Numerical Methods For Scientific And Engineering Computation

This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems.

Numerical Methods for Scientific and Engineering Computation is appropriate as a text book for the first course and partly for the second course in numerical analysis. The book is largely self-contained, the courses in calculus and matrices are essential. Some of the special features of the book are: classical and recently developed numerical methods are derived from the high speed computation view point; comparative study of the numerical methods is given to bring out advantages and disadvantages in the implementation of the methods; about 300 problems including BIT problems (1964-83) are listed at the end of Chapters 2 - 7, to serve as exercises and extension to the text; answers and hints to the problems at the end of the book as well as the solved examples in the body of the text will help the students to understand the basic concepts.

About the Book: This comprehensive textbook covers material for one semester course on Numerical Methods (MA 1251) for B.E./ B. Tech. students of Anna University. The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. The book is written as a textbook rather than as a problem/guide book. The textbook offers a logical presentation of both the theory and techniques for problem solving to motivate the students in the study and application of Numerical Methods. Examples and Problems in Exercises are used to explain.

This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.