Book Description
Still brief - but with the chapters that you wanted - Steven Chapra’s new second edition is written for engineers and scientists who want to learn numerical problem solving. This text focuses on problem-solving (applications) rather than theory, using MATLAB, and is intended for Numerical Methods users; hence theory is included only to inform key concepts. The new second edition feature new material such as Numerical Differentiation and ODE's: Boundary-Value Problems.
Book Description
The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, the new edition remains the most practical, comprehensive handbook of scientific computing available today.
Customer Reviews:
talk about outdated.......2007-06-27
this book was likely a looker back in the day, but its 2007 now. Need to have better details for non "C"-users. wish i had bought "Idiots Guide to C".
A classic book of numerical algorithms.......2006-12-24
This book, although published 15 years ago, is still very useful. In fact, its more recent counterpart "Numerical Algorithms in C++" is a mess, and I wouldn't recommend it to anyone. The explanations of the algorithms that occur in each section of this book are top-notch. It helps with such questions as "Sure you know how to evaluate an integral with pencil and paper, but how do you do it with a computer?" Everything from linear algebra techniques to integration and evaluation of functions to the FFT and spectral applications are explained clearly and coded up in C. The code is great too, with the exception of one problem that several reviewers have already mentioned - the author has a FORTRAN-like programming style in which each implementation has arrays going from 1 to n versus 0 to n-1. This does cause some implementation problems if you want to transfer the algorithms into another programming language. Overall, though, I can't think of one book that does all of the heavy lifting that this one book does as well as it does in the arena of numerical algorithms.
The book is now available online. Just type "Numerical Recipes" into Google and click on the Numerical Recipes Home Page to peruse the entire book free of charge. You might also find the "Numerical Recipes in C Example Book" useful. That book is simply the source programs that demonstrate all of the Numerical Recipes subroutines. Each example program contains comments and is preceded by a short description of how it functions. I know I found it helpful in many cases.
Very nice book.......2006-08-27
A must buy for students or researchers who need numerical methods. Comprehensive topics. A good place to start to deeper levels. Online book is good for quick look.
A classic, and still worth having.......2006-07-12
"Numerical Recipes" has been a staple in computing libraries for many years, and for good reason. It provides immediately usable implementations of all the workhorses of numerical computation, in production-quality form. Maybe there are better implementations out there, FFTW for example, but getting something to work correctly always comes before getting it to work fast. Numerical computation is a specialty, and vanishingly few of us are specialists. As a result, getting this much specialist knowledge for the price of a very few hours' wage, fully debugged and documented, is a great bargain.
I have to agree with the critics who point out that the Gnu Scientific Library (GSL) is more complete in some areas, and offers better licensing terms. This collection has its own strengths, though, and not just in documentation. The writeup, however, is the major interface between the software and us, the bio-ware. GSL's collection of 'man' (help) pages serves a purpose, but this book's exposition describes a lot more of the background and rationale for the routines. The code and man pages are self-evident statements of the implementation - but "what" is a very different question than "what else" or "why."
This one may not serve all needs. You'd be amazed how many it does serve, though. If you need more than a Matlab session for numerical computing, you need this.
//wiredweird
Great compilation of numerical routines for C programmers.......2004-12-17
I found this book indispensible in my effort to develop profitable trading systems for futures and options and in my research in factor analysis and, more recently, in chronic fatigue syndrome and fibromyalgia. Anyone who programs in C or C++ and works with mathematics must have this book. It covers a surprisingly wide range of algorithms: routines are included for everything from handling Julian dates and solving systems of linear equations to determining eigenvectors and singular value decompositions, solving differential equations, doing numerical integration (quadrature), not to mention calculating fast fourier transforms, lomb periodograms and maximum entropy spectral analyses. While not always state-of-the-art, the routines are quite reliable (when used correctly), clearly-written, and easy to understand and use. I would strongly recommend this book (and the companion software) to anyone who programs in C and is literate in mathematics. I always keep a copy nearby.
Jeffrey Owen Katz, Ph.D.
Author: "The Encyclopedia of Trading Strategies" (McGraw Hill, 2000)
Book 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.
Customer Reviews:
Average Elementary Numerical Analysis Text.......2007-07-10
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 field often 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.......2004-09-16
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.
