Department of Fundamental Education in Science and Technology

https://www.univ-soukahras.dz/en/dept/st

Lecturer
Information	Bachelor - Second Year : Electronic Department of Fundamental Education in Science and Technology Website : https://www.univ-soukahras.dz/en/module/5042 Semester : S4 Unit : UEF 2.2.2 Credit : 4 Coefficient: 2
Content	Chapter 1: Nonlinear Equations f(x) = 0 Solving (3 Weeks) Introduction to calculation errors and approximations. Introduction to methods for solving nonlinear equations. Bisection method. Successive approximation method (fixed-point method). Newton-Raphson method. Chapter 2: Polynomial Interpolation (2 Weeks) General introduction. Lagrange polynomial. Newton\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s polynomials. Chapter 3: Function Approximation (2 Weeks) Approximation methods and mean square approximation. Orthogonal or pseudo-orthogonal systems. Approximation using orthogonal polynomials. Trigonometric approximation. Chapter 4: Numerical Integration (2 Weeks) General introduction. Trapezoidal rule. Simpson\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s method. Quadrature formulas. Chapter 5: Solution of Ordinary Differential Equations (Initial Value or Cauchy Problem) (2 Weeks) General introduction. Euler\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s method. Improved Euler\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s method. Runge-Kutta method. Chapter 6: Direct Solution Method for Systems of Linear Equations (2 Weeks) Introduction and definitions. Gaussian elimination and pivoting. LU factorization method. Cholesky factorization method. Thomas algorithm (TDMA) for tridiagonal systems. Chapter 7: Approximate Solution Method for Systems of Linear Equations (2 Weeks) Introduction and definitions. Jacobi method. Gauss-Seidel method. Relaxation method.
Evaluation	Continuous control: 40%; Final exam: 60%.