Preface and Acknowledgements
Chapter 1 Approximation in Numerical Computations
1.1 Introduction
1.2 Exact Number, Approximate Number and Significant Digits/Figures
1.3 Rounding Numbers
1.4 Errors, Truncation and Rounding Errors
1.5 Fixed Point and Floating Point Arithmetic
1.6 Propagation of Errors
1.7 General Error Formula
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 2 Calculus of Finite Differences
2.1 Introduction
2.2 Finite Differences
2.3 Forward Differences
2.4 Backward Differences
2.5 Shift Operator
2.6 Central Difference Operator and Averaging Operator
2.7 Divided Differences
2.8 Factorial Notation
2.9 Propagation of Error in the Difference Table
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 3 Interpolation
3.1 Introduction
3.2 Interpolation and Extrapolation
3.3 Interpolation with Equal Intervals
3.4 Interpolation with Unequal Intervals
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 4 Numerical Integration
4.1 Introduction
4.2 General Quadrature Formula for Equidistant Ordinates
4.3 Trapezoidal Rule
4.4 Simpson’s 1/3 Rule
4.5 Simpson’s 3/8 Rule
4.6 Boole’s Rule
4.7 Weddle’s Rule
4.8 Newton–Cote’s Quadrature Formula
Solved Examples
4.9 Romberg’s Method
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 5 Numerical Solutions of Ordinary Differential Equations
5.1 Introduction
5.2 Taylor Series Method
5.3 Picard’s Method
5.4 Euler’s Method
5.5 Euler’s Modified Formula
5.6 Runge-Kutta Method
5.7 Predictor-Corrector Method
5.8 Finite Difference Method
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 6 Numerical Solutions of Algebraic and Transcendental Equations
6.1 Introduction
6.2 Mathematical Preliminaries
6.3 Order of Convergence
6.4 Method of Iteration
6.5 Bisection Method
6.6 Regula Falsi Method (Method of False Position)
6.7 The Secant Method
6.8 Newton–Raphson Method
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 7 Numerical Solution of a System of Linear Equations
7.1 Introduction
7.2 Direct Methods
7.3 Iterative Methods
Solved Examples
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 8 Curve Fitting and Spline Interpolation
8.1 Curve Fitting
8.2 Spline Interpolation
Short Answer Questions
Long Answer Questions
Chapter 9 Algorithms and Programs in C Language
9.1 Introduction
9.2 Overview of C Language
9.3 Newton’s Forward Interpolation
9.4 Newton’s Backward Interpolation
9.5 Lagrange’s Interpolation
9.6 Trapezoidal Rule
9.7 Simpson’s 1/3 Rule
9.8 Weddle’s Rule
9.9 Bisection Method
9.10 Regula Falsi Method
9.11 The Secant Method
9.12 Newton–Raphson Method
9.13 Euler’s Method
9.14 Runge–Kutta Method of Order Four
9.15 Gauss Elimination Method
9.16 Gauss–Seidel Method
9.17 Fitting the Straight Line y = a + bx
9.18 Fitting the Curve y = ax + bx2
Multiple Choice Questions
Short Answer Questions
Long Answer Questions
Chapter 10 Introduction to Software Packages 34610.1
Introduction to MATLAB
10.2 Introduction to SCILAB
10.3 Introduction to LabVIEW
10.4 Introduction to Mathematica
Appendix: Fourier Series and Fourier Transforms
Index