Corso Vittorio Emanuele II, 39 - Roma 0669207671

Civil Engineering (Academic Year 2016/2017) - Edilizia e Progettazione (ad esaurimento)

Numerical methods


Credits: 6
Content language:English
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
.
Objectives
.
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).
Exercises
.
Professor/Tutor responsible for teaching
Maria Francesca Carfora
Video professors
Prof. Giovanni Monegato - Politecnico di Torino (Torino - Italy)
List of lessons
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
    •  Lesson n. 6: Linear Systems  Go to this lesson
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
    •  Lesson n. 15: Cubic splines  Go to this lesson
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato
Giovanni Monegato