Numerical Methods for Scientists and Engineers (Dover Books on Mathematics) by Richard Hamming (PDF)

Description

Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming (“the Hamming code,” “the Hamming distance,” and “Hamming window,” etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained.The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system.In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include:I. Fundamentals and AlgorithmsII. Polynomial Approximation- Classical TheoryIll. Fourier Approximation- Modern TheoryIV. Exponential Approximation … and moreHighly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a textbook rather than a reference source. Some critical programming formulations I needed that I bought the book for (Radau integration, for example) were homework problems. I’m at work, I don’t need homework, I need well-documented solutions I can work from. This isn’t a fault of the book, and it would have made an excellent textbook for a course 35 years ago. It’s just not a reference source, so keep that in mind before you buy.

⭐Its easy to understand most of the methods included, the math theory or explanation is quite easy to understand in most cases as oppossed to “Numerical Analysis” by L. Burden which is extremely convoluted. However this last book I mentioned is also more complete which brings me to the only downside I noticed on this book, while some numerical methods are described with such elegance and simplicity, other methods are just mentiond and the author didnt provide examples to such methods, other methods are missing, some methods are not described in depth. There are no solutions to any of the excercises at the end of each method/chapter.That being said, overall I think this is the best numerical methods book Ive found so far. If you want a very complete book which include less common topics get Numerical Analysis by L. Burden, otherwise this book by R.W. Hamming is Just great!!!!!

⭐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.

⭐I have been teaching numerical analysis for a long time now. I bought this book based on the author’s name. I was not surprised to find out that my decision was totally correct. The book provides a clear and deep perception of basic concepts and techniques of numerical analysis that I hardly can find in texts on this subject matter.

⭐The book is fairly pedestrian–there is nothing inside the book you won’t find covered in other numerical analysis textbooks. Furthermore, the book is dated (1962) and the techniques are all ‘classical’. The bulk of the text is devoted to polynomial approximation and Fourier approximation with a solid introduction to general numerical methods, algorithms, error analysis, etc. There are two distinguishing features for the book:1. The paperback edition is quite economical.2. The author is R.W. Hamming–inventor of the Hamming code, the Hamming window, etc.

⭐Hamming writes “The purpose of computation is insight, not numbers”. Laudable sentiments, but does the book succeed? I can tell you it does, from my personal experience.I had read it decades ago as a student, and over the years forgotten the book. A few years ago I gave a course on computation, where I tried hard not to use the usual books except as references for more details when needed. I thought I was developing a course structure which was somewhat away from the beaten track which runs next to the information highway, perhaps a little more useful for students who had a knack for numerical hacking. Then, just recently, while browsing on Amazon, I came across this book again and decided to read it, since I had forgotten what it contained. It stunned me: the course I thought I had developed was just this approach, filtered through my own interests. That is how good this book is. Read and understand this book, and it will shape your point of view for ever.

⭐It only covers some parts of modern numerical methods used in engineering and scientific areas. I personally think It is an out-of-date book. But it is still a good and classic book.

⭐It is a good one and a right choice for me. I also recommend everyone to purchase for this item if you need it.

⭐In case a thorough and clear cut explanation and understanding of the numerical methods needed to all of us, Physicist and Engineers, in order to easily transfer solutions of real life problems using ASM, C, C++ onto silicon, then this book is a must. Without hidding details and without filling pages with usually cryptic or rarelly used methods, this book is exactly what a software/firmware or other engineer or programmer would need in order to fearlessly start coding solutions.John Piliounis, Physicist, Athens, Greece

⭐para todos aquellos que quieren devenir un experto verdadero de la numérica y programadores en el camino al desarrollo de un software-engine general de la numérica. En mi primero vistazo encontró muchos métodos que aparecen de ser devenido material didáctico histórico pero merecen de ser recogido y formulado como algoritmo para comparecencia. Especialmente los capítulos de la aproximación y las secuencias infinitas son a resguardar. Originando a 1973, el libro aún tiene relevancia, al menos como estimulación, a la moderna.Doy mis 4 estrellas por que es un simple reprint sin referencia a una colección-biblioteca moderna de métodos numéricos.

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⭐Should you really buy this book in 2021? I bought it two decades ago, but would refer to other more general or specific works nowadays. Take a look at the GSL (GNU Scientific Library). It provides up-to-date code and documentation. It covers most of the book (and more), albeit not being so textual of course. The style is good, Dover book quality and price is great. Check what you really need.

⭐O livro é muito bom em geral. A sua linguagem é excelente e a sequência da apresentação também é ótima. Não mantém o foco na resolução de problemas e tampouco na proposta dos problemas. Apenas há alguns exercícios para verificação ao final de cada tópico. O livro deve ser utilizado em conjunto com outro livro para uma disciplina de Cálculo Numérico e, para estudos iniciantes – essencialmente ao público brasileiro -, é fundamental ter um conhecimento prévio dos processos numéricos para estudá-lo.

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⭐Definitivamente não é um livro para iniciantes. Bom como leitura complementar. Impressão fraca e texto muito denso, quase uma bula de remédio. Merecia um formato mais largo para facilitar a leitura.

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