Numerical Methods for Scientists and Engineers

Contents: 1. Introduction. 2. Roundoff Error. 3. Linear Algebraic Equations. 4. Interpolation. 5. Differentiation. 6. Integration. 7. Nonlinear Algebraic Equations. 8. Optimisation. 9. Statistical Inferences. 10. Functional Approximations. 11. Algebraic Eigenvalue Problem. 12. Ordinary Differential Equations. 13. Integral Equations. 14. Partial Differential Equations, Appendix A: Answers and Hints. Index 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. Over one hundred worked out examples illustrate a variety of numerical algorithms. Their limitations 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, over 500 unsolved problems (with answers) of varying difficulty are included. Further, over 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.…