Customer Reviews (2)

Old, but very, very nice.
This is old but good.It has a similar concept to "Numerical Recipes" by Press, et. al. but covers less ground, and at a more elementary level.Contrary to another reviewer, it does give plenty of examples at an elementary level, which I find quite helpful.That is an advantage sometimes if you don't need to wade through all the heavy artillery in "Numerical Recipes".Algorithms are given as pseudocode, and Fortran code which are easily transcribed into any language, such as VBA.I have owned this since 1980 and this is one of the more heavily worn references on my bookshelf.If you just need to quickly understand and code an algorithm, this is a great book to have handy.I see that used copies are cheap, and available.I recommend grabbing a copy.If the authors are still around to read this review - thanks for a really nice book!

It is a good book but does needs for examples
The book should have more examples per topic, one example is not enoughfor a difficult subject like Numerical Analysis.The book does not providethe answers for the exercises and students do not have a way to check ifthey are doing the exercises correctly. ... Read more

Product Description

Compared to the traditional modeling of computational fluid dynamics, direct numerical simulation (DNS) and large-eddy simulation (LES) provide a very detailed solution of the flow field by offering enhanced capability in predicting the unsteady features of the flow field. In many cases, DNS can obtain results that are impossible using any other means while LES can be employed as an advanced tool for practical applications. Focusing on the numerical needs arising from the applications of DNS and LES, Numerical Techniques for Direct and Large-Eddy Simulations covers basic techniques for DNS and LES that can be applied to practical problems of flow, turbulence, and combustion.

After introducing Navier–Stokes equations and the methodologies of DNS and LES, the book discusses boundary conditions for DNS and LES, along with time integration methods. It then describes the numerical techniques used in the DNS of incompressible and compressible flows. The book also presents LES techniques for simulating incompressible and compressible flows. The final chapter explores current challenges in DNS and LES.

Helping readers understand the vast amount of literature in the field, this book explains how to apply relevant numerical techniques for practical computational fluid dynamics simulations and implement these methods in fluid dynamics computer programs.

Product Description
Hardbound. ... Read more

Product Description

Product Description

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Customer Reviews (1)

Another Maths Book
Again a typical maths book. I am still learning how to apply numerical methods to real life problems, so I have not found this book to be very useful. I am sure that when I have a good grasp of how to apply numerical methods and solve real problems, then this book will be the one to refer back too. ... Read more

Product Description
Hardbound. ... Read more

Product Description
Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. ... Read more

Customer Reviews (12)

It is not worth the high prize
I bought this book at the beginning of this semester since it is required for one of my graduate course.

Before commenting this book, I have to appreciate the efforts of three authors to implement so many C++ codes in this book. Of course it is worthy of its name of "Numerical Recipes" and a good reference for numerical methods and analysis.

However, I cannot find any other values for purchasing this book. Actually I think the better way to use this book is to refer to it in the library. In each chapter, it provides a C++ algorithm for every point. But you have to be very careful if you want to copy them since there may be mistakes among them. Besides, the authors hold the licenses for the codes so that they cannot be copied at will. Moreover, I do not think it is a good way to implement these algothrims through C++. Matlab is much more powerful and sometimes just one order can calculate the final results. So there is no need to program in hundreds of lines and then check them time by time. It is just a waste of time!

Therefore, I do not recommend this book except that you have to solve some problems by C++.

Copyright Idiocy!
People, stop buying and using this book!The copyright is prohibitive.It is not that they are greedy and want to make money from it.They won't sell you the rights to use any of these algorithms in commercial products, period.They are just stupid.

And don't give your code to a friend or coworker.You just violated the copyright.

Several coworkers have given me simulations with NR code buried in it.I can't use them.It is ILLEGAL!

Stop!Stop!Stop!

Use the GNU Scientific Library.It is free.And legal!And there is a free book on it.Use anything but NR.

A licensing disaster
As other reviewers have mentioned, this is basically an annotated code repository of solutions to specific algorithmic problems, and the algorithms are good.However, if you want to *use* these solutions in your products, forget it.You'll need to pay (thousands of dollars per year, potentially) for the privilege of an institutional license, and even then you can't incorporate any of the algorithms into a commercial software product.The code is therefore useless.Worse than useless, actually, because if a company owns the book and then uses an algorithm contained in it - even if derived from a different source - it runs the risk of getting sued for licensing violations because they've seen the book.No thanks.

[...]

If the authors went with some kind of traditional open-source license instead, that would be terrific.Right now, it looks like financial greed has gotten in the way of the dissemination of good ideas.

