Product Description
The new Ninth Edition of Burden and Faires provides a foundation in modern numerical-approximation techniques, explaining how, why, and when the techniques can be expected to work. A wealth of examples and exercises develop conceptual understanding, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. ... Read more

Customer Reviews (38)

Book is okay
I am using this book for a grad numerical methods class for a masters program in mechanical engineering. The book does not explain very well some of the steps taken during some of examples shown. But it goes into some heavy duty math proofs and concepts. Yeah I like advanced math like the next guy but I think they should spend more time and paper space on algorithms and code definitions as their algorithms are spotty. And some of the Matlab code that is provided on their website does not work. This is a Numerical Analysis book and if they provide programming code then it should work. I spent too much time trying to debug their code that I gave up and started writing my own. So my advice to other people is to study the algorithms shown in the book, come up with a cleaner/better algorithm and write your own code. Do that and then the book will get you through.

The book with no (helpful) examples
I am also another physics major taking the numerical analysis course. This book, by all standards has to be one of the most AWFUL books I have read. Maybe it is because the math textbooks are written this way. (different from physics textbooks).

The book expects you to understand every concept from the proofs they include. This is almost an impossible task - the proofs have too many formulas without explanation as to where they came from, they also lack a scope and the general direction towards the proof and lacks explanation.

The book has utmost 1 - 2 examples per chapter, and these are also like a typical "math textbook proof". In other words they are difficult to comprehend and are totally useless in regards to the exercises.

The algorithm and notation in the book is just plain WEIRD. I learnt most of those from wikipedia. In fact, I used wiki for almost everything. My advice to fellow students is to use wiki and mathworld - the notation is much better and they have HELPFUL EXAMPLES - something which this book lacks.

Also, the code included in the book is in "modules" of C++. They sometimes include header files, not given in the CD!!! I had to google one such file. The code throws of syntax errors and sometimes gives wrong results. It is not worth debugging for hours - just writing it yourself from scratch (I did this on C), took me about 30 minutes each. If you have the book, Numerical Recipes on C, it might a lot easier. I recommend getting that book as well.

a great book
A great book for numerical computation study. A lot of methods and examples are listed.

Sergey
Very good service, fast shipping, and it is one the best books to start with. Lots of examples and algorithms for programs.

Good
The first book on the topic that is written in an way that you can understand it. I recommend this book to any frustrated student out there! ... Read more

Product Description
If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples--and lack of dreary minutiae--Schaum's Outlines have sold more than 30 million copies worldwide. This guide will show you why! ... Read more

Customer Reviews (6)

The worst of all Schaums guides
there are several problems with using this book as self-study material:
1) it is dated - though published in 1989, and by definition out of date in 2010, the first 11 chapters list many techniques that even in that period are condsidered to be of historical interest in the computer age - interpolation, collocation operators etc
2) there is not a single worked example
3) the solved problems make several leaps of logic - I wouldnt have got anywhere without referencing Wikipedia, Cliffs briefs on differential equations, Schuams advanced calculus etc.
4) sometimes new formulas are actually introduced in worked problems - eg Everet's formula
5) problems are not self contained - referencing other chapters, other problems and sometimes other problems in other chapters.

In short, this book was a struggle, and although it will give you conceptualization of different techniques, it will not give you a modern or holistic perspective on the field.

Predates the computer age but a LOT of fun!
This isn't a good book on how to do numerical analysis on a computer.It's more about the methods that people used to use when they did numerical analysis with pencil and paper.

This book goes into a lot of depth into how interpolation equations are derived,and into the calculus of finite differences.Personally I think that's a beautiful subject and a lot of fun,be it useful or not - that's what math is for math's sake.

I worked all of the problems in this book when I was in high school and I recognized many of the tricks when I took a combinatorics class years later.

A book with an audience
With no previous background in numerical analysis, I bought this book on the recommendation of my boss who loved the first edition.
I had also ordered a whole lot of other books (many from Dover editions). It turns out this is the one I love to pick up from time to time so as to learn a new idea.
It goes straight to the point and gives your mind something to munch on.
I suppose that with time I'll be completing with some of my other books, to look for the rigorous proofs and so on, but for the time being this book is preparing me.

A book with no audience?
Looking for a supplementary text for my Numerical Analysis course, I had my students pick up this text-I have found that other Outlines give a lot of excellent worked examples and provide good summaries- Not this text.If you are a beginning student, go get yourself a real text (I would highly recommend Burden and Faires, or the new text by Tim Sauer).This text offers little to no insight into the algorithms or the analysis, and spends way too much space on one dimensional interpolation problems.If you're simply looking for summaries of algorithms and practical advice on implementation, a much better text is the "Numerical Recipes" books.In summary, I'm not sure who the audience is for this book-There are many, much better, options out there.

Excellent Solutions Book for Fast Answers!
I've had this outline for years. My only complaint about Schaum's is that sometimes their answers are not in enough detail and their indexes are skimpy. Outlines live and die based on their detailed solutions to solved problems and their index. This particular outline is excellent. All the basic numerical methods are presented with the standard format: theory, solved problems, problems with answers. What could be added, either here, or in future text (separate) would be an optimization methods section: differential search, Hooke & Jeeves min./max. search and the Golden Mean search. The later, especially, is easy to program into Excel so it would useful to show the pitfalls in these methods. All in all, this is a text you want in your engineering collection for those problems that require detailed analysis.

If this review was useful, please say so. ... Read more

Product Description

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study.

 Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added.

Review of earlier edition:

"...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references."

R. Glowinski, SIAM Review, 2003

Customer Reviews (1)

About Theoretical Numerical Analysis <br />by Kendall E. Atkinson
The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations.

If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".

The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods. ... Read more

Product Description
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. 150 additional problems in this edition. Bibliography.
... Read more

Customer Reviews (7)

Excellent text of Numerical Analysis
This book by Hildebrand along with its companion Methods of Applied Mathematics are a perfect match for students of Science and Engineering. It is a must for this era where the blind use of mathematical software is prevalent masking the intricacies of the method.
The details of themethod employed in the software should be understood to have any faith in the software output.

