This comprehensive textbook covers material for one semester for one semester course on Numerical Methods (MA 1251) fo4r B.E./B.Tech. Students of Anna University. The emphasis in the book in 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. 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 Me4thods. Examples and Problems in Exercises are used to explain each theoretical concept and application of these concepts in problem solving. At the end of each important section, a review set of questions and answers are provided to understand and theoretical concepts in the text. About the Author Satteluri R.K. Lyengar (b. 1941), M.A., M.Tech., Ph.D. Was a Professor of Mathematics at the indian Institute of Technology, Delhi. He had also served as the Head of the Department of Mathematics, IIT, Delhi. Presently, Dr. Lyengasr is the Dean (Academic Affairs) and Professor of Mathematics at Gokaraju Rangaraju Instutute of Engineering & Technology, Hyderabad. Dr. lyengar\s research specialisation is Numerical Analysis. He has a large number of research Publications in Int3ernational and National Journals of repute in the area of Numerical Analysis. He is a coauthor of a number of books on Numerical Analys8is and Advanced Engineering Mathematics. Dr. Lyengar worked as a post-doctoral fellow at the Oxfard University Computi9ng Laboratory, U.K. He was also a visiting fellow at the university of Saskatchewan, Canada. Rajinder Kumar Jain (B.1941), M.A., Ph.D. Was a Professor of Mathematics at the Indian Institute of Technology, Delhi. Presently, Dr. Jain is a professor of a Mathematics in the Department of Applied Sciences, Manav Ranchna College of Engineering, Faridabad, Haryana. Dr. Jain\s research specialisation is Numerical Analysis. He has a large number of research publications in International and National Journals of repute in the area of Numerical Analysis. He is a coauthor of number of books on Numerical Analysis Engineering Mathematics. Dr. Jain worked asa visiting faculty at the University of Saskatchewan, Canada; Cranfield Institute of Technology, U.K. And RMIT, Australia. Table of Contents 1. SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS Solution of Algebraic and Transcendental Equations Linear System of Algebraic Equations Introduction Direct Methods Iterative Methods Eigen Value Problems Answers and Hints 2. INTERPOLATION AND APPROXIMATION Introduction Interpolation with Unevenly Spaced Points Interpolation with Evenly Spaced Points Spline Interpolation and Cubic Splines Answers and Hints 3. NUMERICAL DIFFERENTIATION AND INTEGRATION Introduction Numerical Differentiation Numerical integration 4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS introduction Single Step and Multi Step Methods Taylor Series Method Runge-Kutta Methods System of First Order initial Value Problems Multi Step Methods and Predictor-Corrector Methods Answers and Hints 5. BOUNDARY VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS AND INITIAL & BOUNDARY VALUE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS Introductions Boundary value Problems Governed by Second Order Ordinary Differential Equations Classification of Linear Second Order Partial Differential Equations Finite Difference Methods for Laplace and Poisson Equations Finite Difference Method for Heat Conduction Equation Finite Difference Method for Wave Equation Answers and Hints
