Fundamentals of Numerical Methods with MATLAB

MATLAB programming is the premier high-level language used across engineering and science for numerical computation, visualization, and algorithm development. This book leverages the power of MATLAB to bridge the gap between theoretical numerical methods and practical, hands-on applications.

In this book, you will explore truncation, rounding, and error propagation. You will gain essential tools for finding roots of nonlinear equations, like Newton-Raphson, and solving linear systems using direct Gauss and iterative Jacobi, Seidel methods. You will also explore the theories such as splines, Lagrange, Simpson's rules, Runge-Kutta, heat, Laplace, and wave equations. By focusing on implementing algorithms, this book ensures you gain the essential programming skills required to solve real-world mathematical problems that defy traditional analytical solutions.

By the end of this book, you will be proficient in both theory and practical application of numerical methods, equipped with the programming skills necessary to implement and validate sophisticated algorithms. You will possess the competence to confidently solve real-world eigenvalue problems and complex approximation tasks, preparing you for success in advanced technical fields.

WHAT YOU WILL LEARN
● Analyse numerical errors and understand solution accuracy limits.
● Solve nonlinear equations using iterative numerical techniques.
● Implement MATLAB code to solve linear systems efficiently.
● Apply interpolation methods for curve fitting and data modelling.
● Perform numerical differentiation and integration in MATLAB.
● Solve ODEs and PDEs using reliable computational algorithms.
● Analyze numerical error and propagation in MATLAB.
● Implement Newton-Raphson for nonlinear equations.
● Solve linear systems using Gauss elimination.

WHO THIS BOOK IS FOR
This book is for undergraduate and postgraduate students, engineers, and researchers. Readers should have a foundational understanding of calculus, linear algebra, and introductory MATLAB programming to maximize their learning of numerical methods.

1. Accuracy and Errors in Numbers
2. Solution of Nonlinear Equations
3. System of Linear Equations
4. Curve Fitting and Interpolation
5. Numerical Differentiation
6. Numerical Integration
7. Numerical Solution of Ordinary Differential Equations
8. The Algebraic Eigenvalue Problems
9. Numerical Methods Approximation
10. Applications of Partial Differential Equations

● Dr. Kulwinder Singh Parmar is an assistant professor in the department of mathematical sciences, I.K. Gujral Punjab Technical University (IKGPTU), Jalandhar (Punjab). He completed his Ph.D. degree from Guru Gobind Singh Indraprastha University, New Delhi (2014). He did his research work in Shobhit University, Meerut (UP), and the University of Delhi to complete his M.Phil Degree (2008). He completed his M.Sc. (Mathematics) and B.Sc. from Guru Nanak Dev University. Earlier, he served as an assistant professor in the department of mathematics, Dr. B.R. Ambedkar National Institute of Technology, Jalandhar (Punjab)(NIT Jalandhar). He has published more than 65 research papers in the journals of international repute in mathematical modeling, neural networks, wavelet analysis, time series analysis, prediction data modeling, etc. Currently, four Ph.D. scholars are working with him. He has guided three Ph.D. scholars and authored two books. He has attended various short-term training programs, refresher courses, workshops, seminars, and conferences in India, Spain, USA, and Canada.

● Dr. Sachin Kaushal is a Professor of Mathematics at Lovely Professional University, Phagwara. His research focuses on solid mechanics, and he has over 50 publications in internationally reputed journals. His recent work has appeared in Springer Nature, ranked among the top five most-cited journals globally. He has successfully guided six Ph.D. scholars and is presently supervising four more. He has also organized and participated in numerous national and international conferences. In addition, he serves as a reviewer for several leading international journals, reflecting his academic recognition and expertise in applied mathematics and mechanics.

● Dr. Brijesh Bakariya is an assistant professor in the department of computer science and engineering, I.K. Gujral Punjab Technical University (IKGPTU) Campus, Hoshiarpur, Punjab. He completed his Ph.D. from Maulana Azad National Institute of Technology (NIT, Bhopal), Madhya Pradesh (2016). He received his MCA degree from Devi Ahilya Vishwavidyalaya, Indore (Madhya Pradesh) in computer applications (2009). He has been teaching since 2009 and has been guiding M.Tech and Ph.D. students. In the meantime, he has authored three books and published more than 25 research papers in the journals of international repute in the area of data mining, image processing, machine learning, etc.