Obviously a little dated, but very high quality
The quality of the writing is extremely high in this book. It's obvious that the author was a most attentive teacher. It may not have C++ or Matlab code or a lot of the modern techniques.
As an introduction you can't go wrong with this book which is excellent for self-study, especially at the price.

Excellent book with lots of methods
This is an excellent numerical methods book ,covering many techniques especially the polynomials which are not used much by practising engineers today , but who knows,may find applications in odd places.Prof Hildebrand easily builds up so that one can understand the steps from a first course in Calculus...Glad that Dover has reprinted this classic book.

Excellent !!!!!!!
Certainly one of the best books on Numerical Analysis ever written. Since this subject matter is vast, it has not been covered in its entirety, but what has been covered is simply the best. Moreover, it has been written by one of the best mathematicians. A MUST READ for everyone using numerical analysis.

Outstanding, but with a limitation
Although old, this is still an outstanding introduction to a wide range of topics in numerical analysis. I get impatient with the amount of detail Hildebrand devotes to some topics, but that's because those are topics where I already know the techniques and pitfalls.

However, I have one serious criticism of this book. Hildebrand in very many places drags in the question of inherent errors in input data, but fails to distinguish the different views one must take depending on how one got involved with some topic. In 50+ years of doing numerical analysis and numerical software from time to time, I have come to realize that three quite different issues of inherent error occur.

First, one may be working with scientists or engineers to derive results for a specific problem or set of problems. In this case, one must ask two pertinent questions, and keep asking until one gets clear answers: "How are you getting the input data?" and, "What are you going to do with the results?" Given answers to these two questions, one can do analysis and computation knowing from the start how accurate the input data is likely to be, and how much that matters to the results. Hildebrand pays little attention to the quite complicated problem of how one should do the analysis and programming in those situations.

Second, it may happen that there is no input data from the real world, and hence no inherent error; the input data is conjured up out of whole cloth, as happens in many calculations in "computational physics". In those cases, one wants to produce results that accurately reflect the hypotheses provided by the people with the problem to be solved. Usually, one finds in such cases that the more accurately one can do the computation or analysis, the better one can serve one's users.

Third, and most difficult, is the situation where one is writing a utility routine for use by large numbers of people, most of whom one will never encounter. Everyone who has done much numerical programming faces this issue from time to time. Here the problem is that the users are likely to place absolute faith in the results, even in cases where you, as the implementer of the software or originator of the analysis, may know all too well that the results are unstable with respect to very minor variations in input data. This occurs with monotonous regularity, for example, in routines that manipulate matrices to derive such quantities as eigenvalues and eigenvectors. In my own experience, a high proportion of the actual matrices that users present to "utility packages" are ill-conditioned, and there's a reason for this. If the problem were well-conditioned, it wouldn't be a problem for the scientists or engineers or financial types who need a solution; they would know a priori from experience what the answers are.I have no good answer for how one should think about such "utility software" and neither does Hildebrand. The way I deal with it myself is to ensure that mathematically accurate results are provided even for ill-conditioned problems, and to provide documentation for users that includes the equivalent of: "If you ask this software a stupid question, it will give you a stupid (but correct) answer, so if you are unsure about the stability of your data, please call or visit or email me to discuss your specific problem."

In short, despite the virtues of this book, it doesn't come to grips with the issue of numerical analysis and mathematical computation that I have found causes me more headaches than any other.
... Read more

Product Description
Praise for the First Edition

". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."
—Zentrablatt Math

". . . carefully structured with many detailed worked examples . . ."
—The Mathematical Gazette

". . . an up-to-date and user-friendly account . . ."
—Mathematika

An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics.

A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth.

The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis. ... Read more

Product Description
Outstanding text treats numerical analysis with mathematical rigor, but relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency. Problems—some strictly mathematical, others requiring a computer—appear at the end of each chapter.
... Read more

Customer Reviews (5)

5 Stars for undergrads
If you are looking in to 3d Nurbs buy this book. If you are looking to build a robot from scratch buy this book. It may mean taking calculus and linear algebra but the algorithms are very advanced and quick. This is the math that every corporation would like you to have if you are an engineer. Plus it helps you understand many of the mathematicians. After reading this book you have excellent under pinning for your name.

P.S. This may be good for white hatter as well but I don't know since I am not into cryptography.

P.P.S. Did you always think that Sin() was a magical function? Well you will learn more than you every thought possible with this book. The optimization on you code can go through the roof. Plus this seems to be (but I still have not confirmed) a good way of understanding O notation and not to mention NP complete algorithms (Such what classifies a NP Complete problem).

Archaic First Course in Numerical Analysis
A constant in numerical analysis for years the second edition has not kept pace with the way mathematics is contemporarily taught to engineers and scientists.The book appears to assume an older format of learning mathematics was used by the reader. The reader will soon be seeking additional texts to make this one understandable.

A classic and a bargain at that
I lost my original copy during my last move. Therefore, I was overjoyed that an inexpensive paperback version had been printed. A must for the numerical analyst's library.

good intermediate text on numerical analysis
This is a good intermediate text on numerical analysis. The development of the underlying real variable theory is much more rigorous than the closely related and more recent text "Numerical Recipes in C". Also, there is more attention paid to function theoretic considerations such as notions of continuity and compactness. This is basically an introductory numerical functional analysis textbook. There are numerous good examples sprinkled throughout the text. To get the most out of this book, you need a working knowledge of advanced calculus, real analysis and linear algebra.

Simply the best you can get (at this price)
This is the republication of the 2nd edition published by McGraw-Hill, 1978, with minor corrections. This Dover edition also includes 50 pages of Hints and Answers to Problems, which is very helpful. It is one of the 14 reference books listed in the Numerical Recipe in C: The Art of Scientific Computing, and the authors of the Recipe book says, of the 14 books, "These are the books that we like to have within easy reach." A. Ralston, of SUNY Buffalo, also co-wrote a book, Discrete Algorithmic Mathematics(DAM), which is easy and fun to read. But I am puzzled by the words - "Well-known and highly regarded even by those who have never used it." - on the back cover of the A K Peters edition of DAM. What do they mean? ... Read more

Product Description

Numerical Analysis, designed to be used in a one-year course in engineering, science and mathematics, helps the readers gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods.

Customer Reviews (6)

not a very detailed book
Bought this book for my math class Numerical Methods. Overall it's a good reference book. However, you might need to do some research on certain topics.

Numerical Analysis
this is a great text book. it has matlab codes in the back ofthe book and all of those codes are also on the cd so you don't have to retype them. It also uses a lot of examples

A very clear textbook
This textbook is a shining example of what a textbook should be. It is very organized,connects ideas to show the big picture, breaks down topics into the clear, organized elements, provides examples, and is very clearly worded.

My chosen field of study is unrelated to the class I used this book for, but I love it so much I'm going to keep it. If I ever have any questions along these lines in the future, I'll go to it.

Nice book.
This textbook is one of the better books in Numerical analysis. I had the author as my professor for that class and it was a breeze.

An excellent introductory text
I found this book to be very well written-It emphasizes the central themes of Numerical Analysis, and provides insight along with the analysis.I especially liked the projects and "reality checks" that Sauer provides-For example, in the Differential Equations chapter, he provides Matlab code for animating the solutions to the pendulum, double pendulum, and even goes into the "N-body problem". A small critique:The Matlab code could be written better, and some of it needed to be modified to work properly, but these bugs will probably be worked out in future editions.For educators:This book is designed for a year-long course.That being said, I would still highly recommend it for even a one-semester course, even though you will only use half the text. ... Read more

Product Description
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions. ... Read more

Customer Reviews (6)

poor choice of font; obsolete software references
The material is all mostly valid, and the topics presented are treated in a sophisticated manner. This is not meant as an elementary text in numerical analysis.

One unfortunate distraction, that appears on every page, is the obsolete font. By comparison with fonts in more recently written texts, including those books by the same publisher, the printed text of this book appears smudged. Despite the author's claim in the preface to the second edition, it is not true that "all sections have been rewritten". But maths books are notoriously expensive to retype, because of the intricate equations that appear. I suspect what happened here is that the publisher largely went the easy route of re-using the older camera-ready files.

Another backwardness is the reference in the above mentioned preface, written in 1987, to software packages by IMSL and NAG. These certainly still exist. But by now, packages by Mathematica, Maple and Matlab are more prevalent, at least for undergraduate students. Though for readers experienced in this subject or in programming, they should be able to write code implementing the algorithms.

Atkinson writes the best numerical analysis textbooks
In my opinion, Atkinson is the best writer of numerical analysis textbooks. I learned numerical analysis from him and have used his books every time I have taught the course. The algorithms are written in a combination of pseudocode and Pascal-like language, as in the :=being used for assignment. I disagree with the other reviewers who criticize the text for being unreadable. It is completely understandable, provided you have the mathematical background one would expect of a numerical analysis student. Three semesters of calculus are considered the minimum background needed for a numerical analysis class. If you have taken and understood them, then this reading is not that difficult.
I have used this text as a reference in my earlier work and would still be using it if the third edition had not come out. I will continue to use Atkinson's fine texts in my numerical analysis classes and would not hesitate to use this edition if for some reason I could not obtain the later one.

Knowledge that more people need
Numerical analysis is the study and art of determining how to get high quality answers out of computers with finite precision: in other words, all of them. This may not sound like a big issue - you can always use double precision, right? Well, no. Binary computers can't even represent 0.1 exactly. The numbers are wrong from the start, and go downhill fast. This book addresses the twin questions: how fast, and how to preserve as much accuracy as possible.

Atkinson gives a clear, readable exposition. Chapters cover all the classic topics: error analysis, solutions of nonlinear systems, and issues in vector and matrix manipulations. Matrix analysis skips discussion of sparse systems, though, and omits the different kinds of decompositions available for matrices in special form. He also presents chapters on integration and solution of differential equations, also staples of scientific computing, though maybe not quite as common as the other topics. Some of the best material, though, comes in sections on interpolation and function approximation, something that came up in my own work recently. A typical engineer equates polynomial approximation with truncated Taylor series, but that's a real mistake. Atkinson describes techniques based on sets of orthogonal polynomials. For an approximation of given polynomial degree, my application showed an order of magnitude reduction in error when we stopped using Taylor series. Your milage may vary, but orthogonal polynomials never give worse results. Also note that they don't affect how the approximation polynomial is used - just the way you pick the coefficients.

I fault this book only for minor points. First, discussion early on predates general acceptance of IEEE 754 - with denorms and other weirdness, problems are slightly different than before, but wide availability means that almost everyone has the same problems (early Java implementations notwithstanding). Second, it refers to "stable" problems as "well posed." Many problems, molecular dynamics among them, have inherently chaotic features no matter how they're phrased. The problem is what it is, and calling it "badly posed" suggest that beating it into shape will somehow "pose" it better - directing attention away from dealing with its true nature. Despite a few pickable nits, this is an outstanding introduction for a diligent reader, and should be on the shelves of any programmer involved in scientific computing.

//wiredweird

Excellent Book - not for everyone.
One of the best numerical analysis books I ever came across. This describes the theory behind numerical analysis, so if you expect to find a lot of numerical examples and written algorithms, this is NOT the book you're looking for.
Though there are some examples and algorithm, this is a math book, not a computer science oriented book. So buy this book if you are interested in the mathematical theory and ideas behind numerical analysis. Algorithms come and go, but the theory is always the same.
In my work as a computational physicist I use this book extensively and find it invaluable.
It takes some time to get used to, but little effort in understanding math never killed anyone.

thorough, but thoroughly unreadable
This is a standard textbook by a leading authority. There is little hand-waiving here. However, this is hardly a book to learn by.

The typesetting could have been a bit better. I wish the proofs had been set off from the examples and the text a little more. There is also too much referencing to earlier equations. Rather than referring me over and over to equatin (6.2.1), just re-write the equation.

Also, this book is starting to show its age. It is now 11 years old, so its bibliography is a bit outdated, as are references to computer programs.

My most severe criticism of this book is that it is sorely lacking in explanations. There is little intuition provided here. Definately not an undergrad book. A much better text to learn from--but not as useful as a reference as this book is--is Burden and Faires. B&F make lots of use of pseudo-code and I applaud them for it. It helps detangle some of the math. ... Read more

Product Description

The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis

For all readers interested in applied numerical analysis.

Customer Reviews (12)

One of the very best numerical analysis books
I've owned a copy of this since I was an undergrad back in the late 1970's when it was just in its second edition. I haven't seen a book dedicated to the teaching of numerical analysis that explains algorithms more clearly. The authors go into great detail not just on the how's but the why's - the motivation of doing things a certain way. Strangely enough, though, the numerous mistakes just get worse with age, not better. My old original second edition printed in 1980 has relatively few errors. This seventh edition has errors to the point of distraction. If you must have this for a text you might want to also pick up a copy of the very economical Introduction to Numerical Analysis: Second Edition (Dover Books on Advanced Mathematics) by Hillebrand. It's an oldie but a goodie. If you think Gerald's text is in error look up the topic in Hillebrand and insure you understand the topic. Chances are you do and there is a numerical error in Gerald's text that contradicts your own correct understanding. Finally, any student of numerical analysis simply must have a copy of Numerical Recipes 3rd Edition: The Art of Scientific Computing. That one is more of the "give a man a fish" variety and has the source code and some explanation, but is by no means a textbook.

Oddly enough the table of contents is not included in the product description for this book, so I show that next just so you'll know what you're getting

0. Preliminaries.
Analysis versus Numerical Analysis.
Computers and Numerical Analysis.
An Illustrative Example.
Kinds of Errors in Numerical Procedures.
Interval Arithmetic.
Parallel and Distributed Computing.
Measuring the Efficiency of Procedures.
1. Solving Nonlinear Equations.
Interval Halving (Bisection).
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
Fixed-Point Iteration.
Other Methods.
Nonlinear Systems.
2. Solving Sets of Equations.
Matrices and Vectors.
Elimination Methods.
The Inverse of a Matrix and Matrix Pathology.
Almost Singular Matrices - Condition Numbers.
Interactive Methods.
Parallel Processing.
3. Interpolation and Curve Fitting.
Interpolating Polynomials.
Divided Differences.
Spline Curves.
Bezier Curves and B-Splines.
Interpolating on a Surface.
Least Squares Approximations.
4. Approximation of Functions.
Chebyshev Polynomials and Chebyshev Series.
Rational Function Approximations.
Fourier Series.
5. Numerical Differentiation and Integration.
Differentiation with a Computer.
Numerical Integration - The Trapezoidal Rule.
Simpson's Rules.
An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration.
Gaussian Quadrature.
Multiple Integrals.
Applications of Cubic Splines.
6. Numerical Solution of Ordinary Differential Equations.
The Taylor Series Method.
The Euler Method and Its Modification.
Runge-Kutta Methods.
Multistep Methods.
Higher-Order Equations and Systems.
Stiff Equations.
Boundary-Value Problems.
Characteristic-Value Problems.
7. Optimization.
Finding the Minimum of y = f(x).
Minimizing a Function of Several Variables.
Linear Programming.
Nonlinear Programming.
Other Optimizations.
8. Partial Differential Equations.
Elliptic Equations.
Parabolic Equations.
Hyperbolic Equations.
9. Finite Element Analysis.
Mathematical Background.
Finite Elements for Ordinary Differential Equation.
Finite Elements for Partial Differential Equation.
Appendices.
A. Some Basic Information from Calculus.
B. Software Resources.
Answers to Selected Exercises.

poor print quality (7th ed.)
My copy (7th ed, paperback, ISBN 0321133048, bought from amazon.com) is of poor newspaper-like print quality.

The book typography uses black color and three halftones (titles, ref. numbers, chart curves, captions, example boxes), but the halftones are printed only at 85 LPI. Some figure captions are barely readable - you see only coarse black/white screen.

It really upsets me that such flagrant manufactuing defects spoils the impression of otherwise good book.

The content of the book is exactly what I looked for. You can quickly grasp the essentials about solving the nonlinear and linear sets of equations. The book style is motivating and I was quickly able to reveal some false statements about numerical effectivity of algorithms. Navigation in the book is simple, but I would prefer more detailed contents in the beginning of the each chapter - some sections (e.g. LU decomposition) are neither in general contents nor in chapter's contents.

The part on optimization is too brief. There are better introductory level books on this subject.

Pretty Darn Good
Nowadays with all the circuit and matrix computer aided systems out there, the basics of numerical methods gets overlooked.This book keeps to these fundamentals methods and is an excellent bridge between purely closed-form knowledge taught in schools and the open-form procedures quietly employed in most computer aided engineering systems.

Particularly fond of this text's discussion on boundary-value problems.

It now heads my list for potential texts in my numerical methods course
Last academic year, I taught a course in numerical analysis. It was the first time that I had the opportunity to do so and I enjoyed it very much. I do double duty as a mathematician and a computer science instructor, and this was an opportunity to simultaneously exercise both skills. Since I will probably be teaching it again next academic year, I examined this book as a possible text for the course.
I was impressed with the approach and the level of exposition. In general, two assumptions can be made concerning the background of the students. The first is that they know differential and integral calculus and the second that they have some programming experience. While the authors assume the first, they reduce the level of the second assumption. The programming exercises are in Matlab and require very little programming knowledge. There are also few actual programming examples; most of the complex algorithms are expressed in an advanced pseudocode. I am strongly in favor of this approach; most people will be using a system other than Matlab.
There are many exercises at the end of the chapters and the solutions to many of them are included in an appendix. A set of problems called "Applied problems and projects" is also included at the end of each chapter. These are more complex problems that are on the level of significant programming projects. They also are truly real world problems, dealing with topics such as interest computations, solving solution problems, solving differential equations numerically and the history of mathematics. If you regularly give such problems in your numerical methods class, then you will love these sections.
The breadth of coverage is sufficient so that a two-semester sequence could be taught using this book. The chapter headings are:

*) Preliminaries
*) Solving nonlinear equations
*) Solving sets of equations
*) Interpolation and curve fitting
*) Approximation of functions
*) Numerical differentiation and integration
*) Numerical solution of ordinary differential equations
*) Optimization
*) Partial-differential equations
*) Finite-element analysis

At this time, this book is at the top of my list of possible texts for the next time I teach numerical analysis. Since that is still at least a year away, I cannot say that I will definitely adopt it. However, barring no new and better book appearing, it will be the chosen one.

Numerous errors in text
Have to agree with earlier post, book looks nice and clear but numerous errors make actually using (vs. just browsing) the material very difficult.7th edition ADI section has numerous mislabed equations, incorrect data values, unfortunate.Suggest look elsewhere for a numerical analysis book. ... Read more

Product Description
Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians.In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbssampling.Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference. ... Read more

Customer Reviews (2)

best since Ron Thisted's book
Ron Thisted's book on computing algorithms for statisticians was one of the most useful and clearly written texts on the topic. There have also been a few other good ones. Lange brings to the table a more current book that deals with the key new methods such as resampling, Markov chain Monte Carlo, Fourier series and wavelets,the EM algorithm and extensions of it. He also includes useful but uncommon results for power series, exponentiating matrices and continued fraction expansions.
The usual matrix algebra stuff for linear models is also there. You will also find a chapter on nonlinear equations and a chapter on splines. There are asymptotic expansions in Chapter 4 and Edgeworth expansions in Chapter 17. Almost everything that is important in statistical computing today is included.

This book can be used as for a graduate course in statistical computing and is a valuable reference for any statistical researcher.

Look elsewhere
The author states in the introduction "My focus on principles of
numerical analysis is intended to equip students to craft their own
software and to understand the advantages and disadvantages of different
numerical methods".Lets look at a few topics to see whether these
lofty goals were achieved.

Least-squares calculations:The chapter on linear regression is nine
pages.The largest section is on the sweep operator (the problems with
the sweep are not mentioned).Solving least squares is thru the normal
equations only (which numerical analysts agree is the least stable of
the "big three" methods for solving least squares problems).There is a
page on woodbury's formula for determinants.Who uses that!?So many
problems in statistics eventually boil down to a least-squares
calculation.This book has almost nothing useful to say about this
problem.How can students "craft their own software" after reading this
book?They simply can't. Look elsewhere.

Eigenvalues:The chapter on eigenvalues is eight pages and covers only
Jacobi's and the Rayleigh quotient, nothing on the QR, nothing on
bidiagonalization.The nine pages would have been better used for
soemthing else.
Bootstrap calculations:I decided to check out section 22.5,
"importance sampling".After a so-so 2-page inroduction we get an
example.Example 22.5.1 uses the "Hormone Patch Data" from Efron and
Tibshirani's Bootstrap book (a wonderful book, by the way).First, the
analysis is botched, the numerator and denominator variables were
interchanged (relative to Efron and Tibshirani).Now, the denominator
has postive probability of being zero, which is not a problem in of
itself.Then there is a graph based on 100,000 bootstrap samples.The
book says:"Clearly, importance sampling converges more quickly".
Figure 22.1 shows that it actually didn't converge at all!.Then do we
really need importance sampling for this problem?The whole exact
bootstrap distribution has 8^8=16.7 million points (at most).It took just one
minute to write and run a program that computed the exact tail
probability.Why the hell do I need 100,000 bootstrap samples to
approximate something I can compute exaclty with less work?What can
students actually learn from this?

I can go on and on and on, but I'll stop here.What is good about this
book?It does occasionally explain nicely the math behind certain
methods, but even then it really doesn't integrate ideas well enough for
a student. ... Read more

Product Description
Uses introductory problems from particular applications that are easy to understand and show the reader that there is a need for a particular mathematical technique. Numerical techniques are explained from basics with an emphasis on why they work. Discusses the contexts and reasons for selection of each problem and solution method. Worked-out examples are very realistic and not contrived. ... Read more

Customer Reviews (5)

Don't expect to learn from this
If you need a reference for various numerical methods then this book may be of use to you, but do not expect to learn anything from it.You will not be taught 'why' these methods work, or 'how' they came about--it simply lists a bunch of formulas with a few meager attempts at derivations here and there.If you want to actually understand this stuff you'll have to go elsewhere.If you just want a reference...I would still go elsewhere.

Good for reference, but don't expect to learn from this book
I used this book in a college level course, and let me tell you it is close to worthless.I gave it two stars because someone might be able to use this for some kind of whimpy reference book.Don't buy this expectingto learn much from it though.The first few chapters are ok, but later onit just glosses over many things you need in order to understand stuff.

Good Reference Book
This book is exactly as the title says.There are a lot of great sources on applied mathematics and it covers a lot of good material ranging from iterative methods to PDE's.Matlab is the software of choice and the bookdoes a good job of making use of Matlab.The detraction to this book isthe lack of rigor.The book operates under the misconceptiong that appliedmath doesn't have to be very analytical.As a reference book it is goodresource, but as a textbook a little bit more analysis needs to be put in. This is a nice fresh idea for what Numerical Analysis should be, but coulduse a bit more beefing up in the analysis side.Hopefully this will comewith later editions.

