Average customer rating:
- very nice conceptual overview
- Not for the practitioner
- Trash
- Excellent Introduction, Sparse on Details
- A Good Introductory Survey
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Scientific Computing
Michael T. Heath
Manufacturer: The McGraw-Hill Companies, Inc.
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ASIN: 0072399104 |
Book Description
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Customer Reviews:
very nice conceptual overview.......2006-07-22
Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.
Not for the practitioner.......2005-11-17
If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.
Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.
He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.
I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.
Trash.......2005-10-14
If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.
Excellent Introduction, Sparse on Details.......2004-11-20
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
A Good Introductory Survey.......2002-11-05
This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.
Book Description
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.
Customer Reviews:
Great Math Book!.......2007-09-19
I am a pure math student, so I get easily frustrated with applied math books that offer intuitive proofs instead of the mathematical details. Haberman is a great author, not just in the sense that the book offers an easy and interesting reading, but both intuition and a lot of the technical details are provided for each topic. I can only say this about very few of my applied math books, so I am very happy with my purchase. I would recommend this book to anyone who wants precision and more clarity of thought into the subject.
No worked examples.......2007-04-22
While the presentation of the book was very understandable (especially compared to some other partial differential equation textbooks), there are few worked examples in the book. For those who want worked examples, just type in the google key words "haberman site:.edu". If this book could include some of those worked examples, it would be much better.
The book also uses slightly different notation from that of many other books.
Pretty good.......2005-11-27
Pretty good book to learn from. Well laid out. Some areas could be clearer, but will use often!
Absolutely no sense.......2005-09-27
I wouldn't listen to the other reviews. Coming from a student who's done very well so far in all his other engineering courses, nothing in this book makes any sense at all. They jump into topics you've never even heard of, and expect you to know everything right off the bat. There aren't many examples, most of it's derivation, and the book takes a tone that you are a genious and will understand everything without a concrete explanation. I wouldn't get this if its not a required text, if I were you.
Smooth transition to advanced topics!.......2005-08-22
Most books on PDEs either address very basic, introductory concepts or tackle advanced topics requiring Measure theory. In addition, they focus mainly on theoretical concepts and do not provide adequate worked examples. Haberman's text is immensely useful both in bridging the gap between elementary and advanced books as well as in providing many, many completely worked problems. Indeed once you have had a basic course in PDEs you could use this text to teach yourself graduate-level topics such as Green's functions.
I do not try to convey the impression that this is a mere cookbook - "here's a problem, let's look up the solution". To the contrary. Haberman provides the motivation for each kind of mathematical treatment and interprets his results, pointing out their important consequences. His presentation of Gibbs' phenomenon is the most clear and comprehensive I have yet come across.
I heartily recommend this book especially to Math and Physics seniors who hope to continue on to graduate school in either of these subjects. In either case, it is expected of you to be adept at Green's functions and Haberman's book lays the groundwork for this topic.
Book Description
Packed with examples, this book provides a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material understandable even for readers with limited exposure to topics beyond calculus. Encourages the use of computer resources for illustrating results and applications, but is also suitable for use without computer access. Includes additional specialized topics that can be read as desired, and that can be read independently of each other. Denotes exercises requiring use of a computer with computer icons, asking readers to investigate problems using computer-generated graphics and to generate numerical data that cannot be computed by hand. Offers Mathematica files for download from the author's Web site; can be accessed through the Prentice Hall address http://www.prenhall.com/pubguide/. For engineers or anyone looking to brush up on their advanced mathematics skills.
Customer Reviews:
Partial Differential Equations and Boundary Value Problems.......2002-07-18
I think this book is Possibly the best Mathematic book for Engineer I've ever read. This is due to the fact that the material is so much clear and the examples are so easy to follow. The book's explanation is precise and accurate. The exercises on every chapter are helpful. I practise almost most of the exercise problems. In fact, I score an "A" on the first Test. I will recommend it to everyone without hesitation.
Initial impressions.......2000-04-04
Nakhle: Just a quick note to thank you for your book! It arrived Thursday, and I've been reading it and doing the exercises both on paper and in Mathematica 3.0. After a quick review of the whole book and a thorough reading of the first 70 pages so far, I can say I just love it! If I'd only had a book like this in college and graduate school I'd have become a much better electrical engineer. Yours is one of the best expositions of both Fourier series and partial differential equations I've used. Although I haven't gotten very far into the boundary value problems and the orthogonal functions areas of the book yet, my initial review indicates they will be excellent also. I am enjoying your book immensely, and I thank you very much for it. I'll update this with a more thorough review when I have a chance to finish the book, but I wanted to share my initial impressions so others might weigh them into their own decisions to get this excellent book.
