book by Stein and Barcellos. Good luck and I hope you make the right choice, but don't buy this book.
Brilliant method.......2004-05-30
This book is literally the best basic calculus text you can possibly get. Anyone wanting to start learning calculus NOW should get this. No real previous mathematical knowledge is necessary. There are several appendices on algebra and series etc. The book discusses trigonometry, so you can learn the book practically without knowing a thing. The "feeling" of the book is inexplicable. Reading this book really gave me an true understanding of basic calculus. Excellent for people like me who need proofs (especially visual ones) have a solid grasp on concepts. If your only goal in learning calculus is to do well on examinations, this book is definately not for you. You should get "Calculus for Dummies" or something like that. The great thing about the text is that it appeals to almost everyone. If there is a certain chapter you don't care for or doesn't matter to you, for example on methods of graphing, you can just skip it, and it will not do any harm. Highly intelligently organized. If you want some help in you physics class on basic vector algebra, just turn to chaper 18 and just read! This book is full of applications, which is great. It also has several historical notes. The colors make the book very engaging to read. Unless your colorblind, this will help engage your interest. Very adequate spacings on the paper as to keep you clearheaded and focused. The drawings rival those of Picasso. They show calculus to be a LIVELY subject. The examples (inside the chapters) are very helpfull. Stein offers several suggestions on how to solve certain problems. Its a shame; this book does not attract the amount of attention it deserves. I did get stuck a couple times; but that is inevitable. Definately get this one: its a gem to have. I can understand how some people would hate this book; its not very concise. That should not be a hindrance. If you feel there is no need to read on about a subject, skip some pages. At the end of chapters it all comes together with a summary of the most important concepts. The book prepares you for study of calculus-based sciences such as physics, and for more advanced mathematical topics as well. I worship this book.
excellent for basic calculus ...........2004-05-25
This book is the best place to start to learn calculus. It starts from very basic principles and also contains some more advanced stuff like Stokes Theorem etc. Some readers may find that the book contains too many basic trivial explanations, but I see this as a strength. When you start learning calculus, I think it is a good idea to explain even the trivial, to make sure that you have a good understanding of really everything. I am sure that most readers will benifit from this, even those already having some more advanced math knowledge. Yes : even this latter group will appreciate the benifits of this book, they can always skip some explanations but will benifit from the very clear exposition of more advanced concepts like Stokes Theorem etc ... Myself for instance, I like the more rigorous and abstract math like "real mathematical analysis", but when I need to refresh some calculus and geometry techniques, this book is really the best to sharpen my intuition and understanding of calculus.
Another excellent feature of the book : this book should serve as an example for the layout of math books : it contains a lot of spacing (handy to make personnal annotations), contains a lot of examples, and contains a lot of excellent pictures illustrating a concept... Also some nice anecdotes are added to keep the reader interested. I wish all math books were like this.
If math is not your strongest skill and you need to learn some higher calculus this book will be your excellent companion helping you to gain the insight and intuition you need. If you are busy with more advanded and abstract math, this book also has something to offer to you : this book serves as a fallback point for sharpening your mathematical intuition and refreshing some concepts that you might have forgotten.
Small drawbacks are : -Some more advanced concepts (like Stokes Theorem) are very well explained, but others are explained without proof (convergence of series...) or with simplified proofs (for instance limited to two dimensional cases, though excellent again to gain mathematical intuition). Maybe this is acceptable for a calculus course, but may disappoint the reader who is looking for rigour.
Conclusion : perfect book to gain insight in calculus, it suits well on the shelf of everybody busy who needs calculus...
The worst math book ever.......2004-02-08
If you have to buy it, buy it. Otherwise, avoid it like the plague. I was forced to buy it because this ass was a professor at UC Davis and made all Davis math students buy it. Even the other professors hated it, but we were stuck with it becuase of his tenure.
