This book is intended for courses on numerical methods at the junior and senior level as well as at the beginning graduate level. The book also serves as a reference for numerical methods in engineering. Fortran and C programs, along with illustrative examples, are given in each chapter to implement many of the numerical methods discussed in that chapter.
The use of commercial numerical softwares-MatLab Maple and Mathecad-in the solution of practical problems is demonstrated in every chapter. Even when a program from a software package is used, we need to understand the basic principles, purpose, and limitations of the program. Often, in many engineering applications, an available standard program cannot be used directly; we need to adapt and modify it. This invariably requires a sound knowledge of the numerical method as well as some computational experience with the method.
The book is aimed at presenting numerical methods along with their practical applications in a manner that helps student achieve the goals just outlined.
1. Introduction to Numerical Methods
2. Solution of Nonlinear Equations
3. Solution of Simultaneous Linear Algebraic Equations
4. Solution of Matrix Eigenvalue Problem
5. Curve Fitting and Interpolation
6. Statistical Methods
7. Numerical Differentiation
8. Numerical Integration
9. Ordinary Differential Equations: Initial-Value Problems
10. Ordinary Differential Equations: Boundary-Value problems
Etc.