A clear introduction to PDEs, Fourier series.......2000-03-28
This text not only provides a simple and easy-to- read-the-first-time guide to solving PDEs with Fourier series, it also is chock-full with all the necessary details and includes many interesting problems. I took a course out of this book as a sophomore in college and found it very interesting and useful. The style and difficulty is very similar to a typical undergraduate ordinary differential equations book, except this is better organized.
The subjects include a small bit on characteristics for first-order equations, a chapter on trigonometric series, PDEs in rectangular, polar, and spherical systems and associated eigenfunction expansions, Sturm-Liouville theory, the fourier transform, Laplace/Hankel transforms for PDEs, grid-type numerical methods, sampling & discrete Fourier analysis, and quantum mechanics (the Schrödinger equation).
This book is definitely great for applied mathematicians, physicists, or engineers who really need a solid introduction to the topic, written by someone who knows all the details. Any treatment in "mathematical physics" courses on PDEs will fall short of this book's content.
Of particular importance are the inclusion of special sections for Bessel functions, Legendre polynomials, associated Legendre functions, spherical harmonics, etc. All the details of solution and many exercises are included.
The most interesting parts of the book are towards the end, with the Sampling Theorem and discrete Fourier transform; and the proof of Heisenberg's uncertainty principle.
This book is also useful for more theoretical mathematicians or mathematical physicists who need an introduction to PDEs before taking a more difficult course on general theory.
In short, I think that even though this book is of great utility to non-mathematicians, it is proper to learn these concepts and techniques in a proper math setting where care is taken. This text is a solid foundation for confident application and a springboard towards more advanced subjects.
Average customer rating:
- I am VERY Happy with this Book - great 4 self-study
- kinda pointless, same examples you'll encounter in your book
- Great Book!
- Comprehensive & concise
- review of schaum's outline of calculus
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Schaum's Outline of Calculus (Fourth Edition)
Elliott Mendelson , and
Frank Ayres
Manufacturer: McGraw-Hill
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ASIN: 0070419736 |
Book Description
Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators.
Customer Reviews:
I am VERY Happy with this Book - great 4 self-study.......2007-08-01
In order to take an advanced statistics course (since I have been out of college awhile) I have to take a calculus test. They gave me a sample of 60 questions from prior years and recomended a text that cost $180!!!
Well for 1/15 of the price of the expensive text, I can get about 55 out of 60 questions answered through this one. The ones that are not covered in this book pertain to complex integrations - I'll buy the Schaum's Advanced Calc text and get my answers and still have tons of money left over.
*** Another thing is that the first few chapters are an excellent review of pre-calc, something I did not think I would need but it turns out to be more useful than I thought. ****
The covering of some topics, like LaHopital's rule is better than most texts.
I have not encountered typos yet - when I have that that I did - once I plunge into it more - turns out he is right and I was mistaken.
****Having numberous worked out problems and problems with at least the solutions to check yourself is GREAT FOR SELF STUDY ****
kinda pointless, same examples you'll encounter in your book.......2007-06-17
not that great, if you have a good text, you'll notice that the examples are pretty much the same
Great Book!.......2007-03-17
As an engineer and a Math Tutor, I find this to be an invaluable supplement to the students I tutor.
Lenny Laskowski
Comprehensive & concise.......2007-03-09
You couldn't ask much more of a book that covers such a beautiful art so thoroughly.
review of schaum's outline of calculus.......2007-01-06
the product has a lot of examples. i would not recommend this for people who are trying to learn calculus for the first time, but it is a good way to refresh one's memory.
Average customer rating:
- the best network flow book for computer scientists
- Good Introductory Book
- Great book for Network Theory and Application
- Great book for Network Theory and Application
- PLEASE, write a corrected edition!
|
Network Flows: Theory, Algorithms, and Applications
Ravindra K. Ahuja ,
Thomas L. Magnanti , and
James B. Orlin
Manufacturer: Prentice Hall
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ASIN: 013617549X |
Book Description
Bringing together the classic and the contemporary aspects of the field, this comprehensive introduction to network flows provides an integrative view of theory, algorithms, and applications.