Maybe i'm just biased..........2002-01-29
I'm biased because i had the good fortune to take Intro to Numeric Analysis from Ken Atkinson himself. I beta-tested this edition of the text, so my copy is in a loose-leaf binder.
Some reviewers have complained that the book is difficult because examples are in FORTRAN rather than C. I disagree. The real meat of the book is written in mathematical form; what source he provides is merely a convenience. When i took his class, most of the students (myself included) implemented in C rather than FORTRAN. No problem, because he was looking for correct results, not reviewing code.
And yes, this book assumes a solid knowledge of calculus, linear algebra, basic differential equations, and discrete logic. Did you think you'd be able to code mathematics without *understanding* it? If you understand the math in the first place, his implementations are very clear. If you don't understand the math, no amount of clarity will save you.
The real beauty, for me, was how he logically built a progression of topics, with each step providing the foundation for the next one. It was like seeing two years of college math in miniature.
it makes numeric sense.......2001-05-09
i had the pain to use this book for my undergrad. coursework for a 200 level class at Cal Poly. Contrary to the other reviewers, i believe the exercises are mediocre, and the material presented lack depth to provide a solid grounding to numerical analysis. Codes are inconveniently written in fortran-97? instead of the more readable pseudo-code. It may provide a good application supplementary for engineering students, but i strongly advise against it for mathematics undergrads. No fun. Lots of handwaving and smoking mirrors.
A strict NO for starters.......2001-04-22
The author presumes that the reader has an advanced knowledge of calculus even though the book is intended for use by undergrads.the content in the chapters of the book are not enough to solve the questions at the end of ech chapter.if you are looking for an introductory course in NA dont even think of using this book.
Average customer rating:
- very nice conceptual overview
- Not for the practitioner
- Trash
- Excellent Introduction, Sparse on Details
- A Good Introductory Survey
|
Scientific Computing
Michael T. Heath
Manufacturer: The McGraw-Hill Companies, Inc.
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ASIN: 0072399104 |
Book Description
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Customer Reviews:
very nice conceptual overview.......2006-07-22
Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.
Not for the practitioner.......2005-11-17
If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.
Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.
He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.
I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.
Trash.......2005-10-14
If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.
Excellent Introduction, Sparse on Details.......2004-11-20
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
A Good Introductory Survey.......2002-11-05
This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.
Book Description
Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.
Customer Reviews:
Matrix Computations is an excellent guide to understanding and implementing Numerical Linear Algebra.......2007-09-30
This book is an excellent book for the student or researcher who needs to understand clearly the issues that arise in the developement of algorithms for the solution and analysis of linear systems. It gives a great explanation of how one operation like solving a linear system or doing just forward or backward solves can be mapped to basic BLAS primitives and how these variations have been implemented in popular libraries such as Lapack or BLAS and the archetectual reasons why one approach may be more optimized than another, row versus column operations, for example.
For the student it provides a nice walk through on the develpment of these algorithms and for the researcher provides a life long resource for reference to the many algorithms that are laid out here.
This book is clear and easy to follow and it is recomended for anyone who is serious about learning how to design and implement efficient linear algebra algorithms for a variety of archetectual and coding language environments.
bible.......2007-09-24
This book is a bible in matrix computation. While they have a lot of details on everything, though, the notations are rather complicated and hard-to-follow.
Gargantuan Copy and Paste Monument.......2007-05-07
Three stars are for:
(1) Relatively cheap price.
(2) Comprehensive but shallow coverage.
(3) Mass availability.
Hypothesis: The only three prematurely worn keys in Golub & Van Loan's keyboards must be: Control, C and V, since these form the shortcut for copy and paste operations.
There is no depth in this book when compared to classic matrix theory books, although I understand that this may distract from the possible use of the book as a reference manual. But as written, it is of little value in addition to Numerical Recipes; the latter has at least decent text this one does not have character, too much copying and pasting eliminated the book to form a skeleton.
What are the basis books for comparison?
1. Wilkinson, Algebraic Eigenvalue Problem. Super but expensive (>$100).
2. Marcus & Minc, A survey of Matrix Theory and Matrix Inequalities. Super but inexpensive (10$).
3. Horn and Johnson, Matrix Analysis, comprehensive, pretty good, and similarly priced to this ($30).
I am not suggesting that the content should mirror these books but the quality and depth should but despite being in its third edition, the book is full of errors both in pseudo-code and text.
The CTRL-C/CTRL-V effort is so insane that authors' could not help themselves to copy Wilkinson's theorem presentation sequence about the symmetric eigenvalue problem, but Wilkinson's commentary from his book (see Hoffman-Wielandt theorem in Golub & VanLoan second edition).
Whenever someone tells me that they learned something from Golub and Van Loan, I can not help myself to question what they thought they might have learned.
In almost all cases, Golub and Van Loan fans appear to know of a result through memorization without any clue about how it is derived and why it is important. So if this is your bible, then probably you do not deserve a job that requires critical thinking.
The books popularity tells something about the state of the academia: for example, the hotshots of signal processing republished Golub and Van Loan a few times to get their IEEE Fellow titles. Google for 'Multistage Wiener Filter', 'Relationship Conjugate Gradient MSWNF', 'Procrustes Rotations ESPRIT'. Definitely a field that does not appreciate critical thinking but fast copy and paste effort through graduate student slavery.
Exactly what I needed.......2007-03-08
I have been using "canned" programs for matrix calculations, but I needed to learn how they actaully work. This book provided exactly the information that I needed. This book is not for beginners--it requires a pretty good knowledge of linear algebra, but if you have that, this book will be most helpful in understanding sophisticated computational methods
The bible of numerical linear algebra.......2007-01-01
This book is the standard reference for all numerical linear algebra. It is a graduate-level applied math textbook written by practicing professionals for practicing professionals. If you are new to the topic you would probably prefer something like James Demmel's Applied Numerical Linear Algebra.
If you are interested in implementing the algorithms in this book, stop right now and first make sure that you can't use MATLAB or LAPACK instead, or even ScaLAPACK if you need a parallel implementation. Getting these algorithms right is hard, and the hard work has probably already been done by somebody else. LAPACK contains the accumulated wisdom of over forty years of research in numerical linear algebra, and MATLAB contains LAPACK. Don't re-invent the wheel.
On the other hand, if you want to understand how LAPACK works, or if you need to understand its numerical accuracy and stability, then this is the book for you.
Another reviewer has mentioned that this book contains numerous errata in the formulas. This is still true as of the third edition. Usually it is possible to detect and correct these errors by reading and understanding the surrounding text, but beware.
Average customer rating:
- Good book
- Poorly written
- It's engineering-oriented, not science-oriented.
- At times, it is a difficult read
- Not for beginners
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Numerical Analysis
Richard L. Burden , and
J. Douglas Faires
Manufacturer: Brooks Cole
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ASIN: 0534382169 |
Book Description
The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.
Customer Reviews:
Good book.......2007-07-18
If you are studying Maths and you just want to buy a book to read before you fall asleep, then don't choose this book. You need a lot of time to read and understand this book. You will enjoy more and more when you understand every lines in this book.
The problems in this book are close to what you have to know in order to pass the course. Numerical Analysis is actually more fun and interesting than other maths courses such as linear algebra, complex variables, probability (with me).
In my opinion, the worst part of this book is the CD. It will not help anyone who do not know how to code. Instead of giving the straight code (simple code that you will be able to keep track in every line), the author made the code become a program and the input is hard to understand. So if you are not familiar with coding, then you will have a hard time figure out how these codes actually work.
Actually, somehow I think the author wants to use Maple as his coding language, but in my class, we use Mathematica, so it's a little bit different in syntax.
However, these codes cover almost all of algorithms mentioned in the book.
Poorly written.......2007-03-09
This book has been, unfortunately, my first introduction to numerical analysis. I wish that I could have chosen a superior book myself, but this is the one prescribed by the university I attend.
The examples in this book are mostly short and insufficient, especially when they are most needed. The lack of good examples wouldn't be so much of a problem, however, if the text itself were better. Unfortunately, many topics are poorly explained. The notation used in this book is often awkward and confusing.
I'm used reading math textbooks and understanding them. Unfortunately, Numerical Analysis by Burden and Faires expects the reader to understand concepts that aren't even fully explained in the text. Avoid if you can.
