Numerical methods for scientists and engineers / K. Sankara Rao

Description:

With a clarity of approach, this easy-to-comprehend book gives an in-depth analysis of the topics under Numerical Methods, in a systematic manner. Primarily intended for the undergraduate and postgraduate students in many branches of engineering, physics, mathematics and all those pursuing Bachelors/Masters in computer applications. Besides students, those appearing for competitive examinations, research scholars and professionals engaged in numerical computation will also be benefited by this book.

The fourth edition of this book has been updated by adding a current topic of interest on Finite Element Methods, which is a versatile method to solve numerically, several problems that arise in engineering design, claiming many advantages over the existing methods. Besides, it introduces the basics in computing, discusses various direct and iterative methods for solving algebraic and transcendental equations and a system of non-linear equations, linear system of equations, matrix inversion and computation of eigenvalues and eigenvectors of a matrix. It also provides a detailed discussion on Curve fitting, Interpolation, Numerical Differentiation and Integration besides explaining various single step and predictor–corrector methods for solving ordinary differential equations, finite difference methods for solving partial differential equations, and numerical methods for solving Boundary Value Problems. Fourier series approximation to a real continuous function is also presented. The text is augmented with a plethora of examples and solved problems along with well-illustrated figures for a practical understanding of the subject. Chapter-end exercises with answers and a detailed bibliography have also been provided.

NEW TO THIS EDITION

• Includes two new chapters on the basic concepts of the Finite Element Method and Coordinate Systems in Finite Element Methods with Applications in Heat Transfer and Structural Mechanics.

• Provides more than 350 examples including numerous worked-out problems.

• Gives detailed solutions and hints to problems under Exercises.

Rao, K. Sankara
K. SANKARA RAO, Ph.D., has been Professor in Mathematics at Anna University, Chennai. He has also worked as Scientist/Engineer at Tata Institute of Fundamental Research, Mumbai and Vikram Sarabhai Space Centre, Trivandrum. A Fellow of the Aeronautical Society of India, Dr. Rao has several research papers published in national and international journals to his credit, apart from being the author of Introduction to Partial Differential Equations and Classical Mechanics (both published by PHI Learning).

Preface
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
1. Basics in Computing
2. Solution of Algebraic and Transcendental Equations
3. Solution of Linear System of Equations and Matrix Inversion
4. Eigenvalue Problems
5. Curve Fitting
6. Interpolation
7. Numerical Differentiation and Integration
8. Ordinary Differential Equations
9. Parabolic Partial Differential Equations
10. Elliptic Partial Differential Equations
11. Hyperbolic Partial Differential Equations
12. Boundary Value Problems
13. Approximation of Functions
14. Finite Element Method—Basic Concepts
15. Coordinate Systems in FEM and its Applications
Appendix
Bibliography
Answers to Exercises
Index