# Tronc CommunMathematicsAdapted Mathematics I : applied analysis - algebra

Lecturer(s): Abdel-Malek ZINE, Hélène HIVERT
Course ⋅ 18 hTC ⋅ 20 h

## Objectives

We present basic tools for algebra and analysis : vector spaces, polynomials, orthogonalization, matrices and diagonalization, integration, differential calculus, optimization, ordinary differential equations

## Keywords

Polynomials, Hilbert spaces, matrix diagonalization, integration, functional space, ODE, differential calculus, optimisation

## Programme

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.

## Learning Outcomes

• 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

## Assesment

Micro-test (25%) Final exam (75%)