It's engineering-oriented, not science-oriented........2007-01-25
There are two aspects for this topic. Would you like the deeper reason why a certain way works? Or would you like to have some impressions with a certain method and try to implement it? Not many books can balance these two aspects very well and Burden's book is more toward the latter. This can be observed that almost every method is with a pseudo code and many numerical examples are given (many are even in a step-by-step way).
So if one's background is from science such as math or physics, s/he probably regards this book as a failure. For engineering students, especially undergraduates, this book seems to stay at a good balance since it doesn't get too involved.
The pseudo codes are in general well written and helpful. I think it is the strength of this book. There are few books doing better in this aspect than this book. I have one impressive experience about it. Once a graduate student asked me a question and I told him Burden's book can solve his problem. He succeeded very fast and told me he even didn't know how that method works but just did programing based on the pseudo code. For education aspect, of course we don't encourage this kind of working. But for some situations, we need it.
On the other hand, this book is rather elementary than advanced. And I think it is intended for undergraduates, not graduates. This book was my textbook of numerical analysis when I was a junior. It also served as a textbook when I lectured to undergraduate students during pursuing my phd degree in engineering. I will still use it as the textbook next time whenever possible.
I should give it 4 stars or 4 and a half at most for this book. 5 stars are just out of viewpoint balance.
At times, it is a difficult read.......2006-10-25
I examined this book as part of my constant quest for better textbooks. In this case, the course is a one-semester course in numerical analysis. I have been using "Elementary Numerical Analysis Third Edition" by Atkinson and Han and am generally pleased with the results. The first point to make is that this book has more material than I could ever cover in one semester, so from my perspective it is unsuitable. However, if you have a two semester sequence in numerical analysis, then it has enough material so that it could be used both semesters.
There are twelve chapters:
*) Mathematical preliminaries
*) Solutions of equations in one variable
*) Interpolation and polynomial approximation
*) Numerical differentiation and integration
*) Initial-value problems for ordinary differential equations
*) Direct methods for solving linear systems
*) Iterative techniques in matrix algebra
*) Approximation theory
*) Approximating eigenvalues
*) Numerical solutions of nonlinear systems
*) Boundary-value problems for ordinary differential equations
*) Numerical solutions to partial differential equations
with an exercise set at the end of each section and the solutions to the odd numbered problems included at the end.
The level is more rigorous than Atkinson and Han, more of the results are first expressed in the form of theorems as opposed to the Atkinson approach of using worked examples. Once the theorem is presented, Burden then goes on to demonstrate by example. Burden uses Maple code to present the algorithms, which is generally understandable. Since the code is presented in snippets used to solve a specific problem, a lack of experience in Maple is not a serious hindrance. It is easy to infer the meaning of the Maple commands from the context.
However, it lacks the easy readability of the Atkinson book. There were many occasions when I stopped and had to think about what I had read. It eventually made sense, but I had to think about it before it was clear. I don't have that problem with the Atkinson book. Therefore, even if we made a change to a two semester sequence in numerical analysis, I doubt if I would adopt this book.
Not for beginners.......2006-10-17
Examples are few and offer little explaination.
I find this book so hard to follow.
On a good note: algorithms are clear.
Book Description
This example book contains C++ source programs that exercise and demonstrate all of the subroutines, procedures, and functions in Numerical Recipes in C++. The book will be a valuable aid to readers wishing to incorporate Numerical Recipes procedures and subroutines into larger programs and to conduct simple validation tests. Each example program contains comments and is prefaced by a short description of what it does and of which Numerical Recipes routines it exercises. In cases where the demonstration programs require input data, those data are also supplied. In some cases, sample output is also shown.
Customer Reviews:
C++ Recipes Examples.......2006-11-03
Very good with Numerical Recipes. If you are experienced, it is good, if you are a fledgling, complement it with a beginers book. I recomend it.
short subroutines.......2006-02-26
The C++ source code given here can be useful if you are in a hurry to implement an algorithm given in the main Numerical Recipes book. One might consider that a CD of the source code would be more useful. But the examples are short subroutines. Manually typing in the code from the book should not be a big deal for any of you.
