Department of Fundamental Education in Science and Technology

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

Lecturer	Karima BESSIOUD
Information	Bachelor - Second Year : Chemical engineering Department of Fundamental Education in Science and Technology Website : https://www.univ-soukahras.dz/en/module/2391 Semester : S4 Unit : UEF 2.2.2 Credit : 4 Coefficient: 2
Content	Contents : Chapter 1.Solving nonlinear equations f(x)=0 (3 Weeks) 1. Introduction to calculation errors and approximations, 2. Introduction to methods for solving non-linear equations, 3. bisection method, 4. successive approximation method (fixed point), 5. Newton-Raphson method. Chapter 2: Polynomial interpolation (2 weeks) 1. General introduction, 2. Lagrange polynomial, 3. Newton polynomial. Chapter 3. Function Approximation (2 weeks) 1. Approximation method and root mean square. 2. Orthogonal or pseudo-Orthogonal systems. Approximation by orthogonal polynomials, 3. trigonometric approximation. Chapter 4: Numerical Integration (2 weeks) 1. General introduction, 2. trapezium method, 3. Simpson\'s method, 4. quadrature formulas. Chapter 5: Solving ordinary differential equations (Initial condition or Cauchy problem) (2 weeks) 1. General introduction, 2. Euler\'s method, 3. Improved Euler\'s method, 4. Runge-Kutta\'s method. Chapter 6.Method of directly solving systems of linear equations(2 Weeks). 1. Introduction and definitions, 2. Gauss method and pivotation, 3. LU factorization method, 4. ChoeleskiMMt factorization method, 5. Thomas algorithm (TDMA) for tridiagonal systems. Chapter 7: Approximate solution method for systems of linear equations (2 weeks) 1. Introduction and definitions, 2. Jacobi method, 3. Gauss-Seidel method, 4. Use of relaxation.
Evaluation	Continuous assessment: 40%; Final examination: 60%.