Reviews (3)

Excellent
Silverman's book is much clearer than other books on calculus that I have seen recently.Everything is concise and there is no extra "fluff".Some may wonder about some seemengly strange orderings in the book such as introducing the differential before introducing limits but this serves to help create an intuitive understanding of limits before explaining their mathematical meaning.Otherwise, the problems range from extremely simple to challenging.All of the problems are reachable by just having read the previous section and are not out of the reach of a careful reader. Most of the problems have solutions and / or hints at the back of the book.The book's title includes the word "applications" and the book indeed does contain them.After each chapter on a new topic, the following chapter contains applications.In addition, the last two chapters on differential equations and multi variable calculus are better than in most introductory books.Essential Calculus is suited for class study or for self study and should be accessable to all with high school mathematics under their belt.

A Challenging (in a good way) Book
I am a graduate student in computer science, and I've forgotten quite a bit of math from college. I picked up this book and made a point to read it over the summer and do as many problems as I could. It is a very "tight" book, in the sense that there is not a lot of fluff (hence the "essential" in the title). The book seemed to maintain a nice balance between too hard and too easy so that I was always challenged. It is a very good book for me, and has a sufficient level of rigor so that I feel like I get some practice in that area as well. I would highly recommend it to someone wishing to learn calculus. In addition, it's always nice to find an author you like, because it usually means other books by that author will be good. As a bonus, it has solutions (or hints) to all the exercises so you can check your progress.

Reviews (7)

Quick Calculus
This book is great for reviewing fundamentals before you get to the hard stuff. IT explains this in an easy maner in several different ways. I recommend it.

Great book to offer a good working knowledge quickly

I picked up this book as a supplement for getting a better understanding of the math for a computer algorithms analysis course. The course relys heavily on an understanding of calculus to analyze growth rates of functions and function derivitives but it didn't go into a lot of depth of why the math works giving derivations, etc. It mostly assumed that the reader had already been exposed to calculus and was only offering a refresher. I've already read through half of the book and while there are some errors in the text, there isn't anything that can't be reconciled.

The book uses programmed learning so you can systematically skip in depth explainations of practice problems if you don't need them. The two main branches of calculus are covered: differential and integral. The material is initially introducedinformally and uses graphical explanations (when possible) that really help the material sink in faster. After the main themes areexplained, the material is formally defined and offers derivations in the appendices for those who are interested in them. I've found this method helps to distill the purpose of the calculus from the complexity of the equations and terminology.

There is a refresher for graphing linear equations, essential trigonometry, and exponentials/logarithms. The material is given adequate explaination in order "make the jump" to the key concepts of calculus. I've found the text easy to read both in terms of the author's teaching style as well as having crisp text with a large font. A full chapter, designed as an in depth review of both branches of calculus, is included to solidify your understanding of the material as well as offer a context of applying calculus to real world problems. The appendix also has an introduction on some advanced topics of calculus (that I havn't gotten to yet). A caveat is that when you start to work out the practice problems, if you are rusty with algebra you'll probably need a reference for reviewing the basics of factoring, racicals, and manipulating negative/fractional exponents, etc. The algebra is a little light in this respect when equations are solved step by step. The book assumes you have a good working knowledge of algebra and solving/manipulating equations. I found myself having to quickly review how to manipulate radicals and review the eponentation rules.

All in all I am extremely pleased with the text. It's very concise, well thought-out, with an incremental learning slope that is not too steep, offers meaningful exercises that reinforce an understanding of the material, and uncovers the mystique of calculus with intuitive explainations and repetition of key concepts (in key places) to help you retain the material faster.

Reviews (12)

A Bible for Linear Algebra
This is a holy bible for linear algebra beside P R Halmos(Finite dimensional vector spaces). I can assure you that if you understand this book, no one can teach you linear algebra no matter you go. Personally, I will rate this book 7 stars and 7 diamond. It is a superb. Buy and don't miss it. Add to your collection.

Best intro to linear algebra I've seen.
I simply loved this book.Hoffman and Kunze have written a very sturdy book that begins with the most basic concepts of linear algebra(such as echelon form) and goes through cannonical forms, inner product spaces, and Bilinear forms.The proofs are complete and at an appropriate level for a first look at the subject.Perhaps one of my favorite aspects of this book was the treatment of dual spaces and tensors.It seems many linear texts deal with one subject or the other but rarely do I see both subjects dealt with in the same book.

The only non-positive comment I would like to make about this book is that its beauty is not in its appearence.When you open the book and flip through the pages you feel a little uneasy.The typeset looks uninviting.Take heart!The beauty of the book lies in its content.Give it a thorough chance, and I don't think you will be disapointed

I highly recomend this book for both learning and reference.

Reviews (7)

Excellent book
This is very complete and clear book . Excellent for applications. Treats topics usually omited in most linear algebra books . Could be used as reference .

good, but not always a fun to read ...
I only read the first 60 pages and then I stopped reading the book. Reason : while the book contains some interesting topics and certainly goes very deep and treats linear algebra in an abstract and rigorous framework, I had the impression that the proofs were not always the shortest and most elegant ones. Also, linear algebra at this level is not an easy topic, so Dover books, well known for their high quality on the contents, are not always the ideal books to learn from since the editor tries to put as many text on one page as possible in order to keep the price low. This makes it hard to read and also to make annotations.
For learning the basic principles of abstract algebra, I prefer the book : Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza. Valenza 's book succeeds in explaining the same basic ideas in a rigorous way but by choosing much more elegant proofs. This results in less pages to read while having a better understanding of abstract algebra.

Features

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Reviews (5)

An excellent text ... in 1970, not in 2003
I used this text as a reference over 25 years ago and it was great, for its time.Today, however, there are a number of books available with a more "modern" treatment - ones more likely to provide a more realistic view of the subject matter.

Arguably, ODE is a geometry course in disguise and not a collection of "party tricks" as it is often portrayed in older texts.Analytical methods are clean and easy to convey in the classroom but, frankly, they never appear in the "real world".

If you plan to (or do) encounter ODE's in your chosen field you'd do better to spend lots of time looking at qualitative and numerical techniques, i.e., a more up to date approach.

Coddington did a great job with the subtopics he did address but in the late sixties it would have been difficult, if not impossible, to really provide the reader with a solid feel for the depth and breadth of the subject.

A great Introduction or review.
I took an undergraduate ordinary differential equations class and felt I grasped the subject quite well.I wanted an inexpensive text that I could review the subject with and I decided that I would give Coddington's book a try.I was really pleased with the order in which the text was presented which differed from the course I had taken.The author's seem to put things in a very logical order versus some texts I have seen which really confuse you by the order in which the subjects are presented.Another point that I have to make is the depth that the book has.I learned much more in reviewing this text than I ever did in any diff eq class.It shows the distinctionbetween linear and non-linear diff eq's and covered many other methods which I had not learned previously.This is a great text as a "refresher" or as a course text.I just wish I would have previously used this text to learn ordinary differential equations.

Isbn: 0486658465
Sales Rank: 374304
Subjects:  1. Differential Equations    2. Mathematics    3. Science/Mathematics    4. Stability   

Reviews (17)

Excellent for Self-Study
The last time I studied PDE was 7 years ago. I perceived it then as a hard subject to comprehend because of the unsightly series, symbols, subscripts ...etc.I never thought I would come across a well-organized and easy-to-follow book like Farlow's.
This book is very well-organized and class-notes oriented. It has 47 lessons. Each lesson takes about 4 pages and has a clear well-stated objective with no subtitles and misleading branching. I highly recommend this book; it is so helpful especially if you want to self-study PDE.

Good book
I used this book in an undergraduate course, and since I couldn't see the board during lectures, I relied on only the book and it was very easy to read and understand.The major drawback of this book, and I don't know if this accounts for it's abnormally low price, is that there seem to be far more errors in the solutions than most books have.About 100 pages into the book, I had encountered so many errors, that thereafter whenever my solutions were different from the solutions in the book, I wondered first if the book was wrong, not if I had done something wrong.

Reviews (3)

Like no other book on numerical methods I have read.
I sympathise with the reviewer who said this is one of the few
books on numerical methods he could stand.I will go further
and say this is a book that can be enjoyed. Example: section 2.8
"The Frequency Distribution of Mantissas" explains why the
leading digits of of decimal numbers are not uniformly
distributed, a result that is surely counterintuitive. There is
much more material of interest in this book too. It does
contain standard material too but is more readable than many
books. The author offers much practical advice and insight.
(Hamming is a famous name in applied mathematics and electical
engineering).

The Purpose of Computing is Insight, Not Numbers
Throughout the book, that motto is repeated.

By reading and absorbing the material in this book, the reader is left with the tools and the insights necessary to derive their own numerical methods.

No longer willnumerical methods be memorized as textbook formulas -- now the reader canadapt and derive a formula to solve a specific problem, instead of tryingto fit one of a small number of textbook formulas to a problem.

Thedistinction is made between numerical analysis and numerical methods, withemphasis on the latter.

The book is roughly divided into two parts. Thefirst part covers classical numerical methods, using classical erroranalysis (truncation error, roundoff error). The second part reexaminesthese methods under the frequency domain, analyzing how numerical methodsaffect various frequencies (the "transfer function"approach).