It offers in-depth and self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including a description of new and novel polynomial-time algorithms for these core models.
For professionals working with network flows, optimization, and network programming.
Customer Reviews:
the best network flow book for computer scientists.......2004-12-18
I've been using this book as the primary text for my class in
"Network Flow Programming" (senior & graduate level) at the
University of Tennessee for about 10 years. Prior to that time
I had used Jensen & Barnes' Network Flow Programming (now long out
of print). The code in Jensen & Barnes is in FORTRAN (not so fun
or useful for CS majors) and the intended audience seemed to be OR.
Ahuja's code is pascal pseudo-code for the most part, which usually
translates easily into the C language that most of our students
use.
For CS students, there is excellent use of algorithm analysis
(big-O) throughout the book, and there are long discussions
about different approaches and algorithms and the complexity of
each. There is a lot of mathematical notation, but my students
have never had to worry about PDEs and the like here. Any good
advanced CS student (graduate or undergraduate) will find the
book very worthwhile. In my course the students must implement
min-cost spanning trees, shortest paths, critical path/PERT
networks (not in Ahuja), max flow, and min-cost flow. I would
also recommend (for CS majors) Tarjan's excellent (and
succinct) Data Structures and Network Algorithms.
Good Introductory Book .......2004-12-13
This is a good introductory book. I particularly liked the applications of the problems, introduced in the book. The main negative point that I could mention is, the redundant explanations and discussions you might see in different chapters. I would say the volume of the book could have been reduced by some 15%-20%, if the authors had chosen to be more concise.
The book, Combinatorial Optimization by William J. Cook, et al, is an alternative. It covers a whole lot of topics and is just too succinct, a little more elaboration would have been appreciated !
Great book for Network Theory and Application.......2003-09-25
This book contains a lot of great algorithms for network flow theory and it also contains many of the great applications, which are very useful in practice. This book is very completed. Personally, I learn a lot of new things about Multi commodity Flow, which are the use of Lagrangian Relaxation, Column generation, Resource allocation techniques for solving multi commodity flow. There are also the good chapters in Convex cost flow and Generalized Flow and good appendix in complexity. Beside this book is very easy to read and understand. It is a great idea to have if you are in OR or IE major. :)
Great book for Network Theory and Application.......2002-08-01
This book contains a lot of great algorithms for network flow theory and it also contains many of the great applications, which are very useful in practice. This book is very completed. Personally, I learn a lot of new things about Multi commodity Flow, which are the use of Lagrangian Relaxation, Column generation, Resource allocation techniques for solving multi commodity flow. There are also the good chapters in Convex cost flow and Generalized Flow and good appendix in complexity. Beside this book is very easy to read and understand. It is a great idea to have if you are in OR or IE major. :)
PLEASE, write a corrected edition!.......2002-02-28
First of all, I am not surprised that the book
got so many good reviews: at first look, it is truly
impressive, and it is clearly a work of love. I was
looking forward to teaching from it.
It is quite clear from the reviews though, that the
reviewers have not **used** it for teaching; they may
have browsed it at most.
The first disappointments came very soon in the course I
taught. The biggest flaw of the book is the really bad style
in which the proofs are written. They manage to be seemingly
overflowing with explanation, and at the same time difficult
to understand. They gloss over many details: if the teacher
tries to skip these, an alert student could easily make
him/her look pretty silly.
One case in point is the proof of the label correcting
algorithm's correctness starting on page 136. I knew this
material from before, so I thought preparing class from
here would be a breeze. I was wrong: after going back to
my notes, and breaking up the mess into several simple
claims did I manage to make notes from which I could teach.
Whoever missed the class was helpless, when they looked
for explanation in the book.
I only remark, that all classes that I taught from this book
were at some of the top 10 OR depts at the US... so this is
hardly the students' fault.
Many exercises are wrong as well, and although the authors
claim that they will try to fix the mistakes, they hardly ever
reply to reader's comments, as some of my fellow professors
told me.
I can only compare the style of the exposition to the
later written Combinatorial Optimization book by
Cunningham et. al. There is a WORLD of difference.
One can try to look up for instance, the proof
for the label correcting algorithm: the proof in the
Ahuja et. al book is practically creaking at the joints,
while in Cunningham et. al. it flows lucidly.