Fantastic!Stupendous!
Whether you use Matlab or not, if you need information about numerical methods, this is the book for you.It makes the standard, Press, et al, "Numerical Methods In.." look like a first-grade primer bycomparison.

I'm writing my own book on numerical algorithms for embeddedsystems, so I know whereof I speak._GOOD_ books that are both readable byordinary mortals, and usable for serious computing, can be counted on thefingers of one hand. Most are either too pedantic and obtuse, or too simpleand shallow, or directed at a small subtopic of the larger area ofnumerical methods.Somehow, through a combination of simple, no-snowexamples, lots of exercises, and Matlab programs, author Faucett manages toinclude virtually every aspect of numerical methods.Not only that, butshe includes them in depth, in a way that's easy to follow and exercisesthat drive every point home.In my travels, I've seen a lot of referencesto such things as Runge-Kutta and Adams-Moulton methods, solving stiffODE's, solving for eigenvalues and eigenvectors, and Householderand QRtransformations, to name a few.It's rare to find easily intelligibleexplanations, with derivations, for any _ONE_ of them.To find them all inone book is astonishing.

Clearly, by the title, you get the impressionthat having Matlab will make this book more valuable to you, and it will. However, don't get the idea that the book is only for users of Matlab. Whether you have it or not, you will not find another book so loaded withgems of knowledge about numerical methods.

Fantastic!Stupendous!
Whether you use Matlab or not, if you need information about numerical methods, this is the book for you.It makes the standard, Press, et al, "Numerical Methods In.." look like a first-grade primer bycomparison.

I'm writing my own book on numerical algorithms for embeddedsystems, so I know whereof I speak._GOOD_ books that are both readable byordinary mortals, and usable for serious computing, can be counted on thefingers of one hand. Most are either too pedantic and obtuse, or too simpleand shallow, or directed at a small subtopic of the larger area ofnumerical methods.Somehow, through a combination of simple, no-snowexamples, lots of exercises, and Matlab programs, author Faucett manages toinclude virtually every aspect of numerical methods.Not only that, butshe includes them in depth, in a way that's easy to follow and exercisesthat drive every point home.In my travels, I've seen a lot of referencesto such things as Runge-Kutta and Adams-Moulton methods, solving stiffODE's, solving for eigenvalues and eigenvectors, and Householderand QRtransformations, to name a few.It's rare to find easily intelligibleexplanations, with derivations, for any _ONE_ of them.To find them all inone book is astonishing.

Clearly, by the title, you get the impressionthat having Matlab will make this book more valuable to you, and it will. However, don't get the idea that the book is only for users of Matlab. Whether you have it or not, you will not find another book so loaded withgems of knowledge about numerical methods. ... Read more

Product 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. ... Read more

Customer Reviews (9)

Best numerical analysis textbook
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
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
After two weeks They didn't have a stock of quality so they gave mea discount for any other book and a full refund

Incomplete explanations, lack of examples....
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
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. ... Read more

Product Description
Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyze, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods. ... Read more

Customer Reviews (1)

extensive problem sets
Moin offers a first course in numerical analysis. Mostly directed at engineering students who have some computer programming background. Though extensive experience in this is not needed.

Naturally, there is an emphasis on solving differential and integral equations. So old favourites like Runge-Kutta and trapezoidal means make their appearance for the latter, for example. There is also a more advanced treatment of how to tackle partial differential equations.

The problem sets are a good feature of the book. Some may take considerable time to code and debug, but hopefully will help you gain insight into what the author is explaining. ... Read more

Product Description
New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems ... Read more

Customer Reviews (4)

So many typos!
This book is decent as a reference book but it rather dense for someone who is learning the material the first time. (I'm using this book for a graduate course after having seen much of the material as an undergraduate and it's still a little difficult to read.)

It also has an inexcusable amount of typos in it. By the third edition, this really shouldn't be a problem.

Dive into the solid German school of Numerical Analysis
In the course of my graduate studies, I got lots of books in Numerical Mathematics. I read most of them, at least the chapters related to my work in Computer-Aided Design and Simulation of electronic circuits.
I have some ofthe booksin several editions, as happens with this book from Stoer & Bulirsch (I have the 2nd and 3rd eds. of S&B). It isn't an easy read, and I remember having had some "viscous friction" in getting into the notation, a minor annoyment quickly surpassed. But when I had to jump into theorem proofs and fine tuning of algorithms, this book was the preferred. I recommend the chapters on Linear Systems, on solving Nonlinear Equations and on solving Ordinary Differential Equations, which I "used" a lot. This last 3rd edition already has some material about solving Linear Systems of equations with Krylov Space methods, such as GMRES.
As happens with many books, it can be complemented with texts offering a different point of view on Numerical Analysis. I recommend the classics from Hamming Numerical Methods for Scientists and Engineers, from Lanczos Applied Analysis, from Dahlquist and Bjork Numerical Methods, from Atkinson An Introduction to Numerical Analysis, and for electrical engineering CAD the excelent text from Vlach and Singhal Computer Methods for Circuit Analysis and Design (Electrical Engineering), (the old "Circuit Simulation Kama Sutra" from Chua and Lin, ISBN 0131654152, is no longer linkable, but deserves to be remembered here and should be reprinted, e.g by Dover books...). Of course the book from Press et al. Numerical Recipes 3rd Edition: The Art of Scientific Computing has its place, but due to the algorithm descriptions and organization, not to the code.
Compared with these texts, the book from S&B has the solid theory and sound foundation of the methods, as also has the book from Dahlquist which, however, is a bit dated. If you want a Numerical Analysis text that saves you from bad weather, at all times, get S&B from the Numerical Analysis German school which, in recent years gave us excellent texts on the solution of ODES, of DAEs and of PDEs in a broad range of science and engineering domains.

