Average customer rating:
- Advanced probability topics without measure theory
- Just unnecessary
- Another poorly written text book
- Good Introductory Textbook
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Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Michael Mitzenmacher , and
Eli Upfal
Manufacturer: Cambridge University Press
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Randomized Algorithms
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ASIN: 0521835402 |
Book Description
Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.
Customer Reviews:
Advanced probability topics without measure theory.......2007-08-18
This book is underestimated by two reviewers below. I totally do not agree with them. This book covers a wide range of topics in a very readable style. The contents in this book is complementary to the book of Motwani and Raghavan (but this book is much easier to digest).
It, without requiring any knowledge on measure theory, contains excellent introductions to many difficult topics in probability including
- concentration bounds (Chernoff, Azuma-Hoeffding, etc.)
- applications of stochastic processes such as queuing theory
- martingale (Wald's equation)
- coupling of Markov chains and their mixing times
- Shannon's source coding and noisy channel theorems
- Erdos' probabilistic method
- etc.
All of these topics are provided with excellent applications in computing.
The authors illustrate many clever tricks for proving theorems, and these tricks give insights to the readers as well.
Just unnecessary.......2007-05-17
This book, while written by two renowned computer scientists, is truly disappointing. In trying to discuss randomness and computation, this book just does a mediocre job on discussing randomized computation and also an equally poor job discussing relevant aspects of probability theory. Their approach is not novel and many of their examples can be found in other texts. If you really want to learn randomized computation, get Motwani et al's book on Randomized Algorithms. If you want to learn probability theory, get any advanced probability theory book like Spencer and Alon on the probabilistic method, one of Sheldon Ross's books, or even Grimmett and Stirzaker. Whatever you do don't get this weak hybrid of a book that will require you to get another book at some point to supplement your understanding.
Another poorly written text book.......2006-03-19
The authors must be smart guys. They obviously understand alot about this subject but make the mistake that you do too! As a result, the book is inadequate as a teaching tool.
They use only half to a third of the narrative they need to adequately explain a subject. They also like to leave out proof steps or not explain them. The problems at the end of chapters are poor as well, since the authors seem to have forgotten to teach the techniques needed to solve most them in the chapter they belong to.
I am sure to them it is intuitive.
Good Introductory Textbook.......2005-03-16
It's pretty easy to get computers to do things where the answer is yes or no, or 4 or 6, given that the inputs to the problem are known. It's much harder to get an answer to a problem where the answer is that their is a 62% chance that the answer is yes. Unfortunately, in real life it's this second class of problems that predominates.
This book is oriented to solving these kinds of real world problems. The exercises in the book are chosen from real world examples -- what we used to call story problems. This tends to give the student a better understanding of not only the mathematics and programming involved but experience in looking at problems with a view to understanding this approach to solving the problem.
This book is suitable for a one or two semester introductory class at the upper undergraduate or beginning graduate level.
Just a word about the illustration on the front of the book. At the end of the book Alice in Wonderland the queen is about to order Alice beheaded. Alice says, "You're nothing but a pack of cards." At this, the whole pack rose up into the air and came flying down around her. This illustration is by John Tenniel from the original book of 1899. A deck of flying playing cards is a good way to illustrate random and probability.
Book Description
The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, the new edition remains the most practical, comprehensive handbook of scientific computing available today.
Customer Reviews:
talk about outdated.......2007-06-27
this book was likely a looker back in the day, but its 2007 now. Need to have better details for non "C"-users. wish i had bought "Idiots Guide to C".
A classic book of numerical algorithms.......2006-12-24
This book, although published 15 years ago, is still very useful. In fact, its more recent counterpart "Numerical Algorithms in C++" is a mess, and I wouldn't recommend it to anyone. The explanations of the algorithms that occur in each section of this book are top-notch. It helps with such questions as "Sure you know how to evaluate an integral with pencil and paper, but how do you do it with a computer?" Everything from linear algebra techniques to integration and evaluation of functions to the FFT and spectral applications are explained clearly and coded up in C. The code is great too, with the exception of one problem that several reviewers have already mentioned - the author has a FORTRAN-like programming style in which each implementation has arrays going from 1 to n versus 0 to n-1. This does cause some implementation problems if you want to transfer the algorithms into another programming language. Overall, though, I can't think of one book that does all of the heavy lifting that this one book does as well as it does in the arena of numerical algorithms.
