Preface

Applications of mathematics invariably boil down to numerical results. The aim of this book, Numerical Analysis, is to present the important principles, methods and processes used for obtaining these results in a systematic and simple way with accuracy and clarity. The book can cater to the needs of undergraduate and postgraduate students of science and engineering courses offered in Indian universities. Keeping the treatment simple, the procedures are illustrated with typical examples and problems taken from various university question papers.

The topics of the book are presented in 11 chapters.

Chapter 1 gives a brief discussion of errors in approximations.

Chapter 2 deals with the direct and iterative methods of solving algebraic and transcendental equations. These methods include Ramanujan’s method, Muller’s method, Chebyshev’s method, Graffe’s root square method and Lin–Bairstow’s method.

Chapter 3 spells out the direct and iterative methods of solving simultaneous linear equations. It also expounds on eigen value problems and factorization methods.

Chapter 4 elucidates the steps involved in polynomial interpolation when the arguments are spaced equally and unequally. The chapter also encompasses interpolation of cubic splines.

Chapter 5 examines the different methods of inverse interpolation.

Chapter 6 is devoted to numerical differentiation and maxima and minima.

Chapter 7 elaborates on the concepts of numerical integration and double integration.

Chapter 8 delves into the different methods of curve fitting, including the method of sum of exponentials.

Chapter 9 focuses on the numerical solution of ordinary differential equations.

Chapter 10 seeks to determine numerical solutions of partial differential equations of the types, namely elliptic, parabolic and hyperbolic.

Chapter 11 the last chapter, sheds light on the solution of difference equations.

Mathematics is a subject that can be mastered only through hard work and practice. The key word in the learning process of mathematics is practice. Remember the maxim: “Mathematics without practice is blind and practice without understanding is futile”.