[书名]Fundamental Numerical methods and data analysis
[作者]  George W. Collins,
[出版社]  unknown
[出版日期] unknown
[关键词]   Numerical methods \ data analysis
[ISBN]  unknown
[内容简介The basic premise of this book is that it can serve as the basis for a wide range of courses that discuss numerical methods used in science. It is meant to support a series of lectures, not replace them. To reflect this, the subject matter is wide ranging and perhaps too broad for a single course. It is expected that the instructor will neglect some sections and expand on others. For example, the social scientist may choose to emphasize the chapters on interpolation, curve-fitting and statistics, while the physical scientist would stress those chapters dealing with numerical quadrature and the solution of differential and integral equations. Others might choose to spend a large amount of time on the principle of least squares and its ramifications. All these approaches are valid and I hope all will be served by this book. While it is customary to direct a book of this sort at a specific pedagogic audience, I find that task somewhat difficult. Certainly advanced undergraduate science and engineering students will have no difficulty dealing with the concepts and level of this book. However, it is not at all obvious that second year students couldn't cope with the material. Some might suggest that they have not yet had a formal course in differential equations at that point in their career and are therefore not adequately prepared. However, it is far from obvious to me that a student’s first encounter with differential equations should be in a formal mathematics course. Indeed, since most equations they are liable to encounter will require a numerical solution, I feel the case can be made that it is more practical for them to be introduced to the subject from a graphical and numerical point of view. Thus, if the instructor exercises some care in the presentation of material, I see no real barrier to using this text at the second year level in some areas. In any case I hope that the student will at least be exposed to the wide range of the material in the book lest he feel that numerical analysis is limited only to those topics of immediate interest to his particular specialty.
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[分类]  数值分析

Fundamental Numerical Methods and Data Analysis

Author : George W. Collins, II, Astronomy Department, Case Western Reserve University
Publication Date : April 23, 2003

Contents: Introduction and Fundamental Concepts; The Numerical Methods for Linear Equations and Matrices; Polynomial Approximation, Interpolation, and Orthogonal Polynomials; Numerical Evaluation of Derivatives and Integrals; Numerical Solution of Differential and Integral Equations; Least Squares, Fourier Analysis, and Related Approximation Norms; Probability Theory and Statistics; Sampling Distributions of Moments, Statistical Tests, and Procedures.

Book Review:

Today, computers with the power that could be offered only by large institutions decades ago now sit on the desks of individuals. Methods of analysis that were only dreamed of decades ago are now used by students to do homework exercises. Entirely new methods of analysis have appeared that take advantage of computers to perform logical and arithmetic operations at great speed.

Unfortunately, with numerical analysis this has meant that many simply take the tools developed by others and apply them to problems with little knowledge as to the applicability or accuracy of the methods. Numerical algorithms appear as neatly packaged computer programs that are regarded by the user as "black boxes" into which they feed their data and from which come the publishable results. Many of these programs such as MATHCAD are excellent and provide quick and generally accurate "first looks" at problems. However, the researcher would be well advised to understand the methods used by the "black-boxes" to solve their problems. This effort still provides the basis for many of the operations contained in those commercial packages and it is hoped will provide the researcher with the knowledge of their applicability to his/her particular problem. This book is an attempt to gain that knowledge.

Intended Audience:

This book is primarily intended for scientists and engineers so while there is a certain familiarity with mathematics that is assumed, the rigor that one expects with a formal mathematical presentation is lacking. Very little is proved in the traditional mathematical sense of the word. Indeed, derivations are resorted to mainly to emphasize the assumptions that underlie the results.