The Numerical Analysis course provides an in-depth exploration of numerical methods and techniques used to solve mathematical problems effectively. Covering key topics such as error analysis, algebraic equation resolution, interpolation, numerical differentiation, and integration, the course equips students with essential skills for practical applications in science and engineering.
Key elements include:
- Error Concepts: Understanding truncation, rounding, and relative errors to assess numerical accuracy.
- Equation Solving: Employing methods such as bisection, fixed-point iteration, and Newton-Raphson to find roots of equations, along with error estimation techniques.
- Interpolation and Approximation: Utilizing Lagrange and Newton methods for polynomial interpolation, and applying least squares for functional approximation while analyzing associated errors.
- Numerical Differentiation: Exploring methods for approximating derivatives based on discrete data.
- Numerical Integration: Implementing techniques like the trapezoidal rule and Simpson's method for estimating integrals, along with understanding quadrature errors.
This course not only emphasizes theoretical understanding but also practical application, preparing students to tackle real-world problems using numerical analysis. Through a combination of lectures, practical exercises, and software applications, students will develop a robust foundation in numerical techniques crucial for their academic and professional endeavors.
- Enseignant: Ryma RAHLA