Browsing by Author "ATIL, Lynda"

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    Analyse Numérique 2 :Cours et exercices.
    (ummto.faculté des sciences, 2025-12-16) ATIL, Lynda
    Ce polycopié est destiné aux ´étudiants de deuxième année de Licence en Mathématiques, dans le cadre du module d’Analyse Numérique 2. Le présent document est structuré en quatre chapitres : 1. Rappels et compléments sur les matrices : Ce chapitre a pour but de rappeler, et de démontrer, un certain nombre de résultats relatifs aux matrices et aux espaces vectoriels 2.de dimension finie, et dont un usage constant sera fait dans toute la suite du polycopié. Résolution numérique des systèmes d’équations linéaires :Nous y étudions les méthodes directes (méthodes de Gauss, Cholesky) qui permettent d’obtenir la solution en un nombre fini d’opérations et les méthodes itératives (méthodes de Jacobi, Gauss-Seidel) qui recherchent la solution de proche en proche en partant d’un vecteur initial arbitraire pour résoudre un système linéaire. 3. Calcul des valeurs et des vecteurs propres : Ce chapitre aborde les méthodes de calcul des approximations de l’ensemble des valeurs propres d’une matrice A et des vecteurs 4. Propres associés. Résolution numérique des équations différentielles : « Nous abordons différentes méthodes numériques pour les résolutions approchées des équations différentielles ordinaires.
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    Introduction to probability (Course & exercises)
    (ummto.faculté des sciences, 2025-12-16) ATIL, Lynda
    This handout is intended for second-year Mathematics students, as part of the Numerical Analysis 2 module. This document is structured into four chapters: 1. Reminders and supplements on matrices: This chapter aims to recall and demonstrate a number of results related to matrices and vector spaces. 2.of finite dimension, and which will be constantly used throughout the rest of the handout. Numerical resolution of linear equation systems: We study direct methods (Gauss, Cholesky) that allow us to obtain the solution in a finite number of operations and iterative methods (Jacobi, Gauss-Seidel) that seek the solution step by step starting from an arbitrary initial vector to solve a linear system. 3. Calculation of eigenvalues and eigenvectors: This chapter covers methods for calculating approximations of the set of eigenvalues of a matrix A and the associated eigenvectors. 4. Associated eigenvectors. Numerical resolution of differential equations: "We address different numerical methods for the approximate solutions of ordinary differential equations."
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    Introduction to probability (Course & exercises)
    (ummto.faculté des sciences, 2025-12-16) ATIL, Lynda
    This manual has been carefully structured to guide you from fundamental concepts to more advanced topics, ensuring a solid and progressive understanding.The journey begins with Chapter 1, which serves as a crucial recap of fundamental probability notions.Here, we will revisit the axiomatic foundations of probability, combinatorial calculations, conditional probability, and Bayes’ Theorem. This chapter is designed to solidify your intuition and ensure all students have a common, robust starting point. Numerous examples and solved exercises will help you master these essential tools. In Chapter 2, we will move from abstract events to more manageable mathematical objects by introducing Random Variables. We will explore the key distinctions between discrete and continuous random variables, focusing on their characterization through probability mass functions, probability density functions, and cumulative distribution functions. This chapter will also introduce you to the important concepts of expectation and variance, which capture the ”average” behaviour and the spread of a random variable, respectively. Chapter 3 builds directly upon this foundation by delving into the most Common Probability Distributions. You will become acquainted with the essential families of discrete distributions (such as the Binomial, Poisson, and Geometric) and continuous distributions (such as the Uniform, Normal, and Exponential). A significant part of this chapter is dedicated to approximations, particularly the use of the Poisson distribution to approximate the Binomial, a powerful technique for simplifying complex calculations. Furthermore, we will explore the transformation of random variables, a key concept for understanding how distributions change under functional mappings, which is vital for more advanced statistical inference.