The book is now available online. Just type "Numerical Recipes" into Google and click on the Numerical Recipes Home Page to peruse the entire book free of charge. You might also find the "Numerical Recipes in C Example Book" useful. That book is simply the source programs that demonstrate all of the Numerical Recipes subroutines. Each example program contains comments and is preceded by a short description of how it functions. I know I found it helpful in many cases.
Very nice book.......2006-08-27
A must buy for students or researchers who need numerical methods. Comprehensive topics. A good place to start to deeper levels. Online book is good for quick look.
A classic, and still worth having.......2006-07-12
"Numerical Recipes" has been a staple in computing libraries for many years, and for good reason. It provides immediately usable implementations of all the workhorses of numerical computation, in production-quality form. Maybe there are better implementations out there, FFTW for example, but getting something to work correctly always comes before getting it to work fast. Numerical computation is a specialty, and vanishingly few of us are specialists. As a result, getting this much specialist knowledge for the price of a very few hours' wage, fully debugged and documented, is a great bargain.
I have to agree with the critics who point out that the Gnu Scientific Library (GSL) is more complete in some areas, and offers better licensing terms. This collection has its own strengths, though, and not just in documentation. The writeup, however, is the major interface between the software and us, the bio-ware. GSL's collection of 'man' (help) pages serves a purpose, but this book's exposition describes a lot more of the background and rationale for the routines. The code and man pages are self-evident statements of the implementation - but "what" is a very different question than "what else" or "why."
This one may not serve all needs. You'd be amazed how many it does serve, though. If you need more than a Matlab session for numerical computing, you need this.
//wiredweird
Great compilation of numerical routines for C programmers.......2004-12-17
I found this book indispensible in my effort to develop profitable trading systems for futures and options and in my research in factor analysis and, more recently, in chronic fatigue syndrome and fibromyalgia. Anyone who programs in C or C++ and works with mathematics must have this book. It covers a surprisingly wide range of algorithms: routines are included for everything from handling Julian dates and solving systems of linear equations to determining eigenvectors and singular value decompositions, solving differential equations, doing numerical integration (quadrature), not to mention calculating fast fourier transforms, lomb periodograms and maximum entropy spectral analyses. While not always state-of-the-art, the routines are quite reliable (when used correctly), clearly-written, and easy to understand and use. I would strongly recommend this book (and the companion software) to anyone who programs in C and is literate in mathematics. I always keep a copy nearby.
Jeffrey Owen Katz, Ph.D.
Author: "The Encyclopedia of Trading Strategies" (McGraw Hill, 2000)
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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Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)
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.
Average customer rating:
- Okay for a text
- Useful Book
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Introduction to Numerical Methods and MATLAB: Implementations and Applications
Gerald W. Recktenwald , and
Gerald Recktenwald
Manufacturer: Prentice Hall
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ASIN: 0201308606 |
Book Description
From the Back Cover: The outstanding pedagogical features of this book are: o use of numerical experiments as a means of learning
why numerical methods work and how they fail; o a separate chapter reviewing the basics of applied
linear algebra, and how computations involving
matrices and vectors are naturally expressed in MATLAB; o use of a range of examples from those that provide a
succinct illustration of a basic algorithm, to those
that develop solutions to substantial problems in
engineering; o consistent use of well-documented and structured code
written in the MATLAB idiom; o a library of general purpose routines—-the NMM
Toolbox-—that are readily applied to new problems; o a progressive approach to algorithm development
leading the reader to an understanding of the more
sophisticated routines in the built-in MATLAB toolbox.
Customer Reviews:
Okay for a text.......2006-03-18
This book is okay for a text book, however there arent many examples, and the examples that are there are very simple. There are solutions for some problems online, though most of them are very basic and don't help very much.
