📖 General Introduction – Numerical Analysis 2

Modern technologies, especially in telecommunications, computing, robotics, and embedded systems engineering, increasingly rely on complex mathematical models. Often, these models cannot be solved exactly in closed form. Numerical analysis provides the tools to rigorously approximate solutions to mathematical problems using numerical algorithms.

This module is a natural continuation of the first numerical analysis course. It focuses on fundamental numerical techniques essential for any engineer dealing with discrete data, dynamic systems, or calculations that are impossible to perform analytically. The goal is to equip students with a strong ability to model, solve, and interpret mathematical problems using reliable numerical methods.

In the context of telecommunications engineering, these methods have very concrete applications. For example:

• Interpolation and polynomial approximation: used to reconstruct signals from samples (DSP), compress data, or fit curves to experimental measurements.
• Numerical differentiation and integration: applied to process signals, estimate transmitted wave energy, or simulate circuits in transient regimes.
• Numerical solution of ordinary differential equations (ODEs): essential for modeling dynamic phenomena such as transmission systems, RLC circuits, and adaptive control protocols.

The module emphasizes mathematical foundations of the methods, their algorithmic implementation, and their critical analysis (accuracy, stability, computational complexity). It aims to strengthen your autonomy in solving real problems and to develop transferable skills for future technical projects and research work.

Significant attention is also given to numerical simulation using software such as Python, Matlab, or Scilab, helping you test and validate the methods studied on real or simulated cases.

By the end of this module, you will be able to:

• Select the most appropriate numerical method for a given problem;
• Implement it efficiently in a computing environment;
• Evaluate the quality of the results and justify their validity;
• Adopt a rigorous and critical approach to numerical problem analysis.

This module is therefore more than just a theoretical continuation: it provides an essential foundation for modern engineers, bridging the gap between mathematical models and numerical reality.