Análisis y métodos numéricos con Geogebra

Cuaderno de prácticas de Matemáticas II, Grado en Ingeniería Informática, Universidad de Alicante.

Is Maths everywhere? Our students respond

Mathematics expresses itself everywhere, in almost every facet of life - in nature all around us, and in the technologies in our hands. Mathematics is the language of science and engineering - describing our understanding of all that we observe. In fact, Galileo said that Mathematics is the language with which God has written the universe. Aristotle defined mathematics as "the science of quantity", i.e., “the science of the things that can be counted”. Now you can think that counting has a vital role in our daily life; just imagine that there were no mathematics at all, how would it be possible for us to count days, months and years? Unfortunately, people usually ignore the connection between mathematics and the daily life. Most of university degrees require mathematics. Students who choose not to take seriously mathematics or to ignore it in high school, find several difficulties when they come up against them at the university. This study explores the perceptions of how mathematics influences our daily life among our students and how teachers can use this information in order to improve the academic performance. The used research instrument was a questionnaire that was designed to identify their understanding on learning mathematics.

The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

Manual de Matemàtiques II per al Grau de Química

L’edició d’aquest material s’ha fet dins el marc del conveni per a la promoció de l’ús social del valencià signat per la Universitat d’Alacant amb la Conselleria d’Educació de la Generalitat Valenciana.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Exàmens resolts de FMI 2, Grau en Enginyeria Civil, Cursos 2010-2011, 2011-2012 i 2012-2013

Exàmens resolts de Fonaments Matemàtics de l'Enginyeria II del Grau en Enginyeria Civil de la Universitat d'Alacant dels cursos 2010-2011, 2011-2012 i 2012-2013

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Privileged Regions in Critical Strips of Non-lattice Dirichlet Polynomials

This paper shows, by means of Kronecker’s theorem, the existence of infinitely many privileged regions called r -rectangles (rectangles with two semicircles of small radius r ) in the critical strip of each function Ln(z):= 1−∑nk=2kz , n≥2 , containing exactly [Tlogn2π]+1 zeros of Ln(z) , where T is the height of the r -rectangle and [⋅] represents the integer part.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

La Webquest: una metodología apoyada en la red para renovar la docencia en Educación Superior

La WebQuest responde a una estrategia didáctica basada en la incorporación de las TIC en el aula, cuyo sustento teórico está en las corrientes constructivistas y el aprendizaje colaborativo, siendo de este modo pertinente a las directrices del EEES. En virtud de ello, nos hemos propuesto enfocar nuestras prácticas docentes aprovechando dicha estrategia didáctica y los recursos disponibles en la Web 2.0. Ahora bien, consideramos que como paso previo a la implementación de cualquier recurso TIC necesitamos tener un profundo conocimiento sobre el mismo. Es por ello que, para el desarrollo del trabajo, hemos considerado llevar a cabo un proceso gradual dividido en tres fases. La primera, centrada en la apropiación de la WebQuest como herramienta metodológica, la unificación de criterios y significados en torno al qué, al cómo y al para qué de su implementación. La segunda, focalizada en el diseño de WebQuest y la generación de espacios colaborativos de evaluación de las mismas. La tercera, enfatiza la aplicación directa de WebQuest en nuestras clases y el seguimiento de éstas con fines investigativos. En esta comunicación damos cuenta del proceso llevado a cabo en la primera fase, destacando la multidisciplinaridad que caracteriza al equipo de trabajo.

Algunas estructuras matemáticas del campus de la Universidad de Alicante

Las Matemáticas alcanzan mayor interés entre los ciudadanos a partir del contacto y la experimentación con la realidad cotidiana que nos rodea. Es justamente en ella donde es posible plantear actividades de índole matemático que permitan una comprensión más profunda del medio en el que vivimos y, al mismo tiempo, transmitir de forma más directa que las matemáticas son una herramienta imprescindible en nuestra vida diaria. El Campus de la Universidad de Alicante ha sido desde su creación un espacio relevante considerado en algunas ocasiones como uno de los mejores campus universitarios, no sólo de España sino también de Europa. A lo largo de una extensión de alrededor de un millón de metros cuadrados, encontramos motivos suficientes para tratas varios aspectos matemáticos que aparecen en muchos de sus edificios y recintos. En este trabajo mostraremos algunos elementos matemáticos que descubrimos a lo largo de un pequeño itinerario que hemos realizado dentro del campus. Así, el principal objetivo es el de ilustrar muchos conocimientos matemáticos de una forma amena y divertida. De esta manera, el contacto con la realidad llegará entonces a límites insospechados y nos hará, en definitiva, participar de ella e idear otra realidad matemática paralela.