Useful Book.......2004-08-28
This is a nice book for scientists and engineers. There are MATLAB programs already written that you can download from the webpage very easily, and modify for your specific use. I am no programmer, so having programs I can easily modify is a plus. This is meant to only be a review of linear algebra, so if you are trying to learn that subject, you will probably need to supplement this text with another book. This is not terribly in-depth on the MATLAB either. But it is a very useful handbook of plotting and interpolation methods, and how to choose the best methods for your particular set of data.
Book Description
This highly successful and scholarly book introduces readers with diverse backgrounds to the various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with careful proofs and scientific background. An in-depth treatment of the topics of numerical analysis, a more scholarly approach, and a different menu of topics sets this book apart from the authors' well-respected and best-selling text: NUMERICAL MATHEMATICS AND COMPUTING, FOURTH EDITION.
Customer Reviews:
Horrible Book........2007-09-10
Honestly, this has turned out to be a horrible book. Particularly in the disconnect that exists between the text and the problem sets. Very few of the examples are useful to read through because they are trivially simple, while the problem sets seem to take particular delight in finding the hardest tricks to be solve-able.
I would highly suggest that anyone that purchases this book, already know what they are trying to learn, or have an excellent teacher that can fill in the gaps.
Book for the U.......2007-05-29
I bought this book for my college and it was excellent
Great Book.......2006-11-26
I think this book is lucently written and explains various aspects of numerical analysis in great detail. The proofs are stated in an understandable way and algorithms are presented clearly and in such a way that it is easy to implement them in the programming language of one's choice.
Disappointing at best.......2004-01-04
The book was a major disappointment. I am glad that I did not purchase it for my class, but instead borrowed it. The ordering of topics and emphasis choices never seemed to make sense to me. The layout throughout most of the text is like one long, run-on sentence. The underlying structure of numerical analysis never developed and I was left swimming in meaningless details while the basics were short-changed by an over abundance of specialized algorithms. Perhaps the text's curriculum could be saved by a capable professor, but alas my professor was just as scatter-brained as the text. More pictures would also have been helpful. A replacement text I recommend, which covers the first, matrix theory portion of this book, is David S. Watkins' Fundamentals of Matrix Computations.
Book Description
This is the greatly revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, this new edition remains the most practical, comprehensive handbook of scientific computing available today. Highlights of the new material include: -A new chapter on integral equations and inverse methods -Multigrid and other methods for solving partial differential equations -Improved random number routines - Wavelet transforms -The statistical bootstrap method -A new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic. The book retains the informal easy-to-read style that made the first edition so popular, while introducing some more advanced topics. It is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. The Second Edition is availabe in FORTRAN, the traditional language for numerical calculations and in the increasingly popular C language.
Customer Reviews:
Outstanding reference book on numerical algorithms.......2007-04-24
This is the single best book that I have found for teaching numerical methods in science and engineering to upper division undergraduates and graduate students. Students often comment that this should be the selected text even in the programming course because it provides both an overview of the methods and examples that demonstrate the application. The discussions are excellent and the Fortran 77 programs easy to follow even if one is more familiar with C or C++. You should not purchase the Fortran 90 version of this book without getting this book as well because the Fortran 90 book does not contain the excellent discussion of the methods and procedures. Rather it references this book for discussion and simply provides the F90 versions of the routines.
Proprietary source the Achilles' heel for non-students.......2002-12-03
I first bought this text in 1994 while doing scientific programming for graduate school work. A fellow graduate student had suggested I use an undocumented routine that (I later discovered) came from Numerical Recipes (NR). I was impressed enough with NR's presentation of ideas that I also bought the example book ISBN 0521437210 (which I've hardly cracked since) and a diskette of source code (which cost as much as the book but worth it). I was able to do a lot of basic research quickly with NR code, and I still occasionally use NR's routines.
The authors have certainly done a good job assimilating a lot of material. Since other reviewers have done well to highlight the importance and utility of this landmark book, there is no need to repeat those sentiments here. However, to this title's detriment, the authors consider their book to be a proprietary library of source code more valuable than the explanatory text discussing it (one can in fact download the text on-line though it's hardly worth the hassle). This perception is ironic since the authors confess that "the lineage of many programs in common circulation is often unclear" (p.xviii), and many details of presentation, ideas, and algorithms are clearly "borrowed" from other excellent (some now out-of-print) numerical methods books or journals.
