- Docente: Massimo Ferri
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Moduli: Massimo Ferri (Modulo 1) Simonetta Abenda (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Telecommunications Engineering (cod. 9205)
Also valid for Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)
Second cycle degree programme (LM) in Electrical Energy Engineering (cod. 8611)
Learning outcomes
In the first part the student is supposed to learn the different types of graphs, their matrix representations, the related invariants and the problems which can find a model and solution in Graph Theory. In the second part, differential equations of the first and second order are studied. Note: This course is taken from the Second-cycle Degree in Ingegneria Elettronica.
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