- Docente: Fabiana Zama
- Credits: 5
- SSD: MAT/08
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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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
Office hours
See the website of Fabiana Zama