The example data sets used for inputs to some of the subroutines is also useful for unit testing.
Book Description
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Download Description
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Customer Reviews:
an excellent book on hyperbolic equations.......2005-10-18
The author gave almost all the basic knowledge related to hyperbolic equation, at least from the engineering point of view. I read it myself without any help. It's not hard to understand. Moreover, it gives all you need at beginning references.
Good book to start with. Highly recommended........2003-10-24
This book starts from simple things and moves to pretty complicated staff graciously. It is useful even as an introduction to the hyperbolic equations. Finally, this is the only book I use at most every day. This is the book I would strongly recommend to all students who study this field and to researchers. It has a very good and comprehensive reference.
The author develop even the software (unfortunately, this is FORTRAN, not C). The source is available and well discussed in the book (there is a whole chapter). I did not use it but found this is a very good practice. It should be useful for student also.
Many things are really nice. For example, the book gives a very good view of the nature of oscillations in high order schemes, not only formulas. And so on...
However, there are few things I was not satisfied.
1. There are no comprehensive discussion about non-uniform and non-rectangular grids. It is not good, for example, for people who works in spherical coordinates (for example in some brunches of geophysics).
2. There is no information about FCT methods that are still very popular because they give a very straightforward way to use 4th and higher order methods. However, there is a reference to the Oran and Boris book, for instance.
3. It is sometimes really pure mathematical description especially for non-linear equations. It was really inconvenient for me. Fortunately, good reference helped.
There are more things were bothered. However, this is personal. The author works with the advection equation a lot, but does not like to discuss more the conservation form of continuity equation which I would prefer. In spite of author's efforts, I think still that the wave propagation method is not so convenient as flux method even for non-conservative equations. But it depends.
Finally, this book is definitely fine and, I think, it is the best among all books in this field (maybe except the Hirsch book which is "Numerical computation of internal and external flows" 1988). I would highly recommend it to buy.
nice introduction.......2003-07-11
This book provides a nice introduction to the mathematics behind finite-volume methods. After reading through the first half of the book on scalar conservation laws and systems, papers in JCP no longer seem as intimidating. The book is laid out very well, and the notation is consistent throughout. It is the best of the bunch when compared to Toro's Riemann problem book and Laney's Computational Gasdynamics text.
Average customer rating:
- A great book for mathematicians and the best I know for engineers, economists and physicists
- A Classic
- Excellent introductory book on functional analysis
- Good
- Makes you actually WANT to study analysis!
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Introductory Functional Analysis with Applications
Erwin Kreyszig
Manufacturer: Wiley
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Elements of the Theory of Functions and Functional Analysis
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Functional Analysis
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A Course in Functional Analysis
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Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
ASIN: 0471504599 |
Book Description
Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.
Customer Reviews:
A great book for mathematicians and the best I know for engineers, economists and physicists.......2007-01-24
There is no doubt that Professor Kreysig has written one of the best books of functional analysis. The advantages of this book are the absence of advanced pre-requisites (one has only to know basic concepts of calculus and linear algebra), easy of explanation ( the proofs of the book are really clear), the selection of subjects (one may find in this book more specific topics such as the relation between banach algebras and spectral theory and spectral theory of unbounded operators but also applications such as numerical methods which are very useful for engineers) and the structure of the book (divided in sections with many interesting exercises at the end of each section). Finally, I believe that the main advantage of the book is that, if are not a mathematician, it provides you the motivation to learn these some what abstract concepts.
This book may be used as the main reference in the classroom or also for self-study. In fact, this book is particularly suitable for engineers, economists and physicists. In fact, the last chapter of this book presents an introduction to quantum physics.
A Classic.......2006-12-14
This was my textbook for a graduate course in functional analysis, and it is called "classic" by many professors. Don't be fooled by the title of the book: "Introductory" simply means the author assumes you have not seen the subject before, and it is by no means an easy subject. However, the exposition is extremely clear. Kreyszig saved me on numerous occasions as my companion on a treacherous journey through graduate functional analysis.