I often wondered why NR routines occasionally adopted bizarre and/or obviously inefficient programming structures - over time I decided that this was probably done to make these algorithms appear as so not to clearly violate other published material. As a student, NR's legal disclaimers regarding derivative works (p.xvi) never bothered me and I was willing to overlook the sometimes unpolished source code insofar as it functioned properly. However, as a professional I now find the lack of fair-use provisions on the uncompiled source way too restrictive to rely on these routines in good conscience (I have to buy another textbook or license for every soft copy or machine upon which the source code resides!). I suspect this policy ultimately hurts NR's textbook sales: it would be nice to able to use and pass along the source code between professional colleagues without restriction because most would certainly buy (if they don't already own) the textbook to understand what the source does (just as I did). Source code used in scientific programming is practically worthless without proper documentation, and there's no better documentation than a full length textbook!
I have since expanded my numerical methods library to other references supporting true public-domain codes. With an expanded basis of comparison, I regret to say that I am becoming less and less impressed with NR's implementations and explanations. I am finding many of NR's algorithms to be inefficient or unnecessarily approximate, and - on rare occasion - buggy. There have been quite a few bugs uncovered over the years, and the NR web site has done a good job of keeping track of them (although I know of at least one bug uncorrected by NR to this day).
This book is excellent for students wanting a good reference for quick and dirty types of analyses or scientific computing. Professional programmers, scientists, engineers, specialists or analysts performing software development for laboratory or scientific research would be well advised to reference this title, but ultimately they will likely need to rely other resources if they require efficient and/or unrestricted (public-domain) source codes for their work.
(P.S. - A reviewer elsewhere noted that the "quality of the binding was terrible" and I've also found this to be the case. My hardcover is literally had to be taped on after a few years of use.)
A Useful Tool for Programmers, Researchers, and Students.......2002-07-05
This book contains hundreds of "canned codes" in the FORTRAN language. The book provides several variations of many popular numerical techniques and provides the most stream line (comp. time) codes available. Most codes allow for optimization to be build in, such as an RK4 (4th Order Runge-Kutta) with variable steps sizes. Great if you don't want to write your own code for a subroutine, or it you just don't know the method well enough to write it yourself. The book also provides some basic explaination of the techniques and codes with is very helpful so that the code is less of a black box, although its not that detailed.
There is also a CD available that has the codes already written and ready to go. I prefer to type it in on my own, or just make my own because it gives a better udnerstanding of what the code is doing. The biggest turn-off for me is that some codes have subroutines upon subroutines which can make things a mess.
All around a useful tool for programmers, researchers, and students.
Indispensible, a classic in the field.......2001-07-10
This volume, and its companions for other programming languages, is an absolute classic. The authors strike the right balance between cookbook solutions and theory, so that most of us get just enough background to choose the right algorithm but not so much to get drowned in theory. This edition is the first devoted only to Fortran, but is the second edition published by the authors. It includes a number of additions and corrections, many of which appeared in Computers in Physics (now the journal Computing in Science and Engineering published jointly by the IEEE and the APS). My only criticism is, where were these books twenty years ago when I needed them? I would recommend these books to anyone involved in the application of numerical methods. They are tremendous time savers.
I never bothered with the discs, as most of the routines are fairly short and not a problem to type in, but I recommend the companion example books to help get the routines running.
Routines an more routines.......2001-07-05
If you ever had to program a complicated numerical algorithm, such as SVD decomposition, Bessel functions, eigensystems or Fourier transform, you will know how useful this book is. All those problems, and many others, are presented, the theory is explained and the full code of a routine, which solves it, is given. This version brings the codes in FORTRAN 77, but there are versions for Pascal, C++ and Basic. If you need any routine, you just have to "cut and paste" it from the book into your program.
