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## NUMERICAL METHODS

CODE 94789 2021/2022 3 credits during the 1st year of 9269 Mechanical Engineering - Design and Production (LM-33) GENOVA MAT/08 Italian GENOVA (Mechanical Engineering - Design and Production) 2° Semester This unit is a module of: AULAWEB

## OVERVIEW

The use of numerical methods for solving problems whose analytical solution is unknown is of fundamental importance in many applications. The module aims to provide the student knowledge of numerical methods for solving Mechanical Engineering problems. Lectures are supported by laboratory exercises carried out using Matlab.

## AIMS AND CONTENT

### LEARNING OUTCOMES

Many applications require at the end of the theoretical development the resolution of a problem of various nature that cannot be solved analytically, but requires the implementation of numerical methods. The choice and practical implementation of such methods is often complex and can lead to difficulties even when using software, because instability, lack of convergence, etc. may appear. The module aims to provide the student with the ability to correctly choose a numerical method to solve a problem, understand and fix instabilities, and use Matlab to compute the solution.

### AIMS AND LEARNING OUTCOMES

Active participation in lectures and individual study will allow the student to:

- choose the most appropriate numerical method to solve some problems that require numerical resolution;

- understand why numerical instabilities or lack of convergence may appear and how to avoid such difficulties;

- know the basics of numerical methods for solving systems of nonlinear equations, data fitting and least squares, systems of differential equations and constrained and unconstrained optimization, finite differences for partial derivative equations;

- implement these methods using Matlab, the most widely used scientific computing software in the world;

- be able to use Matlab functions other than those seen in the course and debug the code.

### TEACHING METHODS

Each lecture consists of a frontal lecture in which the numerical methods are described, and an exercise carried out in Matlab in which the methods seen are applied to a problem of interest to Mechanical Engineering.

### SYLLABUS/CONTENT

Since the theoretical lectures are complemented by implementation in Matlab, the theoretical part is not particularly extensive. The focus is mainly on the practical aspects of the numerical methods considered.

The main topics covered are listed below:

- introduction to Matlab: matrices and vectors, 1d and 2D graphics, control structures, functions, creation of an app;

- numerical methods for solving equations and nonlinear systems;

- polynomial interpolation, data fitting, least squares method;

- numerical resolution of systems of ordinary differential equations;

- numerical methods for constrained and unconstrained optimization.

The notes taken during the lessons and the material provided ( notes of the theoretical part and tutorial of Matlab) are sufficient for the preparation of the exam. The books listed below are suggested as possible support texts and in-depth study.

- Quarteroni, F. Saleri, Introduzione al Calcolo Scientifico, Sprinter-Verlag 2006

-  Quarteroni, Modellistica Numerica per Problemi Differenziali, Springer-Verlag 2008

- S. Chapra, R. Canale, Numerical methods for Engineers, McGraw-Hill, 2018

## TEACHERS AND EXAM BOARD

### Exam Board

ENRICO MASSA (President)

PATRIZIA BAGNERINI (President Substitute)

DANILO PERCIVALE (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/9269/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

The exam consists in passing an oral test. Examination dates are arranged with the teacher by appointment.

### ASSESSMENT METHODS

Nella prova orale viene richiesto di svolgere una breve applicazione in Matlab (con la possibilità di utilizzare l’help) e di rispondere a una domanda sulla parte teorica.

### Exam schedule

Date Time Location Type Notes
10/01/2022 09:00 LA SPEZIA Scritto
02/02/2022 09:00 LA SPEZIA Scritto
10/06/2022 09:00 LA SPEZIA Scritto
14/07/2022 09:00 LA SPEZIA Scritto
14/09/2022 09:00 LA SPEZIA Scritto