I suspect that the authors of the latter book wrote it, since
they were unhappy with this one; one can hardly be surprised.
On the positive side, the plethora of applications presented
is truly amazing, and the exercises (when correct) are excellent.
To sum it up: A good book, which could have become a great one,
but have not; one which is very useful, but at the
same time very hard to use... I think the community would thank
the authors for a second, revised edition, that would fix
all the mistakes, and all those terrible proofs.
A final word: this text received the prestigious Lanchester
prize. One may surmise that giving prizes to a textbook
would be best done maybe after 5 years, after a book proved
its worth in actual teaching in the trenches,
so to speak, and NOT based on the first impression that the
jury gets.
Book Description
A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.
Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.
Customer Reviews:
Very good for struggling in Real Analysis.......2004-10-24
There is no problem solutions for Real Analysis texts available in U.S. since most of the teachers believe that Math students in grad level should be more creative. However, not all students in Real Analysis are potential mathmatician. If they lost in class and must study by theirselves, they may feel frustrated missing all the stuff contained in problems. The material in "Principles of Real Analysis" may not superior much than other famous text(like Royden, I think Royden is clear enough but too much mysterious things lie in problems.). But use it with this workbook, you will find much comfortable in self study. It helps a lot not only in my homework assignment, but also in my understanding.
A must have!!!.......2004-05-28
This book rocks! It covers practically all the major topics of an introductory course in graduate Real Analysis. Excellent solutions that aid in the understanding of the material. This book's worth is immeasurable, or should I say, non-measurable.
Must have one.......2002-10-23
Great guide, must have for anyone taking Real Analysis.
Must have for anyone taking Real Analysis.......1999-04-11
Before buying this book, I was failing Real Analysis. Now I have a prayer of passing. Thank goodness I found it in time. For it to be of use, you need to buy the companion book "Principles of Real Analysis", same authors. On the down side, it doesn't have an index, but overall, well worth the money. Besides, it is the only source I've found of worked-out Real Analyis problems outside of borrowing from other students who have already taken the course.
Book Description
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.
Customer Reviews:
15 year old math tips.......2007-05-21
This charming book explains why math olympiad puzzles are fun, and gives 15 year old insights ( in two senses --- most of the text was written by the 15 year old Terence Tao, but revised with some additional good exercises 15 years later by 30 year old Fields medalist Terence Tao.) The style is chatty, and the advice and worked examples are very good and do not require any math beyond pre-calculus. The level of difficulty is just right for would be high school math competitors, and adults with some math who enjoy a mild challenge.
Six easy steps to becoming a Fields medalist.......2007-01-31
I came across this book after reading about Terence Tao, a recent Fields medalist. It's interesting to see a book like this by such an accomplished mathematician. The book gives practical approaches to solving the types of math problems encountered in math olympiad competitions. I am not, nor have I ever been, a math olympian, but I found the book to be entertaining and useful for intellectual fortification purposes.
Book Description
This best-selling guide--which has sold more than 340,000 copies since its first publication--has been thoroughly updated throughout to correspons to current advanced calculus courses. A complete and comprehensive review of the subject, this updated edition features important new chapters on topology and Laplace transforms and essential new theorems, with explanatory proofs.
Customer Reviews:
Ideal (solved examples) companion to your calculus textbook.......2006-05-13
If you are studying calculus, the books from Schaum will certainly help you to develop your problem solving ability.
This is NOT a real analysis textbook inspired on Bourbaki topology. So that some readers do not consider the material really advanced. I think they were expecting 18 ways to express the Axiom of Choice (Zorn Lemma for example) Godel conjecture, Fixed point theorems, path and non-path conected sets, differential forms, more terminology (homeomorphism, diffeomorphism, manifolds) etc...
The book has an approach similar to Piskunov or G.B. Thomas Junior books, that is, more elementary approaches (but note that elementary does not mean easy). Many solved problems.
Look at table of contents inside the book at amazon to grasp an idea of what you will get.
Overall, very good companion, practical and with many examples.
Not what I expected.......2006-03-15
This is a good book if you are not looking for true advanced calculus material. This is just calculus--with some tougher topics, but is not a true advanced calculus book (which is much more proof based).
