Numerical Methods for Scientists and Engineers

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. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added. Read more... Abstract: This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. The main addition in the third edition is a new Chapter on Statistical Inferences. Read more... Computation is an indispensable tool in the analysis and exploration of a wide range of physical phenomena. This book presents an exhaustive exposition of the various numerical methods used in scientific and engineering applications. It emphasizes the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. An important addition in this revised third edition is a chapter on basic statistics. More than 100 worked-out examples illustrate a variety of numerical algorithms. The limitations of the algorithms are also discussed, as are pitfalls in numerical computations. A special feature is the inclusion of a discussion of techniques for error-estimation. In addition, more than 500 unsolved problems (with answers) of varying difficulty are included, and more than 200 computer programs in FORTRAN and C, covering all topics, are provided as supplementary material online. These give the book a strong pedagogic focus. Examples and exercises are drawn from areas as diverse as fluid mechanics, celestial mechanics, and seismology. This book will be extremely useful for graduate students and researchers in all branches of science and engineering. Front Matter....Pages i-xxxii Introduction....Pages 1-12 Roundoff Error....Pages 13-58 Linear Algebraic Equations....Pages 59-110 Interpolation....Pages 111-158 Differentiation....Pages 159-174 Integration....Pages 175-270 Nonlinear Algebraic Equations....Pages 271-344 Optimisation....Pages 345-400 Statistical Inferences....Pages 401-424 Functional Approximations....Pages 425-522 Algebraic Eigenvalue Problem....Pages 523-572 Ordinary Differential Equations....Pages 573-656 Integral Equations....Pages 657-700 Partial Differential Equations....Pages 701-772 Back Matter....Pages 773-855 "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. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added."--Résumé de l'éditeur Computation is an indispensable tool in the analysis and exploration of a wide range of physical phenomena. This book presents an exhaustive exposition of the various numerical methods used in scientific and engineering applications. 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. An important addition in this revised third edition is a chapter on basic statistics. [Source : 4e de couverture]