Unifying the Classical Approach with New Technologies: An Innovative Proposal for Teaching Mathematics in Engineering

The aim of this paper is to present a teaching experience developed in the Polytechnic University of Cartagena and, more specifically, in the subject of Mathematical Methods Applied to Civil Engineering, that belongs to the Master Degree of Paths, Channels and Ports. Our classes were a mix between the traditional system and the new educational system. Moreover, we tried to adapt the evaluation process to the new European Framework for Higher Education. We have used videos developed by us and by students in our classes. We have noticed that the interest and motivation in class has grown. Also the grades have improved. We did a survey during this academic year and the results were strongly positive for both students and teachers

Una propuesta de proyecto de innovación docente donde se usan videos didácticos como apoyo en el autoaprendizaje

El objetivo de este proyecto de innovación docente es exponer una experiencia desarrollada en los tres últimos años para la asignatura de Métodos Numéricos de cuarto curso de la titulación de Ingeniero Agrónomo de la UPCT. La mayor novedad es la inclusión de videos docentes y de una evaluación centrada en la presentación oral y defensa de los trabajos realizados en grupo. Los resultados obtenidos fueron gratamente satisfactorios en todos los sentidos. El presente proyecto fue galardonado con el primer premio al mejor proyecto de innovación docente de la Escuela Técnica Superior de Ingeniería Agronómica.Consejo Escolar de la Región de Murcia. Consejería de Educación, Formación y Empleo. Universidad de Murcia. Universidad Politécnica de Cartagena. Centro de Profesores y Recursos de Murcia (CPR)

Convergencia y análisis numérico de un método de tercer orden para sistemas de ecuaciones no lineales

A lo largo de la Historia la resolución de ecuaciones no lineales ha preocupado a gran cantidad de científicos. Hoy en día, con los adelantos tecnológicos, estas ecuaciones son aproximadas de forma eficiente por medio de métodos iterativos. La idea es generar una sucesión de aproximaciones x0, x1, x2, ... que bajo ciertas condiciones converge a la raíz deseada. En este trabajo, presentamos una extensión a espacios de Banach de un método de tercer orden recientemente presentado en el caso escalar [6] M.A. Noor et al., An iterative method with cubic convergence for nonlinear equations, Appl. Math. Comp., 183, (2006), 1249-1255. Se introducirán varios teoremas de convergencia, modificaciones que no necesitan el cómputo de derivadas y varios experimentos numéricos

Unifying the classical approach with new technologies: An innovative proposal for teaching mathematics in engineering

The aim of this paper is to present a teaching experience developed in the Polytechnic University of Cartagena and, more specifically, in the subject of Mathematical Methods Applied to Civil Engineering, that belongs to the Master Degree of Paths, Channels and Ports. Our classes were a mix between the traditional system and the new educational system. Moreover, we tried to adapt the evaluation process to the new European Framework for Higher Education. We have used videos developed by us and by students in our classes. We have noticed that the interest and motivation in class has grown. Also the grades have improved. We did a survey during this academic year and the results were strongly positive for both students and teachers

