#ABOUT Semester 1 in L'Aquila;

Foundations of Applied Mathematics

The first semester at UAQ is common to all students. It provides a sound background in applied mathematics based on advanced theoretical subjects such as functional analysis, applied partial differential equations, dynamical systems, continuum mechanics, and control systems.

This semester prepares the students to perform simulations in diverse modelling frameworks, as well as to successfully tackle subjects in semester 2 such as advanced numerical calculus, optimization, and stochastic calculus. To perform this task, Semester 1 courses provide a systematic approach to the formulation of applied problems in interdisciplinary fields, and a rigorous approach to mathematical modelling. More precisely, students in this semester are provided “exact” resolution methods for (ordinary and partial) differential equations, the “infinite dimensional” approach of functional analysis (needed in approximation theory, variational calculus, and numerical analysis), a modern and “engineering oriented” approach to control, and an introduction to the mathematical theory of continuum media, a subject that is touched by several specialization tracks.

Teaching staff with longstanding experience with international joint programs in applied mathematics is in charge of this semester. The University of L’Aquila features a research group in mathematical analysis combining three generations of applied mathematicians with excellent international reputation in their field and with an outstanding research record, with main focus on partial differential equations with applications to physics, engineering, social sciences, biology and medicine.

#Semester 1 in L'Aquila EMJMD InterMaths Study Track

Foundations of Applied Mathematics;


University of L'Aquila





ECTS Credits



Real and Functional Analysis

ECTS Credits: 6   |   Semester: 1   |   Year: 1   |   Campus: University of L'Aquila   |   Language: English

Unit Coordinator: Marco Di Francesco


  • Introducing basic tools of advanced real analysis such as metric spaces, Banach spaces, Hilbert spaces, bounded operators, weak convergences, compact operators, weak and strong compactness in metric spaces, spectral theory, in order to allow the student to formulate and solve linear ordinary differential equations partial differential equations, classical variational problems, and numerical approximation problems in an "abstract" form.


  • Metric spaces, normed linear spaces. Topology in metric spaces. Compactness.
  • Spaces of continuous functions. Convergence of function sequences. Approximation by polynomials. Compactness in spaces of continuous functions. Arzelà's theorem. Contraction mapping theorem.
  • Crash course on Lebesgue meausre and integration. Limit exchange theorema. Lp spaces. Completeness of Lp spaces.
  • Introduction to the theory of linear bounded operators on Banach spaces. Bounded operators. Dual norm. Examples. Riesz' lemma. Norm convergence for bounded operators.
  • Hilbert spaces. Elementary properties. Orthogonality. Orthogonal projections. Bessel's inequality. Orthonormal bases. Examples.
  • Bounded operators on Hilbert spaces. Dual of a Hilbert space. Adjoin operator, self-adjoint operators, unitary operators. Applications. Weak convergence on Hilbert spaces. Banach-Alaoglu's theorem.
  • Introduction to spectral theory. Compact operators. Spectral theorem for self-adjoint compact operators on Hilbert spaces. Hilbert-Schmidt operators. Functions of operators.
  • Introduction to the theory of unbounded operators. Linear differential operators. Applications.
  • Introduction to infinite-dimensional differential calculus and variational methods.


Basic calculus and analysis in several variables, linear algebra.

Reading list:

  • John K. Hunter, Bruno Nachtergaele, Applied Analysis. World Scientific.
  • H. Brezis, Funtional Analysis, Sobolev Spaces, and partial differential equations. Springer.
Dynamical systems and bifurcation theory

ECTS Credits: 6   |   Semester: 1   |   Year: 1   |   Campus: University of L'Aquila   |   Language: English

Unit Coordinator: Bruno Rubino

Aims: The course is intended to introduce and develop an understanding of the concepts in nonlinear dynamical systems and bifurcation theory, and an ability to analyze nonlinear dynamic models of physical systems. The emphasis is to be on understanding the underlying basis of local bifurcation analysis techniques and their applications to structural and mechanical systems.

Content: Review of: first-order nonlinear ODE, first-order linear systems of autonomous ODE. Local theory for nonlinear dynamical systems: linearization, stable manifold theorem, stability and Liapunov functions, planar non-hyperbolic critical points, center manifold theory, normal form theory. Global theory for nonlinear systems: limit sets and attractors, limit cycles and separatrix cycles, Poincaré map. Hamiltonian systems. Poincaré-Bendixson theory. Bifurcation theory for nonlinear systems: structural stability, bifurcation at non-hyperbolic equilibrium points, Hopf bifurcations, bifurcation at non hyperbolic periodic orbits. Applications.

Pre-requisites: Ordinary differential equations

Reading list: Lawrence Perko, Differential equations and dynamical systems, Springer-Verlag, 2001

Practical information for your semester in L'Aquila

Academic Calendar & Term dates

Key Dates
2021/22 [all dates TBC]
Welcome and Induction Weeks

13 - 24 September 2021

Semester 1

27 September 2020 - 21 January 2021

Christmas vacation

23 December 2021 - 6 January 2022

Semester 1 examinations

24 January - 4 March 2022

Bank Holidays

1 November, 8 December, 6 April, 25 April, 1 May, 2 June, 10 June, 15 August

Course Timetables

Course timetables and updates are available on our department (D.I.S.I.M.) website

Graduation Calendar

Additional graduation sessions might be set for our joint programmes, please refer to your coordinators for more details.

Visa information

Applying for an Italian study visa

Non-EU students selected to study at the University of L'Aquila will need to apply for a student visa at the nearest Italian Embassy/Consulate. The visa application requirements and processing time can be lengthy, taking anywhere from a few weeks up to several months. It is very important that you contact the nearest Italian Embassy for information as early as possible in the application process.

Please notice that, before joining our programmes, you will only need to apply for one visa only at an Italian Embassy/Consulate, as Italy is the location for your first semester/year. Afterwards, while you're spending your semester(s) in Italy, you will have the chance to apply for another visa, e.g. a German one if you're spending your Semester 2 in Hamburg, at the Germany Consulate based in Rome.

Web-based visa application on Universitaly.it

Starting from Academic year 2020-2021, the visa application procedure is completely web-based. Non-EU students not living in Italy are requested to pre-enrol using the online platform called UNIVERSITALY. Once your pre-enrolment request on Universitaly.it has been approved by the University of L'Aquila, you will receive a confirmation email. After that, you will have to get in contact with the local Italian Diplomatic-consular mission for the visa request process. Please note that the university confirmation email does not automatically imply the issue of a study visa. 

Documents required (to be submitted via Universitaly.it)

valid until 3 months after the expiry of your visa
Transcript of records
A transcript of records, issued by the competent academic authority, which records all the subject courses/exams included in the curriculum of your undergraduate studies.

Italian Residence Permit

If you need a visa to stay in Italy, remember that you will also have to apply for an Italian residence permit within 8 days after arriving in our country. A residence permit is indeed required when a foreigner stays in Italy for longer than three months.
The InterMaths team will assist you with preparing all the required documentation, which includes a couple of forms to be filled in and, among others:

A full copy of your passport (every single page, cover included)

A copy of your health insurance card

Accommodation proof

Financial proof

Enrolment certificate

All you need to do is visit any Italian post office and withdraw the required form known as "kit permesso di soggiorno" ("soggiorno" sounds like "sojjorno"). Then, bring it to campus and we'll fill it in together!
All the required documents will have to be put into an envelope and submitted to the local police station (questura) through a post office. At the end of the submission, the clerk at the post office will hand you three different receipts, which will be considered as your temporary residence permit.
When the police station (questura) has received your application, they'll fix an appointment for you (usually within a couple of weeks) to complete the rest of the required procedures, which includes an interview for fingerprints (carry with you passport & ID photos). Eventually, they'll hand out the plastic card you can see on this page.
The whole process will cost you around 120 euros.

Enrolment procedure

Upon arrival in Italy, you'll have to complete your enrolment at the University of L'Aquila, which is the coordinating institution of your MSc programme. The enrolment process involves a preliminary online phase (registration on our university info system, online pre-enrolment and fee payment), which is usually taken care of by our InterMaths team.
To finalize your enrolment, you'll then have to submit your translated and legalized qualifications, which include, depending on the case:

Declaration of Value (DoV)

The DoV is a document providing an official description of your academic certificates, duly legalized by the Consular office of the Italian Embassy in the country where such degree was gained.

CIMEA Statements of comparability

CIMEA has implemented a service of certification and comparison of Italian and foreign qualifications, with a view to rendering qualifications increasingly more comprehensible and recognizable.

