Analysis of Numerical Methods (Dover Books on Mathematics) by Eugene Isaacson (PDF)

Description

In this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods. This text, suitable for advanced undergraduate and graduate-level courses, supplies the required knowledge — not just by listing and describing methods, but by analyzing them carefully and stressing techniques for developing new methods.Based on each author’s more than 40 years of experience in teaching university courses, this book offers lucid, carefully presented coverage of norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, numerical solution of differential equations, and more. No mathematical preparation beyond advanced calculus and elementary linear algebra (or matrix theory) is assumed. Examples and problems are given that extend or amplify the analysis in many cases.

User’s Reviews

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

⭐Isaacson & Keller go into great mathematical detail for the several methods; it fills-in the details which are outside of the scope of the many “Numerical Methods in ” books. The authors include a number of good Physics applications and problems, in addition to theorem/proof stuff one would expect in an applied math text designed for an Upper Division Undergraduate or Graduate Level course.The authors are explicit about the assumed prerequisites of Advanced Calculus (multi-variable) and Linear Algebra. A year of calculus-based Physics would help to provide a conceptual application context. (It’s kind of funny that nearly EVERY PROBLEM boils down to a problem in Linear Algebra!)The table of contents of the many implementation books follow the sequence of this book, such as “Applied Numerical Methods with MATLAB for Engineers and Scientists” by Chapra.The 1993 and 1966 prefaces identify additional topics which are omitted only for the sake of size of the book, but encourages the reader to explore those topics based on this work. The bibliography identifies much of the seminal work published before 1966; the older works tend to be better-written compared to more contemporary ones.

⭐The book is an excellent overview of the fundamental topics of numerical analysis. It does not cover finite element methods, but goes over most other methods that one should know.

⭐great book w/ lots of helpful info. Surprisingly useful for my needs

⭐This was my professor’s chosen text for my undergrad Numerical Analysis course at UC Berkeley (Math 128A). I would not recommend this text to any undergrad or student who has not had numerical analysis before.The author is much too terse (imitating Rudin, but poorly) and incredibly unclear with explanations. Often gives explanations as “exercises to the reader”. (Griffiths does this well, this book does not.) The book also switches notation and indexing haphazardly and without explanation. Simple things like section and equation numbering are woefully neglected and frustrating for the reader.This book was ultimately useless to our class, except as an equation reference, which was also a miserable experience given the careless notation and numbering. Unless you’ve had numerical analysis before, request a different text from your professor.

⭐I got the book as a recommended reference for an advanced CFD class.It presents clearly and rigorously (for what I have read) numerical methods that prove to be useful for higher order accuracy CFD schemes (and probably a lot of other fields).I liked it, and I’ll keep using it at a reference. Last advantage: it is dirt cheap.

⭐It starts with introductory topics and contexts with which many UG Math students can understand, I believe. It is suitable for most mathematics lover.

⭐Numerical Analysis at its best

⭐This is a classic book on the subject (at a great price) that everyone should have as a reference if they do any type of computational work.

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