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  • Description du cours

    Mathematics for Engineering Sciences

    Applied Mathematics in Science and Engineering | Taylor & Francis Online

    Objectives of the Course:


    This course is dedicated to numerical analysis and aims to provide a comprehensive understanding of the algorithms used to solve continuous mathematical problems through numerical discretization. It covers both the theoretical foundations and practical applications of these methods, enabling students to develop the skills necessary to convert complex continuous models into discrete forms that can be efficiently processed by computers. By bridging the gap between abstract mathematical concepts and computational techniques, this course equips learners with the tools required to tackle real-world scientific and engineering challenges.

     cible odince: This course is designed for third-year undergraduate students specializing in Physical Measurements, particularly in Instrumental Techniques and Materials & Physicochemical Control. However, it is also intended for anyone interested in gaining foundational knowledge in numerical analysis.

    Course Content:

    Chapter I: Matrix Analysis

    Chapter II: Resolution of Linear Systems of Equations

    Chapter III: Resolution of Nonlinear Systems of Equations:

    Chapter IV: Interpolation and Polynomial Approximation

    Auteur: Dr.ZAKARIA BAHRI

  • Chapitre I

    Matrix Analysis
    Chapter Objectifs : 

    Define the concepts of:

    • Matrix
    • Operations on matrices
    • Determinant
    • Elementary transformations of a matrix
    • Eigenvalues - Eigenvectors
    • Norms

  • Chapitre II

    Solving Systems of Linear Equations

    Chapter Objective:

    This chapter focuses on solving linear systems AX=B  using both direct and iterative methods:

    Direct Methods:

    • Eigenvalues and Eigenvectors Method fo Solving ODE ( Ordinary Differentionle Eqaution) linear systems
    • Gaussian Elimination Method: Applicable for any square matrix AA.
    • LU Facorisation based on Gaussian Elimination Method: Applicable for any square matrix A.
    • Gauss-Jordan Method: Applicable for any square matrix AA.
    • Cholesky Method: Specifically for symmetric positive-definite matrices AA.

    Iterative Methods:

    • Jacobi Method: Used for approximating solutions iteratively.

    Each method will be explained in detail, including the mathematical principles, algorithms, and practical applications. Where relevant, examples will illustrate the computational steps to enhance understanding.


  • Chapitre III

    Résolution des systèmes d'équations non linéaires


    Objectif du chapitre : 

       Définir la :

    • Méthode de Newton pour la résolution d’une équation non linéaire
    • Méthode de poins-Fixe pour la résolution d’une équation non linéaire.
    • Méthode de Newton pour la résolution d’un système d’équations non linéaires.



  • Chapitre IV

    Interpolation numérique


    Objectif du chapitre : 

        Définir l' (e) :

    • Interpolation polynomiale
    • Polynôme d’interpolation de Lagrange

  • Series TD