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.

Table of Contents
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