Fundamentals of Numerical Methods with MATLAB: An introduction to scientific computing with MATLAB programming

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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.