A Different Take on Advanced Calculus.......2006-02-17
After finishing the first 3 semesters of what is basically applied Calculus, majors in pure mathematics part company with their fellow students and move on to what is called "advanced calculus" or "functional analysis". This jump to the next level of mathematics, in which basically students have to be taught calculus all over again from a rigorous proof-based method, is a rude awakening to many. Most textbooks used in this situation, such as those by Rudin, assume that a talented and enthusiastic instructor will be acting as tour guide for the student, and will fill in the gaps. Unfortunately, this is not always the case. This Schaum's outline works well for such a situation. It not only covers what you would expect to see in undergraduate analysis, it mixes proofs with solved numerical problems and applications so that the student does not get bogged down or bored as can be the case with many of the texts on the subject that have nothing but proofs as exercises. In that way, it is unconventional in its treatment of the subject. Also, it provides more explanation and tutorial than you will find in the average Schaum's outline, and is pretty good at illustrating the correct way to perform a proof. If you can afford it, an excellent companion text to this Schaum's outline is Abbott's "Understanding Analysis", which can be used for self teaching of analysis because it is so detailed and clear.
Helpful for those who need to bridge the knowledge gaps.......2005-06-20
If you're trying to understand a lot of the abstracts in calculus that you might have missed in high school or are tired of college professors simply skipping past material because they assume you've already come across it even when it might not have been the case, then never fear. This book can help refresh your skills in areas that you may have forgotten or might have received little if any attention. Plus, chapter after chapter, even the most difficult concepts are made easier to understand in layman's terms. So the next time you get frustrated that not even your instructor can help, get this book, catch up, and never get left out in the cold again !
Very Useful.......2005-05-20
Whilst as some reviewers have pointed out, the proofs offered are not always the most fundamental and rigorous available, this aspect of the text makes it surprisingly digestible. As an example, the last chapter (on complex variables) seems almost an afterthought. However the text in combination with the solved problems will have the reader performing integration using residues etc in no time. This area of calculus has many weighty tomes devoted to it, offering full and rigorous proofs of each theorem, but to gain a similar working facility to that described above one needs to trawl through almost an entire book, a much more time-consuming exercise. The book works similarly for many other areas of calculus. This I found very rewarding, as I was able to go from clueless to reasonably proficient at problem solving in a short time, which encouraged me to keep learning. The more advanced treatments are also much easier to digest once you have some familiarity and competence in the area.
The only real let-down are the typos, which seem to be more concentrated in some chapters rather than others, however they are generally easily spotted and accounted for.
The book is therefore perfect for scientists and engineers, as with a minimum of fuss it teaches the reader everything they need to know to perform calculations, and makes a good introductory text for aspiring mathematicians. At this price, you'd be crazy to not have it lying around somewhere.
Book Description
Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.
Customer Reviews:
A delicious smorgasbord of inequalities.......2006-06-25
Professor Steele has done a wonderful job in developing the theory behind the Cauchy-Schwarz inequality. He starts off with the basic theory and then through the course of the book he teases out the limitless ways the inequality can be used. There is a breathtaking sweep of applications. What is interesting and valuable about his approach is that as he develops the building blocks he explains why or why not a particular approach might not work. I think there is quite a bit of Polya's inspiration in his approach. For instance, he gives Polya's proof of the Carleman inequality which, on it face, is almost outrageously unbelievable ( where does the "e" come from?) but by that stage you worked through the challenge problems and the other material and it is possible to see why the "e" makes sense.
The challenge problems are excellent and his solutions sometimes skip over some important steps which a teacher could get students to fill in so that they can demonstrate that they understand the material.
There is a lot to learn from this book and it should be read by everyone who is seriously interested in mathematics. The classic Hardy-Littlewood-Polya book on inequalities is a quite different beast but the two together provide the serious reader with a depth of understanding that is hard to surpass.
at the core of mathematics.......2006-03-20
this book deals in a friendly fashion with inequalities (and therefore) with the elementary use of convexity and integrals.
Famous inequalities bear the name of famous mathematicians, e.g: Tchebychev, Hilbert, Cauchy, Hardy, Rademacher...This is one way to understand their significance in maths. This book is about those ones and others such as 3/2
< a/(b+c) + b/(c+a) + c/(a+b) and the many ways to tackle with the fact of proving and using them. Study of this book should be seen as a good and rewarding path towards improving one's mathematical skills .
