Computational Thinking in Engineering: Numerical Methods with MATLAB: A Unified Approach from Mathematical Modeling to Algorithmic Implementation

This book presents a comprehensive guide to numerical methods in engineering, emphasizing both theoretical foundations and practical MATLAB implementation. Developed in connection with the Laboratory of Mechanical Engineering (LGM) at the University of Biskra, it covers linear and nonlinear algebraic equations, interpolation, differentiation, integration, ordinary differential equations, optimization, and fluid-thermal systems, with a focus on 2D heat transfer and incompressible Navier-Stokes simulations. Each method is accompanied by step-by-step MATLAB codes, numerical examples, and engineering applications, enabling readers to solve real-world problems efficiently and accurately. The text also addresses error analysis, stability, algorithm efficiency, and reproducibility, providing essential guidance for research, teaching, and professional practice. Designed for students, engineers, and researchers, the book bridges computational theory and practical engineering solutions, fostering critical thinking, computational skills, and problem-solving abilities.