Yolanda Padilla Domínguez

• University of Malaga

This paper examines a discrete-time retrial queueing system where incoming customers can either choose a last-come, first-served (LCFS) discipline or enter an orbit. It accounts for the possibility of varying service times, which follow an arbitrary distribution, and the retrial times are also governed by an arbitrary distribution. The underlying M...

In this paper, we propose a user-friendly library in CoCoA to address and completely resolve the challenges posed by the highly efficient and intriguing mathematical model introduced in Hernando et al., (2023) for implementing railway interlocking systems. Although the algebraic model (Hernando et al., 2023) allows for fast performance, it requires...

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algeb...

We consider a discrete-time Geo∕G∕1∕∞ system in which a customer that finishes its first essential service may opt to abandon the system, to receive a second optional service or to go at the head of the queue in order to receive another essential service. We study the Markov chain underlying the considered queueing system and its ergodicity conditi...

It is difficult for research in Mathematics Education to have any real impact on teaching practice in the classroom. Conscious of this, we have developed a research model for curricular innovation, involving the teachers responsible for its implementation, improving their training, and providing scientific information whilst maintaining the integri...

In a previous paper, the authors developed new rules for computing improper integrals which allow computer algebra systems (Cas) to deal with a wider range of improper integrals. The theory used in order to develop such rules where Laplace and Fourier transforms and the residue theorem. In this paper, we describe new rules for computing symbolic im...

The “Game of life” model was created in 1970 by the mathematician John Horton Conway using cellular automata. Since then, different extensions of these cellular automata have been used in many applications. In this work, we introduce probabilistic cellular automata which include non-deterministic rules for transitions between successive generations...

Partial Differential Equations (PDE) appear in multiple Physic and Engineering applications. Normally, when modeling an application, the use of well-known and already solved PDE is considered. But what happens if a new PDE is used? Solving a new PDE is not an easy task. In this paper, we use a Computer Algebra System (Cas) in order to find the solu...

Programming with Computer Algebra Systems (CAS) has become an important tool as a support in Computer lectures in Mathematics subjects aimed at Engineering degrees. In this paper, the authors present their teaching experience within the concept "Line Integration" with the help of two specific CAS: DERIVE and MAXIMA. When introducing the new concept...

There are currently several new technologies being used to generate digital elevation models that do not use photogrammetric techniques. For example, LiDAR (Laser Imaging Detection and Ranging) and RADAR (RAdio Detection And Ranging) can generate 3D points and reflectivity information of the surface without using a photogrammetric approach. In the...

PartialDifferential Equations (PDE) is a very important topic in advance Mathematics for Engineering. The three main first-order PDE problems that a basic course must deal with are:1. Pfaff Differential Equations2. Quasi-linear Partial Differential Equations,3. Lagrange-Charpit Method for finding a complete integral for a given general first order...

In this work we will deal with advance techniques to compute certain types of improper integrals using a CAS. Laplace and Fourier transforms or Residue Theorem in Complex Analysis are some advance techniques which can be used for this matter.We will introduce the file ImproperIntegrals.mth, developed in DERIVE 6, which deals with such computations....

For many years, university teaching was based mainly on lectures, but critics point out that lecturing is mainly a one-way method of communication that does not involve significant audience participation. Nowadays e-learning has become a distance learning paradigm using information technology as the Internet, intranets, emails and multimedia produc...

In this work, we present a new application developed in Derive 6 to compose counterpoint for a given melody (''cantus firmus''). The result is non-deterministic, so different counterpoints can be generated for a fixed melody, all of them obeying classical rules of counterpoint. In the case where the counterpoint cannot be generated in a first step,...

In this work, we present a new application developed in Derive 6 to compose counterpoint for a given melody (“cantus firmus”). The result is non-deterministic, so different counterpoints can be generated for a fixed melody, all of them obeying classical rules of counterpoint. In the case where the counterpoint cannot be generated in a first step, b...

This paper establishes the theoretical aspects which have been considered in order to elaborate the Random distiributions package for Derive 6 as well as the description of the different algorithm developed in the package. In section 1 the theory on random number generation is presented (from [Rubinstein, 1981]). After explaining Derive’s random fu...

El objetivo fundamental que se persigue con esta comunicación es transmitir algunas de nuestras experiencias en la utilización del ordenador en el aula de Matemáticas en Secundaria. Empezaremos mostrando cómo con la utilización de la programación con Computer Algebra Systems (CAS) se consigue que el uso del ordenador provoque un aprendizaje de la m...

Hoy en día está bastante extendida la utilización de los ordenadores y en particular los CAS (Computer Algebra Systems) en las clases de Matemáticas de las carreras técnicas. Esto es debido a que los programas de cálculo constituyen herramientas de uso habitual en la actividad profesional de los ingenieros. Además, la utilización del ordenador vien...

El objetivo fundamental que se persigue con la realización de este taller es transmitir algunas de nuestras experiencias en la utilización del ordenador en el aula de Matemáticas tanto en Secundaria como en la Universidad. Se dividirá el taller en dos partes claramente diferenciadas. En la primera parte se mostrará cómo con la utilización de la p...

Hoy en día está bastante extendida la utilización de los ordenadores y en particular los CAS en las clases de Matemáticas de las carreras técnicas. Esto es debido a que los programas de cálculo constituyen herramientas de uso habitual en la actividad profesional de los ingenieros. Además, la utilización del ordenador viene a simplificar enormemente...

El propósito de esta comunicación es presentar los materiales que hemos elaborado un equipo de profesores de Matemáticas, para ser utilizados tanto en la docencia como en el estudio personal del alumno. Los materiales van dirigidos, principalmente, a los alumnos de 2º de Bachillerato, aunque pueden ser utilizados también por alumnos de primer curso...

El propósito de esta comunicación es reflexionar sobre la idoneidad de la utilización como recurso didáctico de los vídeos en asignaturas de Matemáticas que se desarrollen de forma virtual. Presentaremos los vídeos que nosotros hemos elaborado para la impartición de la asignatura Fundamentos básicos de Variable Compleja desde el punto de vista de u...

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm that checks the validity of a formula. The kind of exercises that can be solved using an ATP can be grouped in the following three Logic problems: 1. Checking the sastifiability of a formula (SAT). Satisfiability is the problem of determining if there exists an inte...

In this talk we will describe the file DIFFERENTIAL_EQUATIONS.MTH, created in DERIVE 6 in order to be used in mathematical subjects which deal with differential equations, aimed at Engineering students. Such file contains a series of programs which permit to solve differential equations problems. The programs contained in the file can be grouped w...

In this talk we will describe the file LINE_INTEGRALS.MTH, created in DERIVE 6 in order to be used in subjects that deal with line integrals, aimed at Engineering students. Such file contains a series of programs which permit to solve line integrals problems. The programs contained in the file can be grouped within the following blocks: - Parametri...

In this talk we will describe the file MULTIPLE_INTEGRALS.MTH, created in DERIVE 6 in order to be used in subjects that deal with double and triple integrals, aimed at Engineering students. Such file contains a series of programs which permit to solve multiple integrals problems. The programs contained in the file can be grouped within the followin...

In this work we present an application developed in Derive 6 to compose counterpoints for a given melody (“cantus firmus”). The result is non deterministic, so different counterpoints can be generated for a fixed melody, all of them obeying classical rules of counterpoint. It is also possible that the counterpoint could not be generated, in this ca...

Los continuos avances de las TIC hacen que vayan surgiendo nuevas herramientas adecuadas para el uso del ordenador en la enseñanza. Una de estas herramientas es la plataforma MOODLE. Esta plataforma de aprendizaje a distancia basada en software libre permite trabajar con los alumnos desde diversos puntos de vista (intercambio de material, realizaci...

The use of Computer Algebra Systems (CAS) in mathematical education is widely used as a practical tool. However CAS are not used frequently for teaching topics as automated reasoning. This work is focused on the developing of a package called ATPCL. The package has been developed using DERIVE, but can be rewritten in other CAS. ATPCL includes som...

The field of mathematics covers a wide range of knowledge that shares a specific way of representing reality. It arises from the need to solve certain practical problems and is sustained by its ability to deal with, explain, predict and provide models for real situations and lend consistency and rigor to scientific knowledge. The nature of Mathemat...

In this workshop we will use some examples of programming with DERIVE 6 using the Display function in order to use this software as a PeCAS. We have developed this kind of workshop with our students of Technical Telecommunication Engineering. After the results obtained we think that programming should be part of the teaching of Mathematics at the u...

In this paper we present the file LINE_INTEGRALS.MTH, created to be used in subjects that deal with line integrals, aimed at Engineering students. Such file contains a series of macros which permit to solve line integrals problems. The macros contained in the file can be grouped within the following blocks: - Parametrization of curves. - Exact d...

In this paper we present the file MULTIPLE_INTEGRALS.MTH, created to be used in subjects that deal with double and triple integrals, aimed at Engineering students. Such file contains a series of macros which permit to solve multiple integrals problems. The macros contained in the file can be grouped within the following blocks: - Double integrat...

The use of computers in mathematical lectures in Engineering degrees has been widely introduced in the last few years so that to develop some computer lectures for students within their curriculum is not considered a new task. Even more, the new tendencies make programming with CAS be one of the best tasks to do with computers in the classroom sinc...

Evaluation is the most difficult element of the educational process because the teacher must check if the pupils have grasped the expected objectives by this evaluation. On the other hand, the purpose of evaluation is not only to classify, but also must be used to obtain information about the real knowledge of the pupils and the problems the didact...

En este artículo se realiza un análisis del movimiento que se está produciendo en los últimos años dentro del colectivo de profesores que utilizan los Computer Algebra Systems (CAS) en la enseñanza de las Matemáticas, con el fin de cambiar los usos didácticos tradicionales que se le dan a estas herramientas. Estos cambios van en la línea de modific...

The new tendencies in the use of computers in mathematical lectures in Engineering degrees make programming with Computer Algebra Systems (CAS) be one of the best tasks to do with computers in the classroom. So, the next step would be to develop appropriated tasks to deal with programming within a computer lecture. In this paper we will describe th...

The main goal of this paper is to examine the way that CAS (Computer Algebra Systems) are currently being used in Mathematics courses for Engineering degrees. In this analysis, special attention is paid to the strong movement taking place among teachers to change the traditional didactic uses given to these tools.

En este artículo presentamos FERMAT (Foro Experimental sobre Recursos de Matemática Aplicada a las Telecomunicaciones), portal de Internet alojado en http://www.campusvirtual.uma.es/fermat. Este trabajo ha sido realizado por un grupo de profesores del Departamento de Matemática Aplicada de la Universidad de Málaga y ha consistido, básicamente, en e...

La teoría de funciones de variable compleja es una de las ramas de las Matemáticas más bellas y útiles, a pesar de que durante tres siglos vivió en una atmósfera de desconfianza, como claramente indican los términos "imaginario" y "complejo". En su desarrollo participaron muchos de los matemáticos más grandes de la historia como Cauchy, Euler, Gaus...

Actualmente las Matemáticas son una herramienta fundamental en las aplicaciones a la Ingeniería y a la Física. Concretamente, podríamos decir de la materia objeto del presente formulario, Análisis Vectorial, que es "el lenguaje" de la Mecánica y del Electromagnetismo desde el inicio del siglo XX. Ya desde su nacimiento en el siglo XVII hasta hoy en...

En este artículo presentamos FERMAT (Foro Experimental sobre Recursos de Matemática Aplicada a las Telecomunicaciones), portal de Internet alojado en http://www.campusvirtual.uma.es/fermat. Este trabajo ha sido realizado por un grupo de profesores del Departamento de Matemática Aplicada de la Universidad de Málaga y ha consistido, básicamente, en e...

La presente comunicación es una descripción del proyecto de innovación educativa “El uso de la programación informática como recurso didáctico en la enseñanza de las Matemáticas de las carreras técnicas” desarrollado conjuntamente por tres profesores del Departamento de Matemática Aplicada y un profesor del Departamento de Didáctica de la Matemátic...

La presente comunicación es una descripción del proyecto de innovación educativa “Evaluación en las asignaturas de matemáticas de las carreras técnicas: ¿por qué reducirla a un único examen final?” desarrollado por tres profesores del Departamento de Matemática Aplicada de la Universidad de Málaga. A la hora de evaluar a los alumnos es interesante...

Aunque actualmente es habitual el uso del ordenador en el aula de Matemáticas en la Universidad, su utilización no conduce, en la mayoría de las ocasiones, a que se fomente la creatividad matemática del alumnado. En muchos casos se sigue utilizando para resolver los procedimientos de cálculo de forma inmediata, privando así al alumno de la posibili...

Dado que la mayoría de las Universidades han integrado por completo el uso de CAS (Computer Algebra Systems) en el desarrollo de las asignaturas de Matemáticas de las titulaciones de Ingeniería, nuestro objetivo será reflexionar sobre los usos que se dan hoy en día a estas herramientas en la enseñanza. Como parte de este análisis destacaremos el ca...

El objetivo principal del presente trabajo es describir una experiencia evaluadora que hemos llevado a cabo en las asignaturas de Matemáticas de la titulación de Ingeniería Técnica de Telecomunicación de la Universidad de Málaga. Dicha experiencia se ha venido desarrollando durante los últimos diez años y consiste, básicamente, en la introducción r...

The main goal of this paper is to reflect on the habitual uses that nowadays are given to CAS (Computer Algebra Systems) in the teaching of Mathematics at the degrees of Engineering. The traditional use of computer in mathematical teaching for Engineers is normally reduced to the resolution of some kind of theoretical-practical exercises where the...

Over the last few years, the use of the computer as a tool to support teaching has been extended in University, especially in practical subjects. However, we should think about the following question: are computers under-used in mathematical teaching? Nowadays, computers are being used in university teaching as great powerful calculators, but not...

La teoría de funciones de variable compleja es una de las ramas de las Matemáticas más bellas y útiles, a pesar de que durante tres siglos vivió en una atmósfera de desconfianza, como claramente indican los términos "imaginario" y "complejo". En su desarrollo participaron muchos de los matemáticos más grandes de la historia como Cauchy, Euler, Gaus...

El objetivo principal de este trabajo es reflexionar sobre los usos habituales que se dan hoy en día a los CAS (Computer Algebra Systems) en las clases de Matemáticas de las titulaciones de Ingeniería. Como parte de este análisis se destaca el fuerte movimiento que se está produciendo dentro del colectivo de profesores con el fin de cambiar los uso...

In this paper we present the file RESIDUE.MTH, created to be used in subjects that deal with complex variable, aimed at Engineering students. Such file contains a series of macros which permit to solve integration problems using the residue theorem. The macros contained in the file can be grouped within the following blocks: - Compute of residue...

In this workshop we will use some examples of programming with DERIVE to solve problems of line and multiple integrals. We have developed this kind of workshop with our students of Technical Telecommunication Engineering. After the results obtained we think that programming should be part of the teaching of Mathematics at the undergraduate level....

In this paper the file RANDOM_DISTRIBUTIONS.mth is presented. This file has been developed for generating random values from main continuous and discrete distributions. The macros contained in the file can be grouped within the following blocks: - Random values from uniform distribution: the macro RANDOM_UNIFORM returns an uniform random deviate...

When using a specific software in the teaching of Mathematic subjects, different elements and techniques of it must be combined to solve application problems. In this sense, the main goal of the workshop taller de creación de ficheros de utilidades con DERIVE is to show the participants how to elaborate utility files with DERIVE by means of creatin...

In this lecture a short historic review throw out two of the second order partial differential equations which have an important role in many areas of Physics and Engineering is presented. Such equations are the one-dimensional diffusion equation and the one-dimensional wave equation. We will focus on their origins, first attempts of resolution and...

Presentamos aquí la descripción del taller Elaboración de comandos con DERIVE: Integración Múltiple. El objetivo fundamental de este taller es enseñar a los participantes a elaborar comandos con el programa DERIVE, con el fin de aumentar considerablemente las posibilidades de dicho programa. Con la elaboración de comandos se pretende crear librería...

Los usuarios de DERIVE que quieran trabajar con variable compleja podrán comprobar las grandes limitaciones que presenta dicho programa en este campo de la Matemáticas. Sin embargo, en las carreras técnicas y en especial en la Ingeniería de Telecomunicación, es una de las ramas que más se utilizan. En esta comunicación presentamos el fichero de uti...

The traditional use of computer in mathematical teaching for Engineers is normally reduced to the resolution of some kind of theoretical-practical exercises where the students use a specific mathematical software. In this paper, we present the experience carried out in courses for undergraduate students in Technical Telecommunication Engineering, u...

In this paper we present the file COMPLEX.MTH, created for being used in subjects that deal with complex variable, aimed at Engineering students. Such file contains a series of macros which permit to solve some typical problems related to complex variable. The macros contained in the file can be grouped within the following blocks: - Complex num...

In this paper we present the file ANALVEC.MTH, created for being used in subjects that deal with integration and vector field theory, aimed at Engineering students. Such file contains a series of macros which permit to solve some typical problems related to vector fields. The macros contained in the file can be grouped within the following blocks...

In this paper we present an experience carried out in courses for undergraduate students in Technical Telecommunication Engineering. The normal use given to practicals with computers generally consists of solving specific problems using the primitive functions of the software chosen. The experience we present consists of teaching Mathematics with D...

Mathematic teachers in Engineering usually thought that the task of transmitting information was the only mission of the profession. Also we used to think that our subject was the most important in the formation of students. This is due mainly because we have been formed in a classical teaching method and we just repeat the same topics and use trad...

The use of computer as a tool in teaching has been quite extensive in University over the last years, especially in applied subjects. Nevertheless, we should wonder if the computer is under-utilized in mathematical formation. Nowadays, computers are being used in university teaching as a powerful calculator but they are not being used as tools to...

La comunicación que aquí presentamos es fruto de varios años de trabajo y se enmarca dentro de varios proyectos de innovación educativa que hemos venido realizando en las asignaturas de Matemáticas de la titulación de Ingeniería Técnica en Telecomunicación. Dichos proyectos se han realizado con la colaboración del Instituto de Ciencias de la Educac...

The use of computer is nowadays necessary as an important tool in any subject. So, it would be useful to include practices with computer in any Mathematic subject, even more in Engineers. The use of computer is not only useful for the other subjects of the degree but also prepares the pupil for her/his professional future. In this paper we present...