Customer Reviews:
Calculus with Applications (8th Edition).......2006-05-19
Having taught this material at the community college level for over 15 years, I find this to be one of the best texts we have used. As always, materials from a Lial book are easily understood. Futhermore, the authors have not lost contact with all rigor as in some math books intended for liberal arts usage. For example, the fact that a critical number can occur at an undefined value of the derivative, but only if the function itself is defined at that value, is fully explained.
My friend and teacher........2005-12-19
Man, I have no idea where to begin. So let me start of by stating my mathematical background before I picked up this book. Before I picked up this book, I was fairly good with algebra but not very good at pre-calculus because all I knew about pre-calculus was that there are parabolas, but I knew very small trigonometry, statistics, series, and some other parts of pre-calculus. Anyway, so here I am in my last year of high school, a very terrible high school, with very small knowledge of mathematics, and I really want to see what the big fuss was with Calculus. So I decided to find some books on Calculus. My first three books on Calculus were very hard to follow along with. They were all textbooks, and one of them I bought. So I decided to sacrifice my $150.00 and buy this book from www.aw.com. When I first picked up this book, I had a hard time following along with the pre-calculus material, so I skipped them. I went into Limits and beyond. I understood every thing to my surprise, but when I got to the parts with Logs and Calculus, I went back to the pre-calculus section, and to my surprise, I understood it this time. Therefore, this book opened my mind. It allowed me to understand things I could not before by explaining the complicated subjects in a very easy to follow matter. I am in my first year of college taking Calculus I and I passed every test with a 50/50 except for one that I missed because of a negative sign, finding the equation of the tangent line to a given function. Anyway, I would recommend this book very much to anyone who wants to learn Calculus. I am very proud of what I got out of this book. This book in fact, made me a calculus teacher in a small way because I now tutor kids who are struggling with Calculus.
P.S. This book is teaches material equivalent to Calculus III.
Customer Reviews:
A classic, richness in knowledge few books attempt anymore........2006-05-15
I used these books (Vols. 1&2) in my last two years of high school back in South America. I remember long nights of bad coffee and cigarettes locked in my room reading it over and over. The book is full of really cool knowledge (even for a non-mathematician). Most of today's students learn like little parrots, (without thinking or understanding) just repeating things mindlessly. This will make this book unpopular among these people because having to read a sentence and stop to figure things out on their own is too hard a challenge for them. I guess that like the high standard of the education of old when teachers loved teaching and their subject this book is also going the way of the dinosaurs. I'll get my copy before that if I were you though ;-)
A righteous calculus text.......2005-09-19
This one of the more righteous books in the author's oeuvre and that is saying something! The subject matter is closely akin to a course I took in Freshman year however it excludes manifolds and operatoins on them. In this respect, the book is not as good as some others out there for an integrated view that even a frosh can grasp. However, overlooking this shortcoming, the text is definitely righteous, being one of the few out there with this integrated approach and being a classic of sorts.
Very thorough, but very dense.......2004-11-18
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.......2004-08-25
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.
Review of Tommy Volume 2.......2003-12-27
I am currently enrolled in BC Calculus in my high school as well as linear algebra at a local college. What better way to learn both together than with Tommy. This is a great book to learn the connections between the two and how to do real linear algebra, not straight algebra but differentiating and doing calculus on whatever spaces you want. It's very concise, however not so clear. I skipped into BC and spend a lot of free time doing math and this book is still a bit deep. Also, the tie-ins to LA are definitely not going to be apparent off the bat. I have a really great LA teacher so I find myself skipping over some of his more complicated expressions of very simple items, however if i were a newcomer to LA, this would be totally confusing and Greek. I agree with the other reviewers, if you're familiar with calculus and LA and want to learn more about each and their connections, this is the bible, however, if you're a newcomer to one or both, definitely learn each separately and more simply. The book is very proof based and states it assumes you know how to use the mathematical objects it's presenting, now it's showing you why they work. Some of his expressions are like physics problems mindset, first look you'll have no idea, but if you think about it, eventually the ideas all fall together. A great book and recomended to anyone experienced enough to handle it.
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