Book Description
The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a comprehensive text and reference work on scientific computing. Thoroughly self-contained, it proceeds from mathematical and theoretical considerations to actual, practical computer routines. This new version incorporates completely new C++ versions of the more than 300 Numerical Recipes Second Edition routines widely recognized as the most accessible and practical basis for scientific computing, in addition to including the full mathematical and explanatory contents of Numerical Recipes in C. Key Features:
Includes linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory.
A wealth of tricks and tips for scientific computing in C++
The routines, in ANSI/ISO C++ source code, can be used with almost any existing C++ vector/matrix class library, according to user preference
Includes a simple class library for stand-alone use Other new Numerical Recipes products for your library...
Numerical Recipes Example Book [C++]
Numerical Recipes Code CDROM with Windows, DOS, or Macintosh Single Screen License--v2.10 including C++, Second Edition
Numerical Recipes Code CDROM with LINUX or UNIX Single Screen License v2.10 including C++, Second Edition
Numerical Recipes Code CDROM with Windows, DOS, or Macintosh Single Screen License
Customer Reviews:
Definitive book for scientific computing.......2007-06-29
Forget about the bad comment about this book. Those guys do not understand scientific computing at all.
About C style functions and C++ classes: for speed, C style functions still take the lead. The method provided here considered speed seriously. even in vector wrapping, reference trick is used everywhere to max speed.
If you are professional programmer, you will appreciate the careful design in vector and matrix. I am not saying it is perfect. There are better ways to handle vector and matrix more consistently, like boost lib. but within the limited scope of this book, the care for details is just incredibly good.
And the extra charge for the typed program, it is worth it. So stop complaining please.
Disappointed.......2007-03-12
I returned this book. The licensing is very restrictive. The book comes with an "Immediate License" that allows you to type the routines into your computer and use for personal and noncommercial purposes. Any other use or distribution requires the purchase of an additional license.
Some of the routines (Quicksort, p 336) are not very well coded: a bunch of one letter variable names, loops that only exit on break.
This book contains recipes in C piled together in one class, DON'T BUY.......2007-01-25
Book contains the same numerical procedures as in recipes in C piled up in one class. Using this book is like using C without exploitation of object capacities on C++.
What I would recommend is to get the vector library Blitz++ and Numerical recipes in C; both are available for free on-line. Using Blitz++ you achieve speed of Fortran 90 and easy exposition of C++.
And that's what author of this book should have done, write all the procedures based on blitz++.
This book uses C++ only in its title.
context not included.......2006-11-21
Have only read over the first four chapters but so far the book seems to be little more than a print out of minimally commented source code with no context as to how/where/why one would apply the code or even explanations of what the code is doing. All code seen so far relies heavily on the included classes so the 'guts' of the recipe is not transparent with in the chapter. Sample user input and program output are not always listed with code but rather at the end of the chapter.
Still may prove to be good reference.
C++ Recipes.......2006-11-03
It is very helpful in scientific computing. I recommend it for an experienced programmer. If you are a fledgling, get another book to complement it.
Book Description
Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.
Customer Reviews:
Best numerical analysis textbook.......2007-08-01
In my opinion, this is the best numerical analysis textbook.
Rather than trying to teach and explain everything to the student in detail, it complements the instructor. The idea is that the students learn in class, and use the text book as a reference, and for homeworks. This is a great idea. Unfortunately pretty much all Calculus books try to teach Calculus, but for a regular student, math is very hard to learn from a text-book... A nice instructor, and a clean presentation is a must. I teach the material I see important, the way it makes sense to me. What I need is a book that complements me, not replaces me.
NOT Recommended.......2006-04-07
I was a teaching assistant for an introductory numerical mathematics course which used this text. It's a satisfactory text (nothing special) if you already have a basis in numerical analysis, however students which have no foundation struggle severely.
The problem stems from the fact that the authors, Kincaid and Cheney, first wrote a graduate level numerical analysis text and then they created this text based on the content from the first book. Needless to say, this "introductory" text makes several [invalid] assumptions about the introductory student's abilities.
It's frustrating to see students struggle because numerical analysis is really not that difficult -- but they have to be taught the procedures clearly. This text does not have enough example problems and the ones they included do not describe the steps thoroughly or the logic behind performing them. The text does include a large quantity of homework problems, but the selected answers in the back of the book provide only answers and no explanation of how the answer was arrived at.
