Corso Vittorio Emanuele II, 39 - Roma 0669207671

Computer engineering (Academic Year 2018/2019) - Information and communication technologies engineering (reserved for the students of Helwan University, Cairo, Egypt)

Numerical Methods


Credits: 6
Content language:French
Course description
The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described.
Prerequisites
Basic linear algebra and computer programming.
Program
  • Basic concepts of floating-point arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
  • Linear systems: direct methods (Gaussian eliminitations, LU-decomposition, Choleski) and iterative methods (Jacobi, Gauss-Seidel, SOR).
  • Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.
  • Non-linear equations and systems: Newton's method and its discrete variants, fixed-point iteration.
  • Numerical integration: Newton-Cotes formulas, Gaussian quadrature rules, composite rules.
  • Initial value problems for ordinary differential equations: one-step methods (Runge-Kutta methods) and multistep (Adams) methods. Stiff problems.
Book
“Numerical Methods – Part I ”, Uninettuno University Press - McGraw-Hill, 2013 (available on the Uninettuno University Press bookstore).
“Numerical Methods – Part II ”, Uninettuno University Press - McGraw-Hill, 2013 (available on the Uninettuno University Press bookstore).
Professor/Tutor responsible for teaching
Clemente Cesarano
Video professors
Prof. Giovanni Monegato - Politecnico di Torino (Torino - Italy)