29161 - Mathematical Methods M

Academic Year 2017/2018

  • Docente: Massimo Ferri
  • Credits: 6
  • SSD: MAT/07
  • Language: Italian

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