MC07CM01 - Acquire a vision on the capacity and power of mathematics to solve practical

problems, and of its applications in a wide variety of areas.

M07CM02 - Develop the ability to find solutions, take decisions and propose operational methods

to other sciences or engineering disciplines.

M07CM03 - Foster the ability to use mathematics. Mathematics are also a tool that students need to

learn how to use.

- Learn about interactions between different parts of mathematics towards achieving a common objective.

- Know real situations, practical problems and their mathematical modeling.

- Learn about modeling models, including their origin and their own history.

- Gain experience in decision-making when approaching a practical situation and accepting the model.

1. INTRODUCTION TO MATHEMATICAL MODELLING.

2. MATHEMATICS IN THE PRESENT-DAY SOCIETY OF INFORMATION AND

IMAGES.

Google Mathematics. Image compression. Digitalisation. Corrective codes. Secure data.

Digital signature.

3. MODELS IN BIOLOGY.

Growth models in a population. Interaction models between species. Health-based

models.

4. MODELS IN PHYSICS.

Deformation of a continuous medium. Conservation laws. Introduction to fluid

mechanics.

5. PRACTICAL WORK.



Practical work is done with computers, implementing and applying the algorithms

studied and described in the theoretical part of the subject.

The theoretical content will be explained in lectures, following basic references that

appear in the Bibliography and material of compulsory use. Lectures are complemented

with problem-solving classes (practical sessions) in which students will be asked to

solve questions where the knowledge acquired in the theoretical classes will be applied.

Representative questions and examples of the subject content will be worked on

seminars. These will usually be notified in advance so that the students can work on

them with a view to later reflection and discussion in a dedicated session. Practical work

with computers aimed at acquiring skills in the subject will also be done.



Students will do individual work on theory and problems in periodic seminars with the

support of the professor.



An important part of the student's work is of an individual nature. The professors will

provide guidance for this work and will encourage students to do it with regularity and

enthusiasm. Students are also encouraged to make use of one-to-one tutorials to clarify

any doubt of difficulty they may encounters in the subjects.

CRITERIA FOR CONTINUOUS ASSESSMENT

Written exam: 65%

Preparation, drawing up and presentation of individual work: 20%

Handing in of exercises and active participation in the different sessions: 15%

To pass the subject, the student needs to obtain a mark of 4 out of 10 in the final written

exam.





CRITERIA FOR FINAL ASSESSMENT

A student who does not wish to participate in continuous assessment may officially

withdraw from it in writing to the professor responsible for his/her subject, within 15

weeks of the start of the term. As well as taking the exam, a student who chooses the

final evaluation modality will have to take a complementary test during the official

exam period, designed for the overall assessment of the activities carried out during the

year. This test may consist of an oral presentation, a computer-based demonstration or a

written description of the practical knowledge acquired in the activities carried out

during the year. To pass the complementary test it will be necessary to obtain at least 5

out of 10.





WITHDRAWAL:

A student who has completed the activities during the academic year but who does not

present him/herself for the ordinary call will be graded as "not presented".

- The teachers will upload useful material in the eGela virtual classroom.
- Information obtained from Internet.
- Scientific software as Mathematica.

Basic bibliography

M. BRAUN: Differential Equations and Their Applications: An Introduction to Applied Mathematics, fourth edition, Springer, 1992.

L. EDELSTEIN-KESHET: Mathematical Models in Biology, SIAM, 2005.

R. HABERMAN: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, SIAM, 1998.

P.C. HANSEN, J.G. NAGY Y D.P O LEARY: Deblurring Images: Matrices, Spectra, and Filtering, SIAM, 2006.

E. KALNAY: Atmospheric Modelling, Data Assimilation and Predictability, Cambridge University Press, 2004.

O. PAPINI Y J WOLFMAN: Algèbre discréte et codes correcteurs, Springer, 1995.