Erudite and stimulating problem book in inequalities.......2005-09-11
The classic work in this field is Hardy, Littlewood, and Polya's "Inequalities", but as much as I admire these authors for their other works, I have never gotten much out of their inequality book. Steele's book is different: extremely clear, erudite, and thorough, it almost makes everything obvious. The subject of inequalities is something of a hodge-podge, and Steele isn't able to change that, but he helps tie it together with lots of forward and backward references and with returns to problems after we have learned new methods. A good example is Carleman's inequality (easily the most startling result in the book); Steele provides three different proofs spread out through the book, plus a continuous analog.
Despite the title, the book is not primarily about the Cauchy-Schwarz inequality, although it (and the Arithmetic-Geometric Mean inequality and Jensen's inequality) do recur throughout the book.
The book is structured as a problem book. The body consists of a number of "challenges", each followed by an exploration of how to solve it. Each chapter ends with a copious selection of exercises; they are not as hard as the challenges, but they are hard enough and they will build your mastery of the material. All exercises are worked out in full in the back of the book.
Wonderful Book.......2004-08-20
I rate this book with FIVE STARS *****
Somehow, the review rating software keeps changing the rating to two stars which is incorrect -- again I must emphasize it is FIVE STARS ****.
Get it now -- don't wait!
As might be expected from the title, Steele's book includes an in depth exploration of the Cauchy Schwarz. It, however, includes so much more -- for example, many, many useful inequalities are set forth in its pages. But even its richness in range and number of inequalities (and equalities) is secondary to Prof. Steele's method of explication. For the real fruit of this book is the techniques and confidence built by the exercises and exposure to the examples. The exercises feed and bolster confidence in approching or deriving familiar and more importantly, never-before-seen inequalities, a confidence which grows with each page and exercise. Techniques that might normally only accrete after years of experience in the course of undergraduate and graduate mathematics courses are set forth one after another. On top of that, this is one of that handful of mathematics books that you can read almost like a novel. It's so readable and rewarding/interesting and engaging that when people have asked me what I have been reading lately, I can answer with a good deal of pride and satisfaction: "a book on the Cauchy Schwarz inequality" -- which I never said about Royden, etc. These techniques are vital for many types of research -- applied mathematics, CS, economics, statistics, (and competitions) to name a few -- in all of these areas finding bounds can play a central role in research. Well worth every penny.
Book Description
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Download Description
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Customer Reviews:
an excellent book on hyperbolic equations.......2005-10-18
The author gave almost all the basic knowledge related to hyperbolic equation, at least from the engineering point of view. I read it myself without any help. It's not hard to understand. Moreover, it gives all you need at beginning references.
Good book to start with. Highly recommended........2003-10-24
This book starts from simple things and moves to pretty complicated staff graciously. It is useful even as an introduction to the hyperbolic equations. Finally, this is the only book I use at most every day. This is the book I would strongly recommend to all students who study this field and to researchers. It has a very good and comprehensive reference.
The author develop even the software (unfortunately, this is FORTRAN, not C). The source is available and well discussed in the book (there is a whole chapter). I did not use it but found this is a very good practice. It should be useful for student also.
Many things are really nice. For example, the book gives a very good view of the nature of oscillations in high order schemes, not only formulas. And so on...
However, there are few things I was not satisfied.
1. There are no comprehensive discussion about non-uniform and non-rectangular grids. It is not good, for example, for people who works in spherical coordinates (for example in some brunches of geophysics).
2. There is no information about FCT methods that are still very popular because they give a very straightforward way to use 4th and higher order methods. However, there is a reference to the Oran and Boris book, for instance.
3. It is sometimes really pure mathematical description especially for non-linear equations. It was really inconvenient for me. Fortunately, good reference helped.
There are more things were bothered. However, this is personal. The author works with the advection equation a lot, but does not like to discuss more the conservation form of continuity equation which I would prefer. In spite of author's efforts, I think still that the wave propagation method is not so convenient as flux method even for non-conservative equations. But it depends.
Finally, this book is definitely fine and, I think, it is the best among all books in this field (maybe except the Hirsch book which is "Numerical computation of internal and external flows" 1988). I would highly recommend it to buy.
nice introduction.......2003-07-11
This book provides a nice introduction to the mathematics behind finite-volume methods. After reading through the first half of the book on scalar conservation laws and systems, papers in JCP no longer seem as intimidating. The book is laid out very well, and the notation is consistent throughout. It is the best of the bunch when compared to Toro's Riemann problem book and Laney's Computational Gasdynamics text.
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