A landmark book for computer engineering
A real book on the practical aspects of implementating a wide range of numerical solution.

just keeps getting better
My copy of Edition 2 in C of Numerical Recipes is literally falling apart I have used it so much.There is much new in the 3rd Edition - I have already used the barycentric rational interpolation and Levin series accelerator in my work and am now investigating Kriging or Gaussian Processes - all of these are new, plus much much more.The upgrade to double precision in such routines as the gamma and incomplete gamma functions is very welcome and necessary in my work.The authors' C++ is refreshing - the language is not mis-used.Some of the material I use in Edition 2 has been excised (eg the actual routine for modified Bessel functions of fractional order which I need to implement some probability distributions) to make room for new material, but still available in the very useful WebNotes. I found a bug in one routine but there is an active user community finding them for us already, and was surprised to get a very prompt reply from one of the authors (Saul) when I reported it.The publishers do themselves a disservice by requiring booksellers in the U.S. to purchase a number of these books making it prohibitively expensive for them to hold stock.I have not found it in any store because of this.The 2nd edition was widely available and visible.Thank God for Amazon!In short, an excellent book.Not just a set of programs useful from the get-go but a deep explanation of the whys and wherefores, well referenced, that allow one to dig deeper and innovate.The new Editions are well worth having - they just keep getting better. ... Read more

Product Description
Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.
The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic. ... Read more

Customer Reviews (13)

horrible
Being a university math major, first time in my life i have ever came across a math text with practically no solutions in the back of the book.Since the text is so complex you never know if your doing things right have to time with no answers to assure yourself.Horrible math book, complete failure.

Dissapointing
The book is a chore to read.Many excersizes reference other parts of the book, requiring you to flip back and forth between sections.The proofs are almost all hand waved.The book has obvious typos as well.The book is more appropriate for a high school course than a college one- if you are a mathematician, you will find this book offensive.Buy if you need it for a class, but as a student who was subjected to this book for an entire semester, I highly recommend against using it.

Oh, and the cover is hideous.

Shipping problems ?
I would not recommend ordering this item unless you can wait a long time for it to be shipped. Ordered it almost two weeks ago, and every time I check on it, the shipping time frame gets moved out. If the book is back ordered and there is a problem, it would be nice if amazon was up front about it. I need this text for class and since I was counting on it from amazon, the bookstore is now sold out. If I had known there was a problem I would have paid more at the bookstore and at least been left in a lurch. I have always had good luck with amazon in the past but I must say I am exceptionally disappointed.

Average Elementary Numerical Analysis Text
Just so you know the source of this review and whether or not you should bother trusting me (hmm..maybe not?):
Ph.D. student in Statistics at Iowa State University.
B.S. Computer Science
B.A. Mathematics

Research areas: numerical analysis, analysis of large data sets, stochastic processes
Former research areas: truth maintenance systems, microarray analysis, parallel computing

Note: Not a plug.I like my job.

First off, the book's title is very appropriate.It requires extensive knowledge of calculus and linear algebra, but it uses a fairly non-rigorous "easy" approach to numerical analysis.It's not advanced enough for use in a graduate level class, even for non-majors, but it is very useful and appropriate for sophomore/junior undergraduates.Even though the approach is somewhat non-rigorous, the book doesn't avoid proofs, and though a more advanced mathematician or computer scientist would see holes, it's a book that surely feels complete to most undergraduate math/cs majors/minors.

The explanations and proofs are definitely not perfect.The proofs leave out steps that they assume readers should find obvious.Academic types like Atkinson who have spent years of research in this fieldoften forget just how difficult these concepts are to undergraduates, so some of these "obvious" steps are not going to be obvious to all readers and should not have been omitted.Mixed in with the proofs are some straightforward explanations, but often they are not in layman's terms and I remember scratching my head at times.So I would give the explanations and proofs a C-/D+.

The author does a better job at the exercises.This is a difficult topic, so you don't want to have to work out problems that are too difficult, but some challenge is required to attain mastery of the subject.I think that this book accomplishes that goal.The problems are rarely overly difficult, and though most would be trivial to professors or professionals, they provide enough challenge to undergraduates who are new to the field.The author also does a good job at choosing problems which are relevant.This is nice since many (most, actually) mathematics books include many problems which look contrived and whose results seem meaningless.Anyways, I give the exercises an A.

The content is decent, but a LOT is left out.Traditionally, a two-semester sequence includes a class on numerical analysis as it relates to differential equations and a class on numerical analysis as it relates to linear algebra.Preceding discussion of either one of these topics is a necessary discussion of general iterative methods and analysis of computational error.This book covers all of those topics but none of them extensively.For a one-semester overview, the content is perfect and includes more than enough material.For a traditional two-semester sequence, this book is a bit skimpy.As stated before, the book is also not appropriate for graduate level classes.So if you haven't learned functional analysis, then don't worry--this book is for you.I give the content a B-/C+.

I was a bit disappointed with the computing examples.The examples were not poorly chosen, but there were not enough of them.Also, I think that they should have used a programming language which is easy to read even if you don't know the language.I give the computing examples a D+.

Even though I said that this book is inappropriate for graduate classes, it might serve as a nice reference for graduate students.I always skim through it as a review before certain classes.Though it can be nice as a refresher, a graduate student would probably be happier with something more rigorous like Peter Linz's "Theoretical Numerical Analysis: An Introduction to Advanced Techniques"(overview - very short) or Kendall Atkinson's (the author who wrote this book) "Theoretical Numerical Analysis: A Functional Analysis Framework".

Final note: To those who complain that it requires extensive knowledge of calculus, was that not a prerequisite at your school?The calculus required to understand this book and work the problems is not at a high school level, but it's nothing that a student who has passed college univariate and multivariate calculus shouldn't be able to handle.

2.5 stars

will need supplimentation
Of course this book assumes (advanced?) knowledge of Calc 1 & 2 as well as linear algebra and preferably Dif. EQ. These are all prerequisites for the course in which the book is used.That being said, it is quite annoying when the book *completely* skips over intermediate steps involving calculus leaving the student scratching his head.I find myself with my nose more in my Calc. books trying to figure out what the steps leading to the answer rather than learning Num. Analysis. Would have been nice if at least some intermediate steps were added to most problems, but hey, this is college and hand holding should not be assumed.

