# NUMERICAL CALCULATION AND PROGRAMMING

3 credits during the 3nd year of 8757 Chemistry and Chemical Technologies (L-27) GENOVA

OVERVIEW

The course is an introduction to the Numerical Analysis, and it consists in the description of strategies and algorithms for basic mathematical problems solution. Particular attention is paid to the use of computer and to the analysis of the numerical problems linked to it. Complete the course some laboratory lessons, where numerical techniques are translated into MatLab Programs for solving simple mathematical problems, with particular attention to the interpretation of the numarical results.

## AIMS AND CONTENT

LEARNING OUTCOMES

*Knowledge and understanding** **of concepts** **and** **fundamentals of** **numerical computation**.*

*Particular emphasis** **is given to:*

*•** **the understanding** **of the aspects** **related to the** **numerical** **solution** **of** **problems such as** ** conditioning** **and** **stability**;*

*•** **the understanding** **of the concept of** **approximate solution** **as a means** **to solve real problems**.*

Knowledge and understanding of concepts and fundamentals of numerical calculation . Particular emphasis is given to the understanding of numerical aspects related to the solution of problems , such as air conditioning and stability ; the understanding of the concept of approximate solution as a means to solve real problems .

AIMS AND LEARNING OUTCOMES

Resolution, from the numerical point of view, of basic mathematical problems, such as the root finding of a real function, polynomial interpolation, the solution of square linear systems or of overdetermined linear systems, using direct or iterative methods. Particular attention is paid to some basic numerical concepts, such as the conditioning of a problem and the stability of an algorithm, and to the interpretation of the results obtained by using floating point arithmetic.

Teaching methods

Theoretical lessons complemented by practical lessons using Personal Computer Hours of lectures: 32 (teacher Fassino) Lab hours: 24 (teacher Fassino with Federico Benvenuto )

SYLLABUS/CONTENT

The program covers topics from different areas:

Error Analysis: the use of thefloating point arithmetic and algorithmic errors, the cancellation and round-off error. Conditioning of the problem of in the evaluating a real function. Solution of nonlinear equations: the bisection method, the Newton-like methods. Interpolation: the interpolating polynomial in the Lagrange form, analysys of the interpolation error. Matrix operations, vector and matrix norms. Solution of linear systems: backward substitution method for triangular systems, the Gauss method and Jacobi method for square systems. The condition nuber of a matrix. Overdetermined systems: the method of the normal equations. The regression line. For the laboratory part, the use of the MatLab language.

RECOMMENDED READING/BIBLIOGRAPHY

Bevilacqua-Bini-Capovani-Menchi: “Introduzione alla Matematica Computazionale”, Zanichelli

Bini-Capovani-Menchi: “Metodi Numerici per l’Algebra Lineare”, Zanichelli

## TEACHERS AND EXAM BOARD

**Ricevimento:**
By appointment by sending an email to fassino at dima.unige.it

Exam Board

CLAUDIA FASSINO (President)

FABIO DI BENEDETTO

FEDERICO BENVENUTO

## LESSONS

Teaching methods

Theoretical lessons complemented by practical lessons using Personal Computer Hours of lectures: 32 (teacher Fassino) Lab hours: 24 (teacher Fassino with Federico Benvenuto )

LESSONS START

The course is developed on the first and second semester, following the timetable set out in the "Manifesto"

## EXAMS

Exam description

Laboratory test, written test, oral examination

Assessment methods

Laboratory test , written examination , oral examination