Ok for reference
This text makes a decent reference book, but I find that the introduction of new ideas is not accompanied with sufficient explanation or motivation. I find myself continuously refering back to Burden and Faires, "Numerical Analysis" instead for more clear and concise descriptions of the same concepts. While our professor required the book for the course (because it is on the book list for qualifying exams), he rarely refers to it. I have accumulated about 5 numerical analysis books now, and I would recommend Burden and Faires, "Numerical Analysis" (7th edition) as the best for senior undergradute to 1st-year graduate level, as it has the best combination of theory, explanation, and examples.Stoer presents slightly more theoretical motivation to problems, which I think would be more interesting the second time around, but not as an 'Introduction'.

A classic, but don't expect just recipes, this is maths
A classic. However this book is not a "cookbook" of numericalrecipes, rather it places a strong emphasys in the numerical properties ofalgorithms. Good all-rounder and good sections on linear systems andinterpolation. You'll probably want to complement this book withspecialists on matrix computations, ODE, PDE and optimisation. ... Read more

Product Description
This reader-friendly introduction to the fundamental concepts and techniques of numerical analysis/numerical methods develops concepts and techniques in a clear, concise, easy-to- read manner, followed by fully-worked examples. Application problems drawn from the literature of many different fields prepares readers to use the techniques covered to solve a wide variety of practical problems.Rootfinding. Systems of Equations. Eigenvalues and Eigenvectors. Interpolation and Curve Fitting. Numerical Differentiation and Integration. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. Second-Order One-Dimensional Two-Point Boundary Value Problems. Finite Difference Method for Elliptic Partial Differential Equations. Finite Difference Method for Parabolic Partial Differential Equations. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation.For anyone interested in numerical analysis/methods and their applications in many fields ... Read more

Customer Reviews (2)

Bad Quality (physically)
This textbook is very handy in the field of numerical methods- HOWEVER, do not make the same mistake I did and make sure you order that Hard Cover version of this book because I have had the paper-back for 1 month and numerous pages have already fallen out and no doubt more to come.Pretty disappointing.Even if it's more expensive get the hard-cover.

Good stuffs to begin
Bradie spends time on explaining everything clearly and concisely. I am impressed by the way he starts and the complicated stuffs that he ends with. There are no better stuffs that you can find. I believe that it is the good starting point for anyone who is interested in the numerics. Finer text can be found with Ortega and Wilkinson but this book is the best for beginner.

Enjoy ... Read more

Product Description
For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation— Classical Theory; Fourier Approximation—Modern Therory; Exponential Approximation.
... Read more

Customer Reviews (10)

A beautiful book.
R.W. Hamming instantly became one of my favorite authors after I received this book in the mail. He wasn't afraid to inject his hard-earned experience into a field which even today really is in its infancy. While some of the material is dated in that if you ever are writing serious numerical code, you are very unlikely to implement many of the details in this book yourself, it is a great place to go to understand what your library is doing (or at least provide a general idea).

Hamming wrote this book during a very special period of time for mathematics and computer science. Algorithms and (numerical)mathematics were very much seen as a means to an end, and not an end themselves. Many mathematicians now will provide a numerical analysis of an algorithm, or derive a numerical algorithm only because it's the fashionable thing to do now, and it somehow enbiggens them by portraying a false sense of "application."

There is a sort of purity in this book, everything in it is a solution to what was a serious engineering problem in the implementation of numerics on computers. On top of this, it is written in an absolutely lucid style which I have found to be very characteristic of Hamming.

My favorite chapters are of course chapter 1: "An Essay on Numerical Methods", and chapter 'N+1' "The Art of Computing for Scientists and Engineers" If you bought the book and only read these two chapters, I would say you got your money's worth.

One of the best
Numerical methods for scientists and engineers is a fantastic textbook.I've always been interested in numerical analysis.Numerical analysis to me is the perfect combination: it has both mathematics and programming.A good example of this idea is Numerical Recipes in C, where you have both algorithms and their implementation.That being said, this book delivers where Numerical Recipes misses.It provides insight and understanding and explains the algorithms, not in a cookbook fashion, rather in a linear progressive method.There's not a single piece of code yet the algorithms are clearly expressed.It provides a clear understanding of methods I've used but didn't truly understand.It adds by discussing topics that aren't usually discussed in regular Numerical analysis textbooks, such as universal matrices, Stirling numbers, and Bernoulli numbers, generating functions, Riemann zeta function, Hermite interpolation, Chebyshev approximation, Adams-Bashforth and Milne methods and much, much more.

The book can be read by anyone with graduate level math background: calculus, linear algebra and ordinary differential equations.Previous knowledge of numerical analysis is not required, the first chapters cover the basics extremely well.

An excellent book
This book by Hamming is one of the excellent books which develops the topic with intuitive grasp of basics of functions and approximations...the applications are plenty,but this is not a regular undergrad text in numerical methods...You can go to Chapra & Canale or Ralston's book for an introductory text book,but keep Hamming's book by your side to read the relevant sections for depth of understanding...After all the Dover edition is really cheap and would be a reference work in your shelf.

Good for deep understanding. Not ideal for exams
I am a Grad student and find this book fascinating. As other reviewers pointed out, this book is very good if you wish to have a solid understanding of core issues in numerical methods. The trouble is that students have to do well in exams and for that this book is not the best as it doesnt have many numerical examples. I would not recommend this book for anyone who just has to take one class in Numerical Analysis and do well in exams. But yes if you wish to get a deep understanding of the subject then you must rely on this book and no other.

