Search results for "Calculus"

On Variational Measures Related to Some Bases

2000

Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.

Discrete exterior calculus for photonic crystal waveguides

2022

The discrete exterior calculus (DEC) is very promising, though not yet widely used, discretization method for photonic crystal (PC) waveguides. It can be seen as a generalization of the finite difference time domain (FDTD) method. The DEC enables efficient time evolution by construction and fits well for nonhomogeneous computational domains and obstacles of curved surfaces. These properties are typically present in applications of PC waveguides that are constructed as periodic structures of inhomogeneities in a computational domain. We present a two-dