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## MATHEMATICAL METHODS FOR ENGINEERS

CODE 104823 2020/2021 6 cfu during the 1st year of 11159 BIOENGINEERING(LM-21) - GENOVA ING-IND/31 Italian (English on demand) GENOVA 1° Semester AULAWEB

## OVERVIEW

The course provides the theoretical bases to formulate mathematical models starting from experimental data. Basic knowledge is provided about mathematical models, numerical computation, regularization, numerical simulation of devices and systems.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course aims to provide a complex of knowledge that allows the understanding and use of the main mathematical tools for numerical calculation, treatment and analysis of experimental data, interpretation and formulation of physical models -mathematics.

### AIMS AND LEARNING OUTCOMES

At the end of the course the student will know the numerical methods for approximation, differentiation and integration of functions, the solution of ordinary differential equations systems, the singular values decomposition of matrices. He/she will also know the variational methods and their application to modeling.

Linear algebra

### TEACHING METHODS

lessons: 42 hours

computer laboratory: 10 hours

### SYLLABUS/CONTENT

Normed spaces, orthonormal spaces, operators. Function approximation in a normed space, best uniform approximation. Numerical differentiation and integration. Numerical solution of ordinary differential equations (ODE). Compatibility of linear systems. Least squares solution. Singular value decomposition (SVD) of a matrix with applications. Variational calculus: Euler-Lagrange equations. Variational formulation of physico-mathematical models. Approximate solution of linear and nonlinear ODE - PDE by weighted-residual methods. Applications: traffic models, nonlinear propagation.

-) material provided by the lecturer (PdF notes distributed by the teacher)

-) main reference textbook (in Italian): Mauro Parodi: “Metodi matematici per l’ingegneria” Levrotto&Bella ed., Torino, 2013

## TEACHERS AND EXAM BOARD

### Exam Board

MAURO PARODI (President)

MARCO STORACE

ALBERTO OLIVERI (President Substitute)

## LESSONS

### LESSONS START

Regular (see calendar at http://www.ingegneria.unige.it/index.php/orario-e-calendario-delle-lezi…)

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

The exam is divided in two parts; each of them is referred to a half of the program. Each part consists in the explanation of one topic chosen by the student and one topic chosen by the teacher.

### ASSESSMENT METHODS

The exam will allow assessing the true comprehension of the topics explained during the lessons and the ability of the student to explain a topic in a precise and concise manner.

### Exam schedule

Date Time Location Type Notes
18/02/2021 10:00 GENOVA Esame su appuntamento
17/09/2021 10:00 GENOVA Esame su appuntamento