This course book provides a solid foundation in numerical methods for solving scientific and engineering problems. It begins by exploring function approximation in Euclidean spaces, covering essential techniques like the least-squares problem and cubic spline interpolation for smooth data fitting. The text then details numerical methods for solving Ordinary Differential Equations (ODEs), presenting both single-step methods, such as Euler and Runge-Kutta, and multistep techniques like Adams-Bashforth. A theoretical analysis of their consistency and stability is included to guide the selection of appropriate methods. The final chapter focuses on calculating eigenvalues and eigenvectors, starting with basic power methods and progressing to advanced techniques like QR decomposition for large-scale problems. Each section is reinforced with practical MATLAB examples and exercises to ensure a comprehensive understanding of the concepts.
- Créateur de cours: Houas Amrane