29161 - Mathematical Methods M

Course Unit Page

Academic Year 2020/2021

Learning outcomes

To know and to be able to use some mathematical techniques for the information engineering. Competencies: to know the theory of linear differential equations and systems; to be able to solve constant coefficient linear differential equations and systems; to know the Laplace transform and its use in solving linear differential equations; to have a basic knowledge of dynamical systems. Detailed contents: linear ordinary differential equations, Cauchy problem, existence and uniqueness of solutions. First-order linear equations. Discussion of existence and uniqueness of solutions of first-order differential equations and applications. Higher-order linear differential equations. Numerical solutions of differential equations. Introduction to nonlinear systems. Laplace transform: definition, convergence abscissa; formal properties of the Laplace transform; Laplace transforms of standard functions. Step functions and their transforms. Laplace transforms of some further special functions: the saw-tooth function, the Dirac delta. Applications of Laplace transform to ordinary differential equations: theory and application in solving simple ordinary differential equations with constant coefficients and given boundary conditions. Basic facts about linear transformations; eigenvalues, eigenvectors. Systems of linear differential equations; matrix exponential; dynamical systems, stability; numerical solutions of differential equations. General form of solutions. Transfer function. Stabilization problem.

Course contents

Graph theory (Module1)

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.

A detailed program could be found also on the e-learning platform Insegnamenti On-line.


Graph theory (Modulo 1)

Official textbook

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/

Support textbooks

J.A. Bondy and U.S.R. Murty, "Graph theory",
Springer Series: Graduate Texts in Mathematics, Vol. 244 (2008)

R. Diestel, "Graph theory", Springer Series: Graduate Texts in Mathematics, Vol. 173 (2005)
Freely downloadable at http://diestel-graph-theory.com/basic.html (3 MB).

Teaching methods

Lectures and exercises

Assessment methods

Graph Theory (Module 1)

Both parts of the exam on line will be on Microsoft Teams

The exam is made up of two parts: a mid-term test with exercises and a final oral exam. Students are invited to show the University badge before starting both the parts.

Examples of mid-term test are published on the e-learning platform Insegnamenti On-line. The date of the mid-term test is published at http://www.dm.unibo.it/~ferri/hm/ricapp.htm. The mid-term test MUST be passed with a score of at least 14 (over 24). If a student don't pass, they must recover it; the dates for recovering are published on http://www.dm.unibo.it/~ferri/hm/ricapp.htm.

Apply for the final oral exam at AlmaEsami. The final exam is on the whole program published also on the e-learning platform Insegnamenti On-line and is as follows: Two subjects are proposed to the students (each of which is either the title of a long chapter, or the sum of the titles of two short ones); the students choose one and write down all what they remember about it, without the help of notes, texts, electronic devices; a discussion on their essay and in general about the chosen subject follows. It is an oral examination, so writing is only a help for the student to gather ideas.

Final mark and verbalization

The final grading is given by the arithmetic average of the grades in the mathematical analysis and graph theory part. Verbalization is made by Prof. Ferri. Prof. Ferri signs the grades on Almaesami within 5 days from the completion of the two parts of the exam. The student who does not accept the final grade must communicate his/her decision to Prof. Ferri by e-mail within 5 days from the completion of the exam and, in such case, shall repeat the complete exam (Graph Theory + Mathematical Analysis).

Teaching tools

Graph theory (Module 1)

Textbook available at http://book.huihoo.com/pdf/graph-theory-With-applications/

Additional material is published on the e-learning platform Insegnamenti On-line and on the program page.

Office hours

See the website of Massimo Ferri

See the website of Donatella Giuliani