Diploma Supplement

You may submit a Diploma Supplement (a document accompanying a higher education diploma ) to certify your previous qualification only if you gained your undergraduate degree from an EU institution issuing Diploma Supplements.
Note that the local Diplomatic-consular mission might still require that you obtain a Declaration of Value (DoV) in order to issue your study visa, although our university accepts either CIMEA or DoV as of academic year 2020/2021. If that is the case, you will have to go through the DoV request process instead of the CIMEA statements, which can be much lenghtier, so make sure you start the whole process in good time in advance.


All our students, both European and non-European, must hold valid insurance covering risks related to health, accidents, death, permanent invalidity, civil responsibility (including travel assistance) while they are outside their home country - that is to say, local students won't need any additional health insurance while studying in their home country.

Personal medical cover is required in most European countries, even in those that have a public health system. An insurance card will also be required by local authorities in order to apply for a residence permit after your arrival.

For all the Erasmus Mundus (EMJMD) students: a mandatory insurance coverage, covering risks related to health, accidents, death, permanent invalidity, civil responsibility, is provided to all students (whether they're scholarship holders or not) by the InterMaths Erasmus Mundus Joint Master Degree (EMJMD) Consortium.

To all the other students (double degree programmes, for instance).
In the months that precede your arrival we will send you information by email about the insurance coverage we recommend (the current student intake is being covered by Erasmus Plus Insurance by DrWalter, which costs 99 cents per day - taxes included). Then, you can decide to buy a different one by yourself (but we will not assist you in this case) or keep the one you may already have in your country. But, in any case your insurance coverage will have to comply with some minimum requirements established by the consortium.

Erasmus Plus Insurance by DrWalter

Below you can find some information about finding a place to stay in L'Aquila, which is going to be your first destination in your study programme. For details about housing in the other partner universities, just browse the related section from the top menu (e.g. Consortium > Vienna).

Housing options in L'Aquila

Currently, our university hasn't got its own halls of residence, though there is one in town managed by the Abruzzo Regional Agency for Education, aka A.D.S.U. (a link is provided below). But, as L'Aquila is undergoing huge reconstruction after the 2009 earthquake, we stronly suggest you opt for renting a flat from private owners. The cost per person ranges from 150 to 250 euros per month depending on several factors (e.g. shared or private rooms, utility bills included or not, area). Living near the campus (the area is a in a suburb in west L'Aquila known as Coppito) can be cheaper but this means staying on the outskirts away from the city life (events, night life, restaurants...).
Please make contact with Aquilasmus - ESN L'Aquila to receive support with finding a place to stay in L'Aquila
Housing Contact Form by Aquilasmus

Temporary accommodation in L'Aquila & Useful links

The Aquilasmus staff will typically meet you within a few days after your arrival to help you find a place to stay. For your first days in L'Aquila you may refer to the links below

ADSU Hall of Residence

ADSU (regional agency for education) - for temporary stays only! not available for academic year 2020/2021.

ADs on Univaq.it

Online ADs from private owners available on our university website

FB group

"Cerco/Affitto Casa a L'Aquila!" Facebook group


Vacation rentals in L'Aquila

Bed & Breakfast in L'Aquila

Vacation rentals in L'Aquila

Below you can find some information about how to get to L'Aquila, which is going to be your first destination in your study programme. For details about reaching the other partner universities, just browse the related section from the top menu (e.g. Consortium > Nice).

How to get to L'Aquila

Ideally located in central Italy, L'Aquila is at around 110 Km (68 miles) to the east of Rome and at 100 Km (62 miles) to the west of Pescara. Choose one of the following means of transport to find out more.
By plane
The closest international airports are:

Rome Fiumicino

main hub, aka Leonardo Da Vinci Airport

Rome Ciampino

aka G.B. Pastine Airport
Both airports are connected to L'Aquila by express coach service operated by Gaspari or Flixbus. Read the section below ("By Bus") for further information.
Another coach service (operated by T.U.A., aka as A.R.P.A.) is available from the "Tiburtina train station" (Stazione Tiburtina in Italian) located in East Rome.  But this means you'll have to firstly get on a train/bus/undeground from the airport to get to the "Tiburtina train station", which will take you one hour at least. So, we strongly suggest you use the other option, as such buses will be departing right from inside the aiport parking area.
A bunch of European cities are also connected to the Abruzzo Airport in Pescara, located at about 100 km to the east of L'Aquila.