This textbook presents the frequently used numerical methods in a simple, well-structured and logical manner to enable students to easily grasp the pertinent concepts. All the concepts are accompanied by numerous solved problems of varying levels of difficulty to further strengthen and consolidate the students’ understanding. From a software perspective, algorithms as well as C programs are included to enable the student to optimise their usage of the techniques. The text is well supported with problems, illustrations, assignments, MCQs and long and short answer questions, thereby providing an exam-oriented approach.
Arun Kumar Jalan is Professor in Mathematics and Dean of Students’ Affairs at MCKV Institute of Engineering, Howrah. After obtaining his PhD in Mathematics from Jadavpur University, he joined MCKV Institute of Engineering as lecturer in 2000. He has reviewed and published several research papers in reputed international journals.
Utpal Sarkar is Assistant Professor in Mathematics at MCKV Institute of Engineering, Howrah. He completed his Masters in Mathematics from Jadavpur University and joined MCKV Institute of Engineering as lecturer in 2009. He is currently working on his PhD from West Bengal University of Technology.
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
Chapter 3 Interpolation
3.1 Introduction
3.2 Interpolation and Extrapolation
3.3 Interpolation with Equal Intervals
3.4 Interpolation with Unequal Intervals
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
4.9 Romberg’s Method
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
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
Chapter 7 Numerical Solution of a System of Linear Equations
7.1 Introduction
7.2 Direct Methods
7.3 Iterative Methods
Chapter 8 Curve Fitting and Spline Interpolation
8.1 Curve Fitting
8.2 Spline Interpolation
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
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