An example of introducing new technology at university classes

[SPA] La utilización educativa de los videos en los campus, en los departamentos de todas las disciplinas está aumentando, desde artes, humanidades y ciencias a planes de estudios profesionales y vocacionales. El objetivo de este trabajo es presentar una experiencia docente desarrollada en la Universidad Politécnica de Cartagena y, más concretamente, en la asignatura de Métodos Numéricos para Ingenieros Agrónomos. Hemos utilizado videos en clase para enseñar nuestra asignatura. Los videos fueron realizados por nosotros. Se puede decir que nuestras clases eran una mezcla entre el sistema tradicional y el nuevo sistema educativo. Además, hemos intentado adaptar el proceso de evaluación al Nuevo Marco Europeo de Educación Superior. Hemos realizado un estudio comparativo entre las notas obtenidas por los estudiantes en nuestra asignatura, con el uso de videos en clase, y las notas obtenidas por los estudiantes en el resto de asignaturas de la carrera. Este estudio ha sido realizado durante cuatro cursos académicos y los resultados fueron muy positivos. Se detectó un aumento en la motivación e interés de nuestros estudiantes. También pudimos apreciar un aumento de la concentración de nuestros estudiantes durante las sesiones de video. Lo anteriormente expuesto se vio reflejado en las calificaciones finales. [ENG] The educational use of video on campus is accelerating rapidly in departments across all disciplines from arts, humanities, and sciences to professional and vocational curricula. The aim of this paper is to present a teaching experience developed in the Polytechnic University of Cartagena and, more specifically, in the subject of Numerical Methods for Agricultural Engineers. We used videos to teach our subject at class. The videos were made by ourselves. Our classes were a mixed between the traditional system and the new educational system. Moreover, we tried to adapt the evaluation process to the new European Framework for Higher Education. A survey was carried out using video at class in order to compare our students’ grades with the rest of university students’ grades. We did the survey during four academic years and the results were strongly positive for both students and teachers. We could find an increase in motivation and in the interest of our students. We could also appreciate our student quite concentrated during the video sessions. The previous one was reflected in the final grades. In the future we are going to introduce e-beam at class and we would like to study the students’ performance

On the local convergence study for an efficient k-step iterative method

[EN] This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order derivatives. Moreover only one LU decomposition is required in each iteration. In particular, the methods are real alternatives to the classical Newton method. We present a local convergence analysis based on hypotheses only on the first derivative. These types of local results were usually proved based on hypotheses on the derivative of order higher than two although only the first derivative appears in these types of methods (Bermficlez et al., 2012; Petkovic et al., 2013; Traub, 1964). We apply these methods to an equation related to the nonlinear complementarity problem. Finally, we find the most efficient method in the family for this problem and we perform a theoretical and a numerical study for it. (C) 2018 Elsevier B.V. All rights reserved.Research was supported in part by Programa de Apoyo a Ia investigacion de Ia fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia 19374/PI/14, by the project of Generalitat Valenciana Prometeo/2016/089 and the projects MTM2015-64382-P (MINECO/FEDER), MTM2014-52016-C2-1-P and MTM2014-52016-C2-2-P of the Spanish Ministry of Science and Innovation.Amat, S.; Argyros, IK.; Busquier Saez, S.; Hernández-Verón, MA.; Martínez Molada, E. (2018). On the local convergence study for an efficient k-step iterative method. Journal of Computational and Applied Mathematics. 343:753-761. https://doi.org/10.1016/j.cam.2018.02.028S75376134

On high-order iterative schemes for the matrix pth root avoiding the use of inverses

This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.The research of the authors S.A. and S.B. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by PID2019-108336GB-100 (MINECO/FEDER). The research of the author M.Á.H.-V. was supported in part by Spanish MCINN PGC2018-095896-B-C21. The research of the author Á.A.M. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by Spanish MCINN PGC2018-095896-B-C21

Un esquema de cuarto orden con casi-óptimo gasto computacional para ecuaciones no lineales

En este trabajo, presentamos un método de tres pasos y de cuarto orden que tiene un coste computacional muy aceptable. Esto es debido a que no necesita segundas derivadas y que la matriz de los sistemas lineales asociados es la misma en los tres pasos de cada iteración. Se estudiará su convergencia e implementación

A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators

The aim of this paper is the approximation of nonlinear equations using iterative methods. We present a unified convergence analysis for some two-point type methods. This way we compare specializations of our method using not necessarily the same convergence criteria. We consider both semilocal and local analysis. In the first one, the hypotheses are imposed on the initial guess and in the second on the solution. The results can be applied for smooth and nonsmooth operators.Research of the first and third authors supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by MTM2015-64382-P. Research of the fourth and fifth authors supported by Ministerio de Economía y Competitividad under grant MTM2014-52016-C2-1P. This research received no external funding

Zoom de imágenes digitales usando esquemas de subdivisión

Escueal Técnica Superior de Ingeniería de Telecomunicació