Elements of Numerical Analysis [Paperback]

This textbook provides detailed discussion on fundamental concepts and applications of numerical analysis.This textbook introduces the basic concepts of numerical analysis conforming to the module syllabus designed by the University Grant Commission (UGC) for undergraduate courses in science and engineering for Indian universities. The mathematical derivations discussed here are presented in a simplified and systematic manner.This textbook introduces the basic concepts of numerical analysis conforming to the module syllabus designed by the University Grant Commission (UGC) for undergraduate courses in science and engineering for Indian universities. The mathematical derivations discussed here are presented in a simplified and systematic manner.Numerical Analysis deals with manipulation of numbers to solve a particular problem. This book discusses in detail the creation, analysis and implementation of algorithms to solve the problems of continuous mathematics. An input is provided in form of numerical data or it is generated as required by the system to solve a mathematical problem. Subsequently this input is processed through arithmetic operations together with logical operations in a systematic manner and output is produced in the form of numbers. Covering the fundamentals of numerical analysis and its applications in one volume, this book offers detailed discussion on relevant topics including difference equations, Fourier series, discrete Fourier transforms and finite element methods. In addition, the important concepts of integral equations, Chebyshev Approximation and Eigen Values of Symmetric Matrices are elaborated in separate chapters. It serves as a textbook for undergraduate students in science and engineering across all major universities in India.Preface; 1. Errors in computation; 2. Linear equations and eigenvalue problem; 3. Nonlinear equations; 4. Interpolation; 5. Numerical differentiation; 6. Numerical integration; 7. Ordinary differential equationsl³"