- Docente: Massimo Ferri
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Moduli: Massimo Ferri (Modulo 1) Simonetta Abenda (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
-
Corso:
Second cycle degree programme (LM) in
Electrical Energy Engineering (cod. 8611)
Also valid for Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)
Second cycle degree programme (LM) in Telecommunications Engineering (cod. 9205)
Learning outcomes
At the end of the course the students know and are able able to use some mathematical techniques for the information engineering. They gather competencies on theory of linear differential equations and systems; they are able to solve constant coefficient linear differential equations and systems; they know the Laplace transform and its use in solving linear differential equations; they eventually get a basic knowledge of dynamical systems.
Course contents
Module 1
Graphs and subgraphs. Trees. Connectivity. Euler tours and Hamilton cycles. Matchings. Edge colourings. Independent sets and cliques. Vertex colourings. Planar graphs. Directed graphs. Hints at networks. Detailed information in http://www.dm.unibo.it/~ferri/hm/progmame.htm
Module 2
Normed spaces. Hilbert spaces. Fourier series and applications. Functions of a complex variable. Harmonic functions. Dirichlet's problem for Laplace equations. Fourier transform. Applications to the equations of heat transfer and waves. Hints of spectral theory.Readings/Bibliography
Module 1
J.A. Bondy and U.S.R. Murty, "Graph theory with applications",
North Holland, 1976.
Freely downloadable at http://book.huihoo.com/pdf/graph-theory-With-applications/
Module 2
Lecture notes of the teacher. The notes (pdf) will be made available through the institutional site AMS-Campus. Students can also make use of the following textbooks:
- Davide Guidetti: Notes of the course Mathematical Methods (Pdf file available on AMS-Campus:
http://campus.unibo.it/id/ eprint/157317) : Chapters 2 (normed spaces, Fourier series) and Chapter 4 (Fourier transform)
- Erwin Kreyszig: Advanced Engineering Mathematics, 10th Edition J. Wiley (2014) Chapters 6
(Laplace transform), Chapter 11 (Fouries series and Fourier transform ) and Chapter 12 (PDEs)
Teaching methods
Lectures and exercises.
Assessment methods
Module 1
A mid-term test with exercises. An oral exam.
Module 2
Written test with exercises and theory questions.
Teaching tools
Module 1
Textbook available at http://book.huihoo.com/pdf/graph-theory-With-applications/
Additional material at http://www.dm.unibo.it/~ferri/hm/progmame.htm
Module 2
Notes and exercises will be made available at AMS-Campus.
Office hours
See the website of Massimo Ferri
See the website of Simonetta Abenda