There are 3 main gripes which contribute to the low rating.

1. The Cost.For the price of the book, (considering the way the material is presented (see 2.) there should be a solution manual bundled with it. (see 3.)

2. The explanations of the material is cut and dry and not verbose at all, [which adds 2 stars to an original 0 rating] however,there is usually only one example for a topic, followed by 10-15 excercises associated with that topic.This often leads to pure frustration and having to "google" for supplimentary material to help me through the problems due to the fact that the example is far more elemantary than the excercises.

3. Lack of solutions. Coupled with the lack of GOOD examples is the lack of solutions for the excercises you just struggled to drudge through. Chapters that typically have 10-15 problems, some with sub-problems in them usually have 5 or so solutions in the back. (so if there is say question 1, parts a-h, question 2, question 3 a - k....there would be a solution for question 1 part c, question 3 part g...).

If you take this course and this is the required text, pray that your professor has great lectures and notes(neither of which my prof. has) or be prepared to spend many hours on google looking for other references. ... Read more

Product Description

This book details the necessary numerical methods, the theoretical background and foundations and the techniques involved in creating computer particle models, including linked-cell method, SPME-method, tree codes, amd multipol technique. It illustrates modeling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. The text offers step-by-step explanations of numerical simulation, providing illustrative code examples. With the description of the algorithms and the presentation of the results of various simulations from fields such as material science, nanotechnology, biochemistry and astrophysics, the reader of this book will learn how to write programs capable of running successful experiments for molecular dynamics.

Product Description
Garcia, Alejandro, Numerical Methods for Physics, Second Edition This book covers a broad spectrum of the mostimportant, basic numerical and analytical techniques used in physics —including ordinary and partial differential equations, linearalgebra, Fourier transforms, integration and probability.Now language-independent. Features attractive new 3-D graphics. Offers new and significantly revised exercises. Replaces FORTRAN listings with C++, with updated versions of the FORTRAN programs now available on-line. Devotes a third of the book to partial differential equations—e.g.,Maxwell's equations, the diffusion equation, the wave equation, etc. This numerical analysis book is designed for the programmer with a physics background. ... Read more

Customer Reviews (6)

An excellent introductory text
I cannot recommend this book highly enough for physics or engineering students undertaking a first course in numerical methods.The presentation is clear, comprehensive and illustrated with copious examples.The material covered includes most of that a theoretical/computational physicist should be familiar with.The mathematics required is not particularly taxing.If you've got a good understanding of ODEs and a basic understanding of PDEs, then this book should be accessible.

However, it should be noted who this book is NOT for.This book is not for those seeking a deeper understanding of numerical methods.For that, you're much better off reaching for a mathematics text (such as Shampine/Gordon).This book is also not for practicing scientists or engineers who require more advanced or computationally efficient methods.This book is meant as an introduction, and the author sticks to that rigorously.That said, after mastering the material in this book, there should be nothing preventing you from moving on to more advanced methods and difficult problems.

If you are looking for an introductory text though, you'd be hard pressed to top this one.

Good for novices
This book is an outstanding introduction to practical numerical methods for (budding) physicists who have no experience with these vital tools. The author states the book is aimed at undergraduate seniors or first-year graduates. This seems pessimistic to me: I think any competent undergraduate who has taken a course in ordinary differential equations could hack it.

The book ignores the usual approach taken by numerical analysis texts, which is to build up from the fundamental ideas (e.g., finite precision arithmetic, error propagation, fixed point iteration, finite difference approximation to the derivative), instead jumping almost immediately into a projectile motion ODE problem. This allows the author to move on quickly to adaptive Runge-Kutta in Chapter 3, Fast Fourier Transforms in Chapter 5, PDEs in Chapter 6 and finish with a discussion of Monte Carlo methods; whereas more traditional books will only begin to cover PDEs near the end and usually do not discuss FFTs or Monte Carlo.

Of course, this comes at a price. I took a senior level course taught in the traditional manner described above, and happened to pick up a copy of this book in the middle of the semester. This book has far more physical insight than my assigned text, and leaves the student able to appoach a far greater set of practical problems, but I think those who are serious about computational work should cover the basics more thoroughly. One outstanding feature of the book is the end of chapter projects that unify and apply what has been learned, and offer a chance for better students to stretch their muscles.

On the other side, what the author says in the preface bears repeating here: the methods in described in this book are (almost all) foundational, and nowhere near the state of the art. This is particularly true of the relaxational methods for PDEs described in Chapter 8. Nor do I think this would make a very useful reference book: anyone experienced enough to be able to read and understand (say) Numerical Recipes will not learn much from this book. Also, for a modestly-sized paperback with only black-and-white printing, it is amazingly expensive.

Well done.
Excellent introduction to numerical methods in physics. As an undergraduate with little prior programming experience, I had no real trouble with this book. But it isn't exactly a walk in the park, either. Genuinely challenging and interesting problems, many of them theoretical in nature (try the problem on Numerov's method!). Extensive references. ...

