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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Arturo Vieiro Yanes, [en] The integral over a bounded interval $[a, b]$ of a continuous $f$ function can be numerically approximated using interpolation or Gaussian quadrature formulas, which evaluate the function $f$ in $m + 1$ abscissas. The choice of abscissas is essential in Gaussian integration to obtain exact formulas for polynomials of degree less than or equal to $2m + 1$, improving the accuracy of interpolation formulas. From a numerical point of view, quadrature formulas that provide a small error with few evaluations of $f$ are needed. One of these formulas is the one provided by the double exponential method, which consist of using a suitable transformation that maps the endpoints of the interval of integration to infinity, in order to obtain a double exponential decay of the integrant, and then apply the trapezoidal formula. We will see that this method allows to approximate converging improper integrals with singularities at the endpoints and that it can be adapted to approximate oscillatory integrals with different types of decay. Oscillatory integrals with a fast decay of the integrand are naturally found in dynamical systems when the Melnikov integral is considered to measure the splitting of separatrices. Throughout the work, some examples are analyzed and compared with numerical implementations using Pari/GP software.

La televisió local és molt important a dia d'avui. Dels 84 canals de televisió que hi ha a Catalunya, 50 són de televisions locals. Per tant, més de la meitat dels canals són televisions de proximitat. Quina és la clau de l'èxit de les televisons locals? Com es treballa el periodisme de proximitat? Aquestes preguntes són la base per fer un breu recorregut per la història de la primera televisió local i la seva evolució, i per investigar un cas concret, el de la Vallès Visió, la televisió local de referència del Baix Vallès (Vallès Oriental). La televisión local es muy importante a día de hoy. De los 84 canales de televisión que hay en Cataluña, 50 son de televisiones locales. Por lo tanto, más de la mitad de los canales son televisiones de proximidad. Cuál es la clave del éxito de las televisiones locales? Cómo se trabaja el periodismo de proximidad? Estas preguntas son la base para hacer un breve recorrido por la historia de la primera televisión local y su evolución, y para investigar un caso concreto, el de Vallés Visió, la televisión local de referencia del Baix Vallés (Vallés Oriental). Nowadays the local television is very important. From the 84 television channels that there are in Catalonia, 50 are of local televisions. Therefore, more than the half of the television channels are local. Which is the key of the local television's success? How does it work local television? These questions are the base of a short tour through the history of the first local television and its evolution, and to investigate a specific case, the one of Vallès Visió, the reference local television of Baix Vallès (Vallès Oriental).

My starting point for the elaboration of this project was the promotion of a dwelling with orientation to the north and energy performance certificate grade B, given that dwelling orientation renders difficult obtaining such certificate, a factor that appeared relevant to me. Therefore, after undertaking the DAC of environmental impact on the building, it was so clear to me that I wanted to focus my final project on energy efficiency that I did not hesitate whatsoever when I was proposed the possibility to collaborate in the elaboration and follow-up of the construction of this project. The main objective of this project was to undertake the full monitoring of the construction of the above-described dwelling thus valuing the use of all the constructive solutions in order to obtain an energy performance certificate grade B. The methodology required to execute this project was focused on three main aspects: preliminary study of the project, follow-up of the construction’s execution through weekly visits on the ground together with the drafting of different minutes, and lastly the analysis of the whole executive process thus reflecting this whole process in this project. Finally, I expose some conclusions where I link the experience lived in this project through the practicum, in addition to the viability of a project execution leading to an energy performance certificate grade B and its possible variations.