Numerical methods are derived under an information theorymodel, such as by finding a quadrature formula of the highest polynomialdegree of accuracy, given limited information about the function and itsderivatives.

Matrices and linear systems are not discussed as much as onemight expect, although one chapter convincingly leads the reader toquestion some classical methods.

The content is well-rounded, introducingmany readersto topics such as random number generators, differenceequations and summation formulas, digital filters and quantization,discrete fourier transforms and the FFT, and orthogonal polynomials. Abackground in calculus is all that is needed.

Many real-world examplesand anecdotes are cited, but without too much detail or too manyillustrations given.

This book encourages the reader to ask: "Whatinformation is available about the problem?How can it be used to solvethe problem?What are the limits of this information?"The approachis practical, not merely analytical.

This book teaches what most othernumerical books fail to teach: How to derive your own formulas, and thusyour own solutions to problems. And that is perhaps the mostimportantlesson of all.

Reviews (7)

Too much in too-little space.
I would only recommend this book to people already fairly well-versed in the topics it covers.In this book, the authors attempt to cover FAR TOO MUCH material for such a short text.As a result, the reader ends up confused and with a feeling that the author isn't telling them NEARLY everything he knows, even about the basics.The book's coverage of complex analysis is truly pitiful, and I would recommend A Course of Modern Analysis by Whittaker and Watson, even at the much higher 60 dollar price, as a useful source on this topic.Concerning such topics as Lebesgue integration, Hilbert Space, and orthonormal bases--consult good books on real-analysis and/or functional analysis rather than this book.Perhaps the author's greatest mistake is the book's complete lack of excercizes and it's few-and-far-between, weak examples of applications to problems.That said, the reason I still gave this book three stars is that it is good in one way--namely, as a reference for those who already know the material.

A very good book
I strongly recommend this book! I am university lecturer and I was using it over recent years as a main source for the course
"Mathematical Methods in Physics". The material is well chosen,
supplemented with good examples which illustrate interesting and
non-trivial issues in an accessible for a student way.
It is a safe and a good buy!

Reviews (6)

Getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

Possibly too simple
As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin.

A wonderful text -- Highly recommended!
I purchased this book as a reference book for my first analysis course.It is very well written, and easy to follow.Dr. Shilov has a very nice way of organizing this text:He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions.It makes for a very quick reference.His presentation of the included proofs is also very nice.There were several occasions I found myself thumbing through it for a second perspecitve.

As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology.He does keep in mind this is intended for undergrads and first year grads though.

Reviews (3)

Available under the GNU General Public License
This book is freely available under the GNU General Public License, in PDF format.The GPL allows free usage to anyone, and free modification and redistribution with the restriction that your changes have to remain free under the same license.This is the same license Linux and much open source software is released under.

Try a web search for the authors/title.For a course, you might want to purchase the physical copy anyway.

I am starting on the book now, so ignore my rating of the book itself - I had to include a rating to post.

good
covers fundamentals well, easy to read, good variety of problems, historic sections are interesting

Isbn: 0471572780
Sales Rank: 257358
Subjects:  1. Mathematics    2. Probabilities    3. Probability & Statistics - General    4. Science/Mathematics    5. Mathematics / Statistics    6. Probability & statistics   

Reviews (2)

A great work
An invaluable instruction to Applied Mathematics as the language to approaching the essence of Physics and Modern Engineering. A balance to the today overcomputerized mathematical methodology.

Isbn: 0471166111
Sales Rank: 2552489
Subjects:  1. General    2. Philosophy & Social Aspects    3. Science    4. Science/Mathematics    5. Linear algebra    6. Mathematics for scientists & engineers    7. Science / General   

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Reviews (10)

Merely a list of mathematical subjects one should know
This book is simply a list of mathematical subjects one should have a working knowledge of for physics. It should not be advertised as anything more than that, since it can not claim to sufficiently teach any of these subjects. The examples are simplistic, and will not help you when working problems in this book. If you are required to get this book for a course, then look at the syllabus for your course to find out what math books you'll need to find.

Concise, but very useful
Most mathematical physics textbooks are huge tomes (Arfken),multiple volume sets (Courant and Hilbert), or both (Morse and Feshbach).This book covers the essentials in a reader-friendly way without pages and pages of exposition.The discussion of integral equations with separable kernels is a perfect example, rather than going on and on with the theory, Mathews and Walker just give an example that illustrates the technique; this approach makes it easier to follow than the rest.The book was originally based on lectures by Feynman, and his mark is apparent on it. If you just want to see how to solve problems and aren't interested in long-winded discussions of the range of applicability of a technique, this is your book.

Isbn: 0471886394
Sales Rank: 1066247
Subjects:  1. Mathematical Physics    2. Science    3. PHYSICS