Anyways, if you're still going to buy this book its probably becausre you're a student. Hang in there. It's really not that hard but seek help from other textbooks if needed.
Numerical Mathematics and Computing.......2005-09-17
After two weeks They didn't have a stock of quality so they gave me a discount for any other book and a full refund
Incomplete explanations, lack of examples.... .......2005-02-12
The true test of a textbook's value is whether it can be used to learn the material without the benefit of a thorough and clear lecturer. Considering a textbook's value when supplemented with a good professor isn't proper, because the professor can fill in the book's gaps, making it harder to tell whether the book is good or not.
"Numerical Mathematics and Computing" fails miserably at this test of value. The explanations are very short and feel incomplete, leaving students unsure of how to find the correct answers. The examples which are given to clarify the material are few and far between, and good examples are practically non-exsistant. In general, they skip right over the finer details of how to work through problems, and assume the reader understands what's going on. This might work if the student had already been introduced to the material, or if they had a good professor to fill in the gaps, but that shouldn't be assumed. It certainly seems like it was when this book was written.
I would absolutely discourage anyone from getting this book!
From a student's view......Garbage.......2002-05-05
I had to use this book for an undergraduate Numerical Analysis class. I'm a Computer Science major with a math minor and this is my last semester. I found this book to be horrible when coupled with an instructor that is equally as horrible. The explainations are too short and lack examples, the problems in each chapter are hard to solve based on the chapter's explaination; they seem to deviate far beyond what was explained in the corresponding chapter. There are some formulas and theorem's mentioned that have no examples to show how they work.
The book is not totally at fault in my case. I also have a horrible instructor and have to rely soley on this book to learn the material. This book just makes it very, very hard to teach myself. My only praise of the book is it's pseudocode for implementing the methods explained. They can easily be used to program them in C++ or other languages.
Overall the book is very confusing but it is still far better than my instructor who doesn't explain anything or answer questions.
Book Description
Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.
This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.
* An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment
* Contains an introduction to numerical methods for both ordinary and partial differential equations
* Concentrates on ordinary differential equations, especially boundary-value problems
* Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course
* Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level
Customer Reviews:
Does the job well.......2001-06-30
This book is an excellent introduction to the field of scientific computing and serves well as a textbook, given the many exercises included in it. Although the software packages quoted in the book have been considerably revised since the time of publication of the book, one can still use it effectively as a guide to the construction of algorithms and software for scientific applications. The level of the book makes it suitable for a course in numerical analysis at the advanced undergraduate level. After a brief review of the concepts and strategies employed in mathematical modeling in chapter 1, the author begins in chapter 2 with the study of initial value problems for ordinary differential equations. He motivates the discussion with the predator-prey problem from mathematical biology and the ballistic trajectory problem with air resistance from physics. The initial-value problem for the general case of systems of ordinary differential equations is then solved using finite difference methods. The author treats thoroughly Euler's method along with its discretization error. Recognizing that first-order methods have very slow rates of convergence, Runge-Kutta methods are discussed next to alleviate this problem. The Heun method, fourth-order method, and more general one-step methods are discussed in detail. The sample initial value problems are then treated using some of these techniques. The technique of polynomial interpolation, so popular as a solution technique in high-level symbolic programming languages such as Mathematica, is discussed in this chapter also. Multistep methods, such as the Adams-Bashforth, Adams-Moulton, and predictor-corrector methods are treated also. The author also discusses the important concept of stability in this chapter. Although he does not give a rigorous definition of stability, due to the mathematical formalism needed for such a definition, he does give several examples of differential equations that are not stable, and also examples of instabilities in the actual numerical methods employed.
Boundary value problems for ordinary differential equations are treated in the next chapter. The author motivates the problem via a two-point boundary value problem, but only concentrates on linear boundary value problems in this chapter, with the nonlinear case treated in chapter 5. The author carefully distinguishes between Dirichlet and Neumann boundary conditions. The solution of the discretized problem is solved appropriately with Gaussian elimination, and the author gives a numerical example. The case of periodic boundary conditions is also treated, and the author chooses to solve the resulting linear system using the Sherman-Morrison technique, instead of Gaussian elimination, arguing (correctly) that this method only needs code for solving tridiagonal matrices.