Shall I
What can you say of a hamming book. Ofcourse its a classic. the style would tell you, why the guy has to be so famous. I love the nonlinear root finding treatment. ... Read more

Product Description
Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for courses in numerical analysis and as a reference for practicing engineers and scientists, this book presents the theoretical concepts of numerical analysis and the practical justification of these methods through computer examples with the latest version of MATLAB. The book addresses a variety of questions ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations, with particular emphasis on the stability, accuracy, efficiency and reliability of numerical algorithms. The CD-ROM which accompanies the book includes source code, a numerical toolbox, executables, and simulations. FEATURES*Presents each numerical method by first providing examples and geometric motivation, then the steps to perform the computation, and finally the mathematical derivation of the process *Provides short programs in MATLAB that can be used for scientific applications with or without modifications *Shows the visual representation of mathematical concepts in 2D graphics and is compatible with the current MATLAB v.7.5. *Accompanied by a CD-ROM featuring source code, executables, figures, and simulations *Includes an introduction to MATLAB commands *Features an Instructor s Resource Disc for use as a textbook BRIEF TABLE OF CONTENTS 1. Number Systems and Errors. 2. Nonlinear Equations. 3. Systems of Linear Equations. 4. Approximating Functions. 5. Numerical Differentiation and Integration. 6. Ordinary Differential Equations. 7. The Eigenvalue problems. Appendix A. Mathematical Preliminaries. B. Introduction to MATLAB. ... Read more

Customer Reviews (1)

An outstanding reference.
College-level courses strong in numerical analysis as well as those catering to engineers and scientists will appreciate this introduction: the first to present the theory of numerical analysis and the practical justifications of methodology using the latest version of MATLAB. This will also make a fine college-level text for primary or supplemental reading: it provides short programs in MATLAB to be used for scientific applications, surveys MATLAB commands and processes, includes a CD-ROM featuring source code and simulations, and reinforces theory with applications. An outstanding reference. ... Read more

Product Description
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems. ... Read more

Customer Reviews (3)

Payback in longrun; not a Cookbook.
In the graduate school, a Math professor used this book, as it talked about a bit of everything. Everything as in initial value problems (IVP) in ODE, 2 point boundary value problems ( BVP ) for ODE, finite difference schemes for boundary value elliptic PDE's and initial-boundary type hypebolic PDE's.

However, the book is written for a mathematician in mind,as the author clearly mentions in the preface. It is not for the light hearted. Book would serve as a
starting point for rigourous foundations in numerical analysis methods for solving
ODE/PDE. Excellent book over all, with numerical examples, watertight arguments,
and crisp prose, without being boring.

Informal, nice text
A very informal style of writing with lots of explanation.He doesn't skip large steps like in the old-fashioned terse style of math texts, which makes it very readable, though some readers may not like it.Not very rigorous, but he's upfront about it.

The original version from 1996 has quite a few errors, and the author maintains information on errata on his website.The most recent reprinting has corrected most of these errors.So, even though there is only a single edition, some versions have errors and some don't.So, BEWARE BUYING USED EDITIONS because they will most likely be from an earlier printing and thus have more errors.I assume the new version on amazon is the corrected version.

Excellent for a graduate course on numerical DE
This is an excellent reference and textbook for someone hoping to go beyond the introduction to numerical DE found in any of the standard numerical analysis textbooks.It is not a research monograph, but is also not easy reading.It has already become a fairly standard reference in the literature because of its complete coverage and further references to more specialized sources.I have used it as the textbook for a graduate courseon numerical differential equations.I highly recommend it for that purpose and as a reference for someone doing independent reading. ... Read more

Product Description
Excellent advanced-undergraduate and graduate text covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation and more. Careful analysis and stress on techniques for developing new methods. Examples and problems. 1966 edition. Bibliography.
... Read more

Customer Reviews (5)

Heavy Water
Very heavy on analysis. Am sure would appeal to the rigorous guys, but I couldnt get much out of it. I switched to another title by Devorich.

A Classic Text
For a modest price you can own a cornerstone in the discipline ofNumerical Analysis. There has been many changes in computing and the study of numericalanalysis, but this reference provides a wonderful foundation to this topic. The work on numerical methods for ordinary differential equations is a true asset to the book, but this big little book contains material on a variety of topics. All the contemporary undergraduate textbooks can trace some part of their structure to this source. This book has surprising breadth in the topics it covers, but still supplies a depth of analysis for many of the numerical methods. This book is a wonderful reference and everyone that has any work to do in Numerical Analysis should have this book on their shelf.

stability,consistence and convergence
consistence,stability and convergence of multistep numerical methods for ordinary differential equations.

Not a cookbook w/code.For folks serious about NA.
This is a mathematics book, not a cookbook.It's worth buying this classic just to read the hidden sentence formed by the first letter of each sentence in their preface.

Maximum Numerical Analysis / $ in print today!
This is the classic work that explainsin detail why numerical methods perform well or poorly. It's the best book I've ever read on Numerical Analysis. Great problems too!From Numerical Linear Algebra to PDE's the basic theory is explained beautifully.If you've ever wondered why iterating the corrector in the predictor-corrector method for solving ODE's doesn't do any good this is the book for you.As an inexpensive Dover paperback this is a real bargain! ... Read more

Product Description

Covering a wide range of techniques, this book describes methods for the solution of partial differential equations which govern wave propagation and are used in modeling atmospheric and oceanic flows. The presentation establishes a concrete link between theory and practice.

Customer Reviews (1)

A great textbook!
In this introductory text space is equally divided into traditional methods (finite difference and spectral) and more modern methods (finite volume and semi-Lagrangian) for solving GFD-related PDEs.The book also contains chapters on filtering of physically insignificant fast waves andon open boundary conditions.Arguably these subjects can be learned bystudying a collection of specialty books, but very seldom one findseven-handed treatment of all major techniques in a single book like this. More important, the breadth in scope does not come at the cost of depth orconciseness in presentation.Rather, the book achieves a delightfulbalance between breadth and depth, as well as between theory and practice. Not only is it an important successer to the long-respected Haltiner andWilliams (1984), but it is much more readable.

I used the book toteach a graduate course on numerical methods at the University of Chicago. I could not cover the entire book in a 10-week quarter, but was able tocover chapters 2,3,4 and 5.The clearly written text was very helpful inorganizing the class material.

The problems sets at the end of eachchapter are also well designed, albeit mostly theoretical.It would behelpful to have separate programming assignments based on these problems,so students can learn how to apply principles into practice. ... Read more