73485 - Numerical Analysis M

Academic Year 2017/2018

  • Docente: Fabiana Zama
  • Credits: 5
  • SSD: MAT/08
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Chemical and Process Engineering (cod. 8896)

    Also valid for Second cycle degree programme (LM) in Environmental Engineering (cod. 8894)

Learning outcomes

The course aims to provide the knowledge of computational tools necessary for the solution of classical engineering  applied mathematical problems. The course includes a laboratory activity in which  MATLAB software and advanced software packages  are used.

Course contents


The student has the knowledge of mathematical analysis and geometry taught in courses of Mathematical Analysis and Geometry of the Environmental Engineering  Bachelor course.

All lectures will be held in Italian. It is therefore necessary to understand the Italian language to successfully attend the course and to be able to use the educational material provided.

Program

Definition of numerical problems and main sources of error.

Conditioning of a problem. Stability of an algorithm.

Numerical solution of linear systems

Study of the Problem conditioning. Algorithm for the lower and upper triangular system. LU factorization algorithm with and without row interchanges. algorithm stability pivoting methods.
Direct methods for special matrices.

Numerical Methods for equations and non-linear systems.

Conditioning and error parameters.
Methods for nonlinear equations: bisections, Secant Newton.
Methods for non-linear systems of equations.

interpolation Polynomial

Linear Least Squares Problem: QR factorization and SVD


Ordinary Differential Equations

Cauchy problem; existence of the solution; stability; One-step methods; error check; Multi-Step Methods;
Convergence Consistency and Stability;
Stiff problems;

Readings/Bibliography

G. Monegato, Fondamenti di Calcolo Numerico, Levrotto & Bella.

M.T.Heath, Scientific Computing, Mc Graw Hill, 2002

S. Attaway, Matlab: A Practical Introduction to Programming and
Problem Solving, Elsevier 2009


Teaching methods


Lectures and guided exercises in the laboratory.

Assessment methods


Laboratory projects and written test.

The final assessment consists of the average of the scores obtained in the two tests.

Teaching tools


Lecture slides available on AMS Campus.

Links to further information

http://www.dm.unibo.it/~zama/

Office hours

See the website of Fabiana Zama