The study of the solution of linear systems of equations is taken up in more detail in the next chapter, with emphasis on solution techniques for banded or full matrices. The class of least square problems is treated first, with least square polynomials and their calculation using orthogonal polynomials. The author then treats Gaussian elimination in more detail in this chapter, with treatments of LU factorization and banded matrices being treated. The author gives the reader more details on the performance issues involved in the different solution techniques. Ill-conditioning and error analysis are first discussed here in the context of solution of systems of linear equations, along with definitions and calculations of condition numbers. The author also gives good overviews of alternative factorization techniques, such as Cholesky and QR factorization.
The most important application of numerical methods is in the class of nonlinear problems, since these usually do not have analytical solutions. Even if analytical solutions are found in terms of special functions, the calculation of these special functions typically must be done using techniques from numerical analysis. Nonlinear problems are discussed in chapter 5 of this book, wherein the author again uses the projectile problem to introduce shooting methods. This is followed by a very detailed discussion of the solution of a nonlinear equation using bisection, secant, and Newton's methods. Systems of nonlinear equations are then discussed, with the infamous Picard iteration technique leading the discussion, followed again by a treatment using Newton's method.
Then in the next chapter, the author switches gears somewhat by moving away from techniques based on finite differences and discussing ones such as finite element, Galerkin's and Rayleigh-Ritz methods. The mathematical considerations employed in this chapter are a little more involved than the other chapters, but the author explains the ideas well, and the assigned exercises shed more light on the issues involved. Spine approximations are also discussed, along with the numerical evaluation of the integrals that naturally arise in Galerkin methods.
Eigenvalue problems, so ubiquitous in all areas of science and engineering, are the subject of the next chapter. Interestingly, the author discusses Gerschgorin's theorem, which usually does not appear in a book at this level. Most of the popular techniques for solving eigenvalue problems, such as QR and iterative methods, are discussed thoroughly.
The author gives the reader a taste of the numerical solution of partial differential equations starting in the next chapter, where the heat equation, wave equation, and Poisson's equation lead off the discussion. Separation of variables is discussed briefly as a technique of solution, but the author places emphasis first on finite difference methods for solving these equations. The stability and error analysis of these methods are first studied for the heat and wave equations, and this is followed by a discussion of implicit methods, with a brief treatment given of the Crank-Nicolson method. After a discussion of semi-discrete methods, the author then moves on in last chapter to problems in dimensions two and three. The sparse matrices arising from the discretization of the problems are shown for the Poisson and heat equations. The ADI method, along with Gaussian elimination, Jacobi's, Gauss-Seidel, SOR, and conjugate gradient methods are all given fine treatments.
Book Description
Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures.
Topics covered include:
- Two- and three-dimensional integral equation/method-of-moments formulations
- Open-region finite-element formulations based on the scalar and vector Helmholtz equations
- Finite difference time-domain methods
- Direct and iterative algorithms for the solutions of linear systems
- Error analysis and the convergence behavior of numerical results
- Radiation boundary conditions
- Acceleration methods for periodic Green's functions
- Vector finite elements
Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries.
Customer Reviews:
A great book for those with an existing background in EM.......2003-10-24
I used this book during my MSEE research and found it to be invaluable. While I also had the benefit of the principal author being my Advisor, this book easily stands by itself. This book describes several different methods and concepts in the computational analysis of EM problems, including issues related to computer optimization. It's somewhat dense in that the authors assume you already have a thorough knowledge of EM, so I wouldn't recommend it for beginners. If you work in the field, however, this book is a must-have.
Computational Methods for Electromagnetics.......2003-04-29
This is a specialist book - indispensable for those involved in computational electromagnetics. It gives a lucid and indepth treatment of a wide variety of computational EM problems and associated theory. It is packed full of appropriately placed references which are at the coalface of research in this area. A great book! Well done!
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