We present basic tools for algebra and analysis : vector spaces, polynomials, orthogonalization, matrices and diagonalization, integration, differential calculus, optimization, ordinary differential equations
Polynomials, Hilbert spaces, matrix diagonalization, integration, functional space, ODE, differential calculus, optimisation
Algebra : Polynomials. Hilbert spaces, euclidean spaces. Matrices, determinant. Eigenvalues, eigenvectors and applications.
Analysis : Recap and complements. Lebesgue's integration. Integration : theorems and functional spaces. Differential calculus and optimization. Ordinary differential equations.
- Be able to use the fundamental tools of algebra.
- Be able to justify the computation of an integral with several variables.
- Be able to determine the extrema of a function defined over R^d.
- Be able to determine qualitative properties of the solution of an ordinary differential equation
Micro-test (25%) Final exam (75%)