This book does what few math textbooks do, though all of them should do. Rather than assail you with theorem, proof, theorem, proof, Kreyszig first tells you what he is about to show you, then explains the motivation -- i.e., why we need the following theorem. Then, once outlined, properly motivated, and placed in context, he delivers the theorem and its proof. Furthermore, Kreyszig explicitly spells out what other texts might assume you will "read between the lines", explaining why and how we are able to take each step forward during a proof.
The problems in the book are also good. They are at a level such that you can attempt them and solve them on your own, while at the same time they give you the hands-on experience you need in order to gain a deeper understanding of the principles at hand. They serve as a great confidence-builder before you venture onward and attempt harder problems (for example, in other texts or in research).
As a final treat for physicists, the last chapter takes the mathematics you've learned throughout the book and applies it in an introduction to quantum mechanics. My only gripe with this final chapter (and indeed my only -- minor -- complaint for the entire book) is that most of the interesting results of quantum mechanics arise not from the book's exposition, but as problems for the reader to work out. Of course, if you want to learn quantum mechanics, this isn't the book to begin with but rather a very nice mathematical supplement.
I highly recommend this book to anyone wanting to learn functional analysis.
Excellent introductory book on functional analysis.......2006-06-16
This book is excellent for so many reasons. The book is self-contained; it is much more accessible than a number of other books. The writing is very clear, occasional use of diagrams is very helpful. Proofs are very easy to follow, and the author gives you a sense of the big picture of the subject before you get to the proof, keeping the reader motivated in a subject that can often seem abstract and boring. The typesetting and layout of the book are also unusually well-executed for a mathematics book: definitions are easy to spot, and the material is presented clearly on the page. The book as a whole is exceptionally well-organized, making it easy to skip around, and making this book an outstanding reference.
One of the best aspects of this book are the examples; the text is rich in examples, especially in the beginning. This aspect drops off a little as you progress in the book, which was honestly a little bit disappointing, since if anything I think it should be the other way around.
The exercises are not particularly difficult, but are appropriate to the level of the book--they will be difficult for people with less background in analysis. Some of them are very easy, others are tedious and/or technical but not particularly deep. I did not work exercises in the advanced chapters as much as the easier chapters though so I can't say about them.
I think some of the more critical reviewers are ignoring the title and audience of this book: this is an introductory book, designed to make the subject accessible at a lower level. For that role, it is simply amazing. Any criticism of this book needs to take this into account--it is not an advanced graduate-level text and should not be evaluated as such.
Good.......2006-01-16
This book is especially good for those who are not mathematicians, and just need some knowledge of functional analysis for computation or application of rigorous theory. This book is well organized in the sense that the shortest path is easily identified for what we want to learn out of this book. I would strongly recommend.
Makes you actually WANT to study analysis!.......2005-12-23
Functional analysis is the branch of mathematics concerned with the study of spaces of functions. It has its historical roots in the study of transformations, such as the Fourier transform, and in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Most textbooks claiming to be introductions to this subject are just one proof after another without a clue as to WHY you would want to study this stuff in the first place. Mr. Kreyszig's book is a welcome addition to the family of textbooks that claim to be introductions to the subject because the material is explained in an accessible fashion alongside applications to the material. So YES as one reviewer put it, this book smells like an engineer's text, but to this reader that is a good thing because I get a feel for how to use the information thus motivating me for further study. I particularly liked the sections applying Banach's Fixed Point Theorem to the solution of differential equations and linear equations. As for the suggestions of other reviewers to reject this book in favor of Rudin's, I think that is a bad suggestion for someone other than a graduate student of pure mathematics. Rudin does a great job of explaining all of the theory, but I think that this book is better at providing motivations for the study of functional analysis through the demonstration of applications. Eventually, you should probably read both books.
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Fundamentals of Engineering Numerical Analysis
Parviz Moin
Manufacturer: Cambridge University Press
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A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics)
ASIN: 0521805260 |
Book Description
Engineers need hands-on experience in solving complex engineering problems with computers. This text introduces numerical methods and shows how to develop, analyze, and use them. A thorough and practical book, it is intended for use in a first course in numerical analysis. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods. They will learn what factors affect accuracy, stability, and convergence, and how to evaluate critically the numerical output from a computer. Special features are the numerous examples and exercises that give students first-hand experience.
Customer Reviews:
extensive problem sets.......2005-01-08
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.
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