A very useful book with alot of useful code
I have attended Professor Garcia's first year grad class in computational physics and it was very good. Professor Garcia is a very clear lecturer and I think this comes through in his book. The book breaks down the problem of numerical methods to very simple bite size chunks and provides a very interesting way to learn numerical methods by immediately applying it to interesting real world problems. this book allows you to feel like you are learning and applying numerical methods almost

immediately. There are entire programs listed in the book and in an accompanying disk which can be used in the solution of the problems. One simply edits and adds to these programs to solve most of the problems. Afterwards you have a good collection ofgeneric code which can be put together to solve other problems.The book includes the code in C++ and Matlab. (older edition had fortran and matlab) Professor Garcia is a person who works in the area of computational fluid dynamics and statistical mechanics, both very computational areas, hence he is well qualified to write this text. There are a good number of problems and answers to a number of these, so the book is also useful forself study. Try it you'll like it.

Book Great for Students, Working Engineers and the Layman!
I got this book because I wanted a more modern reading on numerical techniques. This book delivers this and more. Not only does it include psuedo code, but it also includes actual USEFUL code in matlab and in C++.The examples are all useful for doing either problems for the workplace, or as a textbook/supplement for a course on numerical analysis.The book also gives good physical and 'numerical' insight to the code and technique involved.

If I had one numerical book to take with me, this would be it.I'm sure I would develop other techniques based on what I learned from this book. ... Read more

Product Description

Product Description
Java Number Cruncher: The Java Programmer's Guide to Numerical Computing, by topic expert Ronald Mak, provides practical information for Java programmers who write mathematical programs. Without excessive mathematical theory, he animates the algorithms on the computer screen with interactive graphical programs and applets. ... Read more

Customer Reviews (10)

Great coverage of numerical computing in Java
This book is an introduction to numerical computing that is both comprehensive and fun. It is not a textbook on numerical methods or numerical analysis, although it shows many key numerical algorithms all coded up in Java. The book examines these algorithms enough that you get a feel for how they work and why they're useful, without formally proving why they work. There are also demonstrations ofmany of the algorithms with interactive graphical programs. Overall I enjoyed this book a great deal. It is not a beginner's book on Java - you should be a pretty good Java programmer already. Also, you should be at least somewhat mathematically mature for the material past part one. That is, you should have had some Calculus and some Linear Algebra prior to reading the last 3 of the 4 parts of this book. I further describe this book in the context of its table of contents.

Part 1: WHY GOOD COMPUTATIONS GO BAD - Simply copying formulas out of a math or statistics textbook to plug into a program will almost certainly lead to wrong results. The first part of this book covers the pitfalls of basic numerical computation.

Chapter 1 discusses floating-point numbers in general and how they're different from the real numbers of mathematics. Not understanding these differences, such as the occurrence of roundoff errors, and not obeying some basic laws of algebra can lead to computations that go bad.

Chapter 2 looks at the seemingly benign integer types. They don't behave entirely as the whole numbers of mathematics do. Arithmetic operations such as addition, subtraction, and multiplication take place not on a number line, but on a clock face.

Chapter 3 examines how Java implements its floating-point types. The chapter examines the IEEE 754 floating-point standard and shows how well Java meets its provisions.

Part 2: ITERATIVE COMPUTATIONS - Computers are certainly good at looping, and many computations are iterative. But loops are where errors can build up and overwhelm the chance for any meaningful results.

Chapter 4 shows that even seemingly innocuous operations, such as summing a list of numbers, can cause trouble. Examples show how running floating-point sums can gradually lose precision and offer some ways to prevent this from happening.

Chapter 5 is about finding the roots of an algebraic equation, which is another way of saying, "Solve for x." It introduces several iterative algorithms that converge upon solutions: bisection, regula falsi, improved regula falsi, secant, Newton's, and fixed-point. This chapter also discusses how to decide which algorithm is appropriate.

Chapter 6 poses the question, Given a set of points in a plane, can you construct a smooth curve that passes through all the points, or how about a straight line that passes the closest to all the points? This chapter presents algorithms for polynomial interpolation and linear regression.

Chapter 7 tackles some integration problems from freshman calculus, but it solves them numerically. It introduces two basic algorithms, the trapezoidal algorithm and Simpson's algorithm.

Chapter 8 is about solving differential equations numerically. It covers several popular algorithms, Euler's, predictor-corrector, and Runge-Kutta.

Part 3: A MATRIX PACKAGE - This part of the book incrementally develops a practical matrix package. You can then import the classes of this package into any Java application that uses matrices.

Chapter 9 develops the matrix class for the basic operations of addition, subtraction, and multiplication. It also covers subclasses for vectors and square matrices. The chapter's interactive demo uses graphic transformation matrices to animate a three-dimensional wire-frame cube.

Chapter 10 first reviews the manual procedure you learned in high school to solve systems of linear equations. It then introduces LU decomposition to solve linear systems using matrices. An interactive demo creates polynomial regression functions of any order from 1 through 9, which requires solving a system of "normal" equations.

Chapter 11 uses LU decomposition to compute the inverse of a matrix efficiently and reliably. A demo program tests how well you can invert the dreaded Hilbert matrices, which are notoriously difficult to invert accurately. The chapter also computes determinants and condition numbers of matrices, and it compares different algorithms for solving linear systems.

Part 4: THE JOYS OF COMPUTATION -The final part of this book covers its lighter side of numerical computation.

