Numerical Methods: A Programming-based Approach
Arun Kumar Jalan and Utpal Sarkar
Price
695.00
ISBN
9788173719585
Language
English
Pages
432
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2015
Territorial Rights
World
Imprint
Universities Press
Catalogues

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

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

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

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

Solved Examples

4.9 Romberg’s Method

Multiple Choice 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

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

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

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

Multiple Choice 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

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