Metodos Numericos

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ISBN (13) : 978-81-224-2707-3

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Preface
This book is based on the experience and the lecture notes of the authors while teaching NumericalAnalysis for almost four decades at the Indian Institute of Technology, New Delhi. This comprehensive textbook covers material for one semester course on Numerical Methods 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. Thetextbook offers a logical presentation of both the theory and techniques for problem solving to motivate the students for the study and application of Numerical Methods. Examples and Problems in Exercises are used to explain each theoretical concept and application of these concepts in problem solving. Answers for every problem and hints for difficult problems are provided to encourage thestudents for selflearning. The authors are highly grateful to Prof. M.K. Jain, who was their teacher, colleague and co-author of their earlier books on Numerical Analysis. With his approval, we have freely used the material from our book, Numerical Methods for Scientific and Engineering Computation, published by the same publishers. This book is the outcome of the request of Mr. Saumya Gupta, ManagingDirector, New Age International Publishers, for writing a good book on Numerical Methods for Anna University. The authors are thankful to him for following it up until the book is complete. The first author is thankful to Dr. Gokaraju Gangaraju, President of the college, Prof. P.S. Raju, Director and Prof. Jandhyala N. Murthy, Principal, Gokaraju Rangaraju Institute of Engineering and Technology,Hyderabad for their encouragement during the preparation of the manuscript. The second author is thankful to the entire management of Manav Rachna Educational Institutions, Faridabad and the Director-Principal of Manav Rachna College of Engineering, Faridabad for providing a congenial environment during the writing of this book. S.R.K. Iyengar R.K. Jain

This page intentionally left blankContents
Preface 1. SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS 1.1 Solution of Algebraic and Transcendental Equations, 1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6 1.2.1 1.2.2 Introduction, 1 Initial Approximation for an Iterative Procedure, 4 Method of False Position, 6 Newton-Raphson Method, 11 General Iteration Method, 15 Convergence of Iteration Methods, 19 Introduction, 25 Direct Methods, 261.2.2.1 Gauss Elimination Method, 28 1.2.2.2 Gauss-Jordan Method, 33 1.2.2.3 Inverse of a Matrix by Gauss-Jordan Method, 35 1.2.3 Iterative Methods, 41 1.2.3.1 Gauss-Jacobi Iteration Method, 41 1.2.3.2 Gauss-Seidel Iteration Method, 46 1.3 Eigen Value Problems, 52 1.3.1 1.3.2 Introduction, 52 Power Method, 53 63–108 (v) 1–62

1.2 Linear System of Algebraic Equations, 25

1.4 Answers and Hints, 592. INTERPOLATION AND APPROXIMATION 2.1 Introduction, 63 2.2 Interpolation with Unevenly Spaced Points, 64 2.2.1 Lagrange Interpolation, 64 2.2.2 Newton’s Divided Difference Interpolation, 72 2.3 Interpolation with Evenly Spaced Points, 80 2.3.1 Newton’s Forward Difference Interpolation Formula, 89 2.3.2 Newton’s Backward Difference Interpolation Formula, 92 2.4 Spline Interpolation and Cubic...