OVERVIEW

The course will introduce and analyze fundamental tools for the numerical solution of mathematical problems and for the mathematical modeling of complex systems, with application in the field of Bioengineering.

AIMS AND CONTENT

LEARNING OUTCOMES

The module aims at introducing some of the main mathematical tools that are largely used in applications, and experimenting with them using the PC. Specific topics include: iterative algorithms The module aims at introducing some of the main mathematical tools that are largely used in applications, and experimenting with them using the PC. Specific topics include: iterative algorithms and gradient methods, interpolation, regularization and inverse problems.

AIMS AND LEARNING OUTCOMES

The course will provide the mathematical basis allowing the student to treat a diverse class of problems of interest in the field of bioengineering; lectures will focus on both computational techniques, as well as modeling tools for complex systems. In order to better understand the presented topics, theoretical lectures will be complemented by exercises also involving the use of the PC.

At the end of the couse, the student will be able to

• select the proper mathematical tools for solving a large class of problems;
• understand potential and limitations of the learned techniques;
• use the PC to analyze and explore mathematical models of complex systems;
• work in a small team, sharing ideas and discussing how to best develop a project.

PREREQUISITES

elements of calculus and linear algebta

TEACHING METHODS

Lectures and computer exercises, done in groups and consisting in realizing a small project and writing a report.

SYLLABUS/CONTENT

• Elements of linear algebra and matrix computation
• Iterative algorithms
• Polinomial interpolation and splines
• Numerical integration
• Least squares and inverse problems
• Statistical approach to inverse problems

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes provided by the teacher

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/11159/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam

ASSESSMENT METHODS

During the oral test the candidate may be required to

• address and solve a given problem;
• introduce and address a general topic, such as ‘Lagrange interpolation’ or ‘Iterative algorithms for zeros of functions’;
• graphically represent one of the problems studied;
• discuss the operation of one of the Matlab codes developed during the exercises.

Laboratory exercises carried out during the year are also handed in, in order to test the ability to use complex mathematical models on the computer.