Chapter 12 covers Java's BigNumber and BigDecimal classes, which support "arbitrary precision" arithmetic--subject to memory constraints, you can have numbers with as many digits as you like. This chapter explores how these classes can be useful. You compute a large prime number with more than 3,000 digits, and you write functions that can compute values such as the square root of two and e^x to an arbitrary number of digits of precision.

Mathematicians over the centuries have created formulas for computing the value of pi. Enigmatic Indian mathematician Ramanujan devised several very ingenious ones in the early 20th century. An iterative algorithm supposedly can compute more than 2 billion decimal digits of pi. Chapter 13 uses the big number functions from Chapter 12 to test some of these formulas and algorithms.

Chapter 14 is about random number generation. A well-known algorithm generates uniformly distributed random values. It examine algorithms that generate random normally distributed and exponentially distributed random values. The chapter concludes with a Monte Carlo algorithm that uses random numbers to compute the value of pi.

Mathematicians have mulled over prime numbers since nearly prehistoric times. Chapter 15 explores primality testing and investigates formulas that generate prime numbers, and it looks for patterns in the distribution of prime numbers.

Chapter 16 introduces fractals, which are beautiful and intricate shapes that are recursively defined. There are various algorithms for generating different types of fractals, such as Julia sets and the Mandelbrot set. In fact, Newton's algorithm for finding roots, when applied to the complex plane, can generate a fractal.

Nice Book
The book doesn't teach you Java. It is assumed that you already know Java.
doesn't cover all of Numerical calculus and not all of mathematical proofs but great if you are looking study practical programming with Java.

I recommend this book only if you know Java and have basic numerical knowledge.

Excellent coverage of many aspects in numerical computing
I have got hold of this book just recently.This is an excellent book on numerical computing using Java that covers many important aspects in numerical computing.I have been writing numerical methods in Java back in graduate school as well as in my professional career for mission critical programs.I must say this book has addressed many issues that must be taken into account such as machine epsilon, choices of numerical methods for different problems, limitations and precautions in using different data types, etc in Java in which if taken for granted, would produce disastrous results.

Ronald Mak has taken the trouble to explain IEEE floating point standards in a fun and easy-to-understand manner.

Another thing about this book that is worthy of a mention is its great OO programming styles.Codes are also well commented and reader friendly.Overall, it is a great source to learn not just on how to program numerical methods in Java but how to write good OO programs.

The only two bad things I could say about this book is that I should have gotten of this book much earlier and if only Amazon allows a Six Stars rating.

if(java!=eCommerce){ ...
As the author says, last time I looked Java still had the +, -, /, *and % mathematical operators.. though most programmers end up forgetting it lost as they are in the boring, vulgar and repetitive coding of boiler-plate "enterprise" (read "sell sell sell") applications. This book does a very good job of introducing a Java programmer to one of the most fun and interesting powers that Java can offer ... that is playing with numbers and exploring the world of mathematics. Forget (at least for a little while) Servlets, JSP, EJB, and database massaging... and givea look to how you can use your JDK to study functions, solve differential equations, integrals, system of equations, discover prime numbers and admire the beauty of fractals. Thetreatment of the various subjects is done is sufficient detail to be clear and sound, but without burderdening the reader
with detail and depth best left for more specialized and hard-core texts that the curious reader can explore after this one. Refreshing.

Educational, interesting, and fun
At one time or another, most of us will likely have to write code performing some amount of numerical computation beyond simple integer arithmetic.As many of us are neither mathematicians nor intimately familiar with the bit gymnastics our machines must perform in order to manipulate numbers, we can get ourselves into trouble if we're not careful.Luckily, "Java Number Cruncher" comes to the rescue.

This book is an introduction to numerical computing using Java providing "non-theoretical explanations of practical numerical algorithms."While this sounds like heady stuff, freshman level calculus should be sufficient to get the most out of this text.

The first three chapters are amazingly useful, and worth the price of admission alone.Mak does a fine job explaining in simple terms the pitfalls of even routine integer and floating-point calculations, and how to mitigate these problems.Along the way the reader learns the details of how Java represents numbers and why good math goes bad.The remainder of the book covers iterative computations, matrix operations, and several "fun" topics, including fractals and random number generation.

The author conveys his excitement for the subject in an easy-to-read, easy-to-understand manner.Examples in Java clearly demonstrate the topics covered.Some may not like that the complete source is in-line with the text, but this is subjective. Overall, I found this book educational, interesting, and quite enjoyable to read. ... Read more

Product Description
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems.In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined.Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation.This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems. ... Read more

Product Description
This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.

. Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics
. Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences
. Contributions uniquely address central problems and provide a survey of the frontier of research ... Read more

Product Description

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations.

From the reviews:

"The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Customer Reviews (2)

A reference book in the domain
Much literature is published on numerical methods for stochastic differential systems but most of it focuses on their use in pricing financial products. There is genuinely a lack of reference books that provide a stronger mathematical basis for the domain. Luckily, this is one of the few books that fill that gap. An excellent book, although the scope of numerical methods presented is limited.

Excellent
This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve the relevant equations of interest. Since it emphasizes the numerical solution of stochastic differential equations, the authors do not give the details behind the theory, but references are given for the interested reader.

As preparation for the study of SDEs, the authors detail some preliminary background on probability, statistics, and stochastic processes in Part 1 of the book. Particularly well-written is the discussion on random number generators and efficient methods for generating random numbers, such as the Box-Muller and Polar Marsaglia methods. Both discrete and continuous Markov processes are discussed, and the authors review the connection between Weiner processes (Brownian motion for the physicist reader) and white noise. The measure-theory foundations of the subject are outlined briefly for the interested reader.

Part 2 begins naturally with an overview of stochastic calculus, with the Ito calculus chosen to show how to generalize ordinary calculus to the stochastic realm. The authors motivate the subject as one in which the functional form of stochastic processes was emphasized, with Ito attempting to find out just when local properties such as the drift and diffusion coefficients can characterize the stochastic process. The Ito formula is shown to be a generalization of the chain rule of ordinary calculus to the case where stochasticity is present. The authors are also careful to distinguish between "random" differential equations and "stochastic" differential equations. The former can be solved by integrating over differentiable sample paths, but in the latter one has to face the nondifferentiability of the sample paths, and hence solutions are more difficult to obtain. The authors give many examples of SDEs that can be solved explicitly, and prove existence and uniqueness theorems for strong solutions of the SDEs. And since ordinary differential equations are usually tackled by Taylor series expansions, it is perhaps not surprising that this technique would be generalized to SDEs, which the authors do in detail in this part. They also outline the differences between the Ito and Stratonovich interpretations of stochastic integrals and SDEs.

Part 3 is definitely of great interest to those who must develop mathematical models using SDEs. The authors carefully outline the reasons where Ito versus the Stratonovich formulations are used, this being largely dependent on the degree of autocorrelation in the processes at hand. The Stratonovich SDE is recommended for cases when the white noise is used as an idealization of a (smooth) real noise process. The authors also show how to approximate Markov chain problems with diffusion processes, which are the solutions of Ito SDEs. Several very interesting examples are given of the applications of stochastic differential equations; the particular ones of direct interest to me were the ones on population dynamics, protein kinetics, and genetics; option pricing, and blood clotting dynamics/cellular energetics.

After a review of discrete time approzimations in ordinary deterministic differential equations, in part 4 the authors show to solve SDEs using this approximation. The familiar Euler approximation is considered, with a simple example having an explicit solution compared with its Euler approximate solution. They also show how to use simulations when an explicit solution is lacking. The importance notions of strong and weak convergence ofthe approximate solutions are discussed in detail. Strong convergence is basically a convergence in norm (absolute value), while weak convergence is taken with respect to a collection of test functions. Both of these types of convergence reduce to the ordinary deterministic sense of convergence when the random elements are removed.

The discussion of convergence in part 4 leads to a very extensive discussion of strongly convergent approximations in part 5, and weakly convergent approximations in part 6. Stochastic Taylor expansions done with respect to the strong convergence criterion are discussed, beginning with the Euler approximation. More complicated strongly convergent stochastic approximation schemes are also considered, such as the Milstein scheme, which reduces to the Euler scheme when the diffusion coefficients only depend on time. The strong Taylor schemes of all orders are treated in detail. Since Taylor approximations make evaluations of the derivatives necessary, which is computational intensive, the authors discuss strong approximation schemes that do not require this, much like the Runge-Kutta methods in the deterministic case , but the authors are careful to point out that the Runge-Kutta analogy is problematic in the stochastic case. Several ofthese "derivative-free" schemes are considered by the authors. The authors also consider implicit strong approximation schemes for stiff SDEs, wherein numerical instabilities are problematic. Interesting applications are given for strong approximations for SDEs, such as the Duffing-Van der Pol oscillator, which is very important system in engineering mechanics and phyics, and has been subjected to an incredible amount of research.

More detailed consideration of weak Taylor approximations is given in part 6. The Euler scheme is examined first in the weak approximation, with the higher-order schemes following. Since weak convergence is more stringent than strong convergence, it should come as no surprise that fewer terms are required to obtain convergence, as compared with strong convergence at the same order. This intuition is indeed verified in the discussion, and the authors treat both explicit and implicit weak approximations, along with extrapolation and predictor-corrector methods. And most importantly, the authors give an introduction to the Girsanov methods for variance reduction of weak approximations to Ito diffusions, along with other techniques for doing the same. Those readers involved in constructive quantum field theory will value the treatment on using weak approximations to calculate functional integrals. The approximation of Lyapunov exponents for stochastic dynamical systems is also treated, along with the approximation of invariant measures. ... Read more

Product Description
Presents a methodology for systematically constructing individual computer programs, emphasizing the finite difference approach for solving differential equations, and with new consideration for the finite element method. Each chapter includes FORTRAN programs for implementing algorithms, with more than 2600 mathematical expressions. Previous edition not cited. ... Read more

Customer Reviews (5)

excellent if this is your first exposure to numerics
I had Dr. Hoffman as the instructor.He is an excellent teacher and writer.Many math books are horrible for self-study and first timers.But this book sets up a standard.A lot of details are given with plenty of detailed examples.I am sure first timers will appreciate his huge effort put into the book.

But keep in mind one feature (not drawback).This book uses heavily finite difference method (400 pages in the 1st edition and 200 pages in the 2nd).This method is good for only 1d problems.Coordinate transformation needed to extend this to 2d or 3d (even just non-uniform 1d) is not easy especially for 3d.I wish there was an equally good book on finite volume method, which is popular for 3d CFD.Anyways, this book is intended for beginners and thus the choice of finite difference method is an appropriate one.

A book for life!
I am so glad that I had the opportunity to take the course offered by Prof. Joe D. Hoffman where he used this textbook at Purdue University. Here agin a fabulous teacher and an expert has written a fabulous book, what more you can expect! It was a phenomenal class where I learned (from my non-engineering background) the basics and advance of numerical methods that I am able to still apply today. The algorithms are fluently explained in very simple language with great examples. I would recommend this book to anyone who is looking to pursue a career in science and engineering.

Perfectnumerical methods book as one can get for a 1st course.
A great textbook for a first course in Numerical Methods as it gives an extensive yet detailed coverage of numerical techniques that form the base for more advanced work in CFD. This book is based almost entirely on the finite difference method for solving differential equations. A chapter addresses finite element techniques but it only a primer; you will need a textbook solely devoted to FEM. This book is written for a mechanical engineer, as most of the governing equations are invariably from the areas of heat transfer, fluid flow, gas dynamics and solid mechanics.

The good points are
1. Each method described comes with a index notated formula that takes the head ache out of programming. Plus there are plenty of FORTRAN subroutines to look at.

2. Not only does Hoffman give you the finite difference equation he also throws in a solved example with one or two iterations worked out in full detail; the benefit of this cannot be overstated.

3. Plenty of practice problems with results at the back of the book.

4. Enough math to give the reader an insight into how the method works. If you care for rigor this is not the book.

The drawbacks are
1. Hoffman has condensed the portions dealing with PDE's from previous editions cutting out some theoretical development. Since most wouldn't have had a course in PDE's (like me) a few more pages might have better squared away a few difficult concepts (eg. characteristic lines of PDE's).

2. Could use another round of proof-reading. This book is littered with typos; which one runs into even in key formulas. This is unacceptable in what is otherwise a pedagogically sound book.

3. I would have liked to see some more elaboration on multidimensional problems in PDE's apart from the 1D unsteady examples which form the workhorse. Hoffman mentions that the explicit methods for 1D unsteady problems work for higher while the implicit schemes introduce numerical complexity which merit advanced methods. These specialized methods for higher dimensional parabolic and hyperbolic PDE's are not developed. As it stands the book is packed with enough material for 3 semesters study.

This book works well for self study. Everything from linear algebra (direct and iterative methods, LU factorization, eigenproblems), non-linear eqns, interpolation, numerical integration and differentiation, ODE's, BVP's, and PDE's is touched upon. Unlike most introductory texts Hoffman doesn't shy away from non-linear problems in differential equations.

I used it for the num. methods course even though the prescribed text was Heath's Scientific Computing which was the worst textbook I ever read (thankfully never purchased it). If you are getting started in CFD then this book provides a solid first step.

An excellent work!
Dr. Hoffman has written a splendid book. For an introduction to numerical methods it is lucid and in-depth simultaneously. Provides fundamentally important knowledge on the whole gamut of numerical solutions techniquesand issues.

it is the best book i have ever come across
the best book for numerical methods which i feel personally. the topics on taylors series was very interesting.

the numerical integration and other topics were really enlightening ... Read more

Product Description

During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field.

Key features and topics:

* Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers.

* An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces.

* Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets.

* Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames.

* Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets.

Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Product Description
This textbook is written primarily for undergraduate mathematicians and also appeals to students working at an advanced level in other disciplines. The text begins with a clear motivation for the study of numerical analysis based on real-world problems. The authors then develop the necessary machinery including iteration, interpolation, boundary-value problems and finite elements. Throughout, the authors keep an eye on the analytical basis for the work and add historical notes on the development of the subject. There are numerous exercises for students. ... Read more

Customer Reviews (4)

Great textbook, great reference
This book was used for a one semester course in numerical analysis.The companion
book was Numerical Linear Algebra.Together, these books make an
outstanding start to a personal numerical analysis reference shelf.

The first half of the book is where pure math students may find trouble since the
presentation of linear algebra in math departments varies widely.A practical working
knowledge of basic linear algebra is necessary.A poor linear algebra background will
require remediation before starting this book.

Topics covered in this text that I have found particularly useful over the years
include polynomial interpolation and quadrature.The presentation is perfect and easy
to understand.

Of course, no text can be everything to everyone.It helps to have an enthusiastic and
knowledgeable professor leading you through the material.That said, the dedicated
student should have no problem navigating this text.

Confusing, Complicated, Poor Textbook
I had to use this textbook for a first course in Numerical Analysis.It might be one of the worst textbooks I have ever used.It contains a lot of material, but I do not feel it is well suited for a first course in Numerical Analysis at an undergraduate university.

The main problem is the textbook assumes too much previous knowledge.I had difficulty understanding even the "simplest" explanations in this textbook because even those were too complicated.I often found myself searching the web and other texts for the concepts that I needed to learn, and I almost always found descriptions that I perfectly understood.Sometimes I could then go back and understand it from this textbook, but only after reading material elsewhere on the subject.

Simply put, this textbook might be a decent resource for someone who already knows Numerical Analysis and has a really strong background in Math (I took the class my final semester as part of a BS in Mathematics degree, and my background was not strong enough).However, for "An intro to Numerical Analysis" as this title states, this is NOT the textbook to use.

Numerical analysis focusing on foundation
This book has emphasis on analysis of numerical methods, including
error bound, consistency, convergence, stability. In most cases, a
numerical method is introduced, followed by analysis and proofs. For
engineering students, who like to know more algorithms and a little
bit of analysis, this book may not be the best choice.

Although this book is mainly about analysis, it does include clear
presentation of many numerical methods, including topics in nonlinear
equations solving, numerical linear algebra, polynomial interpolation
and integration, numerical solution of ODE. In numerical linear
algebra, it includes LU factorization with pivoting, Gerschgorin's
theorem of eigenvalue positions, Calculating eigenvalues by Jacobi
plane rotation, Householder tridiagonalization, Sturm sequence
property for tridiagonal symmetric matrix. Interpolation includes
Lagrange polynomial, Hermite polynomial, Newton-Cotes integration,
Improved Trapezium integration through Romberg method, Oscillation
theorem for minimax approximation, Chebyshev polynomial, least square
polynomial approximation to a known function, Gauss quadrature using
Hermite polynomial, Piecewise linear/cubic splines. Ordinary
ddifferential equations section includes initial value problems with
one-step and multiple steps, boundary value problems using finite
difference and shooting method, Galerkin finite element method.
The book gives basic definitions including norms, matrix condition
numbers, real symmetric positive definite matrix, Rayleigh quotient,
orthogonal polynomials, stiffness, Sobolev space.

One place that is not clear is about QR algorithm for tridiagonal
matrix.

In summary, the book is written clearly. Every numerical method is
presented based on mathematics. There are many proofs (there is one
proof with more than 3 pages), most of them that I decided to read are
pretty easy to follow. There are not much implementation details and
tricks. But this book will tell you when a method will converge and
when a method is better. As a non-math major reader, I wish it could
present more algorithms, such as algorithms for eigenvalues of
nonsymmetric matrix, more details in finite difference method, a
little bit of partial differential equations etc.

A textbook for the theory of numerical analysis
Many people naively believe that with the growing power of symbolic mathematics packages such as Mathematica?, knowledge in numerical analysis is increasingly irrelevant. That is not true, all programmers should have some knowledge of numerical techniques and even power users of a symbolic mathematics package should have some theoretical knowledge in numerical techniques. The packages will perform operations such as polynomial interpolation and at the very least a user should know when to use a specific type.
This book is a solid text in the basics of numerical mathematics, using more of a theoretical background than most. There are a large number of theorem-proof instances, so in that respect, it resembles a math book. The material covered is:

* Solutions of linear equations and systems of linear equations.
* Matrices, eigenvalues and eigenvectors.
* Polynomial interpolation and polynomial approximation.
* Numerical integration.
* Initial value and boundary value problems for ODEs.
* The finite element method.

There are a small number of exercises at the end of each chapter and no solutions are included.
If you are looking for a book to use in a course in numerical analysis where there is an emphasis on the theoretical background, then this one will serve your needs.
... Read more

Product Description
This book is the first of its kind to provide a large collection of bioinformatics problems with accompanying solutions. Notably, the problem set includes all of the problems offered in Biological Sequence Analysis (BSA), by Durbin et al., widely adopted as a required text for bioinformatics courses at leading universities worldwide. Although many of the problems included in BSA as exercises for its readers have been repeatedly used for homework and tests, no detailed solutions for the problems were available. Bioinformatics instructors had therefore frequently expressed a need for fully worked solutions and a larger set of problems for use on courses.This book provides just that: following the same structure as BSA and significantly extending the set of workable problems it will facilitate a better understanding of the contents of the chapters in BSA and will help its readers develop problem solving skills that are vitally important for conducting successful research in the growing field of bioinformatics. All of the material has been class-tested by the authors at Georgia Tech, where the first ever M.Sc. degree program in Bioinformatics was held.MARK BORODOVSKY is the Regents' Professor of Biology and Biomedical Engineering and Director of the Center for Bioinformatics and Computational Biology at Georgia Institute of Technology in Atlanta. He is the founder of the Georgia Tech M.Sc. and Ph.D. degree programs in Bioinformatics. His research interests are in bioinformatics and systems biology. He has taught Bioinformatics courses since 1994.SVETLANA EKISHEVA is a Research Scientist at the School of Biology, Georgia Institute of Technology, Atlanta. Her research interests are in bioinformatics, applied statistics and stochastic processes. Her expertise includes teaching probability theory and statistics at universities in Russia and in the USA. ... Read more

Customer Reviews (1)

A Supplement to Biological Sequence Analysis
Biological Sequence Analysis (BSA) by Durbin et al has become almost the defacto standard textbooy for teaching bioinformatics. And like most texts it presents a series of problems for the student to solve.

Because of the rapid growth of bioinformatics, the schools have attracted a large number of students that have come from a wide variety of educational backgrounds. As a result, the presumptions made by the authors on the mathematical ability of the students studying BSA is at variance from the students now using the book.

This book is intended to provide these students with a 'cram course' in the mathematics they will need to tackle the BSA problems. It starts by providing detailed solutions to the problems presented in BSA, it then extends the set of workable problems to further develop the problem solving skills of the students.

This book might be viewed as a 360 page supplement to BSA. It's mathematics is not trivial, but is necessary for the student to succeed in the bioinformatics field. It is a book that the unprepared student will spend many hours studying. ... Read more