Numerical Analysis

A Programming Approach

Vinay Vachharajani

• Publisher: BPB Publications
• Year: 2020
• eBook ISBN: 9788183335515
• Topic: Computer Science
• Subtopic: Programming Algorithms
• Index: Computer Science

Learn the concept of algorithms from beginners to advanced levelIn the present scenario where the knowledge of computers has become an absolute necessity, there has been an increasing desire for numerical answers to any applied problem. This has led to high demand for courses in numerical analysis. Many real world problems are solved first by converting them into mathematical models and then applying analytical methods to solve that model. In several cases, where ordinary analytical methods fail, numerical methods can give the result.The book is divided into twelve chapters, describing the concept of computer arithmetic, errors, iterative methods to find the roots of transcendental and algebraic equations, curve fitting, numerical differentiation, integration, and so on.In the book the major emphasis is given on numerous solved and unsolved examples. Many topics in this book such as process graph, cubic spline method, Taylor series, Legendre and Chebyshev polynomials, Gauss - Chebyshev integration method and boundary value problems make this book unique. KEY FEATURES• Chapters include objectives, learning outcomes, multiple-choice questions, exercises for practice and solutions.• Programs are written in C Language for Numerical methods.• Topics are explained with suitable examples.• Arrangement (Logical order), clarity, detailed presentation and explanation of each topic with numerous solved and unsolved examples.• Concise but lucid and student-friendly presentation for derivation of formulas used in various numerical methods.WHAT WILL YOU LEARN• Concept of numbers and their accuracy, binary and decimal number system, limitations of floating point representation.• Concept of error and their types, propagation of errors through process graph.Iterative methods for finding the roots of algebraic and transcendental equations with their convergence, methods to solve the set of nonlinear equations, methods to obtain complex roots.• Concept of matrices, the direct and iterative methods to solve a system of linear algebraic equations.Finite differences, interpolation and extrapolation methods, cubic spline, concept of curve fitting.• Differentiation and integration methods.Solution of ordinary and partial differential equationsWHO THIS BOOK IS FORThis book is designed to serve as a textbook for the undergraduate as well as post graduate students of Mathematics, Engineering, Computer science (MCA, BCA), Information Technology and M.Sc. (IT).AUTHOR BIOVinay Vachharajani is a senior faculty member in School of Computer Studies at Ahmedabad University, Gujarat. He received his Bachelor of Science and first Master degree in Mathematics from Gujarat University and the second Master degree in Computer Applications (MCA) from Gujarat University. He has more than 12 years of teaching experience at UG and PG level. His research interests include e-learning, Natural Language Processing, Technology for Education and Business Analytics. He has published/presented several research papers in prestigious national and international journals/conferences.