# 72687 - Applied Mathematics (2nd cycle)

### Course Unit Page

• Teacher Marco Antonio Boschetti

• Learning modules Marco Antonio Boschetti (Modulo 1)
Eleonora Cinti (Modulo 2)

• Credits 6

• SSD MAT/09

• Teaching Mode Traditional lectures (Modulo 1)

• Language Italian

• Campus of Cesena

• Degree Programme Second cycle degree programme (LM) in Electronics and Telecommunications Engineering for Energy (cod. 8770)

• Course Timetable from Sep 15, 2022 to Dec 15, 2022

Course Timetable from Sep 21, 2022 to Dec 21, 2022

## Learning outcomes

The student will have knowledge of Physical and Engineering models formulated through partial derivatives and operations research techniques. In particular the student will be able to: i) identify and manage some well defined problems formulated through differential equations of the second order of parabolic type (diffusion), elliptic (Laplace/Poisson), hyperbolic (wave equations); ii) formulate a decision and optimization model and analyze its complexity. The student will be able to define advanced solution algorithms for these problems.

## Course contents

Module 1 (Optimization):

• Models of optimization and decision problems
• Computational complexity
• Linear and nonlinear optimization models
• Exact algorithms for linear and non linear problems
• Heuristic algorithms for linear and non linear problems
• The use of mathematics in heuristic algorithms
• Construnction algorithms and local search methods
• Classical MetaHeuristics
• Applications

Use of the proposed techniques to solve families of optimization problems in specific application areas (e.g., network design, packing, location, etc...)

Module 2

1. Diffusion. The heat/diffusion equation with one-dimensional space variable. Dirichlet, Neumann and Cauchy problems. Existence, uniqueness and continuos dependence of solutions.

2. Laplace/PoissonHarmonic functions of two real variables, average formula, maximum principle. Dirichlet and Neumann problem for the Laplace operator in a circle.

3. Waves and vibrationsThe D’Alembert equation with one-dimensional space variable. Dirichlet, Neumann and Cauchy problems. Existence, uniqueness and continuos dependence of solutions.

Slides of the lectures available online

## Teaching methods

Frontal lectures and exercises

## Assessment methods

Module 1

The exam aims to test the understanding of course content through the development of a project. The project can also be carried out in groups with a maximum of two students. Groups must register by the end of the module by sending an email to the lecturer. The teacher assigns the group a specific problem and the objectives to be achieved by a fixed date, usually the first exam date after the conclusion of the course. Students can interact with the teacher during this period by appointment. At the end of the period, students must submit to the teacher a short report that describes the project and summarizes the results achieved. The teacher evaluates the report and fixes a meeting with the students in which the content is examined and it is verified the individual contribution of each student to the results achieved.

For students who do not attend to the course and do not carry out the project during the course it will be defined by the teacher a specific timing according to the specifications above.

The evaluation of the module is expressed as a mark in thirtieths.

Module 2

The exam aims to test the understanding of course content through an oral test including theory questions and exercises.

The evaluation of the module is expressed as a mark in thirtieths.

Overall evaluation

The overall mark is the average of the marks obtained in the two modules.

## Teaching tools

Teaching Material, slides and exercise available online

## Office hours

See the website of Marco Antonio Boschetti

See the website of Eleonora Cinti