Fondements Mathématiques pour l'ingénieur

Learning objectives

Upon completion of this module, students will be able to:
- Apply fundamental concepts of sequences, complex numbers, and series to solve applied mathematical problems;
- Analyze the properties of continuous, differentiable, and multivariable functions;
- Master integral calculus for evaluating physical quantities and signal metrics;
- Manipulate vector spaces, inner products, and bases to formalize multidimensional problems;
- Utilize matrix calculus and linear maps to model data flows and transformations (the core foundations of Machine Learning);
- Leverage Fourier bases for frequency analysis and digital signal processing;
- Implement optimization methods on multivariable functions (key to model training and loss minimization).

Additional Learning Outcomes (VAP AIR/MAIA):
- Determine the characteristic polynomial and perform spectral decomposition/diagonalization of matrices to simplify dynamic systems;
- Deepen the study of vector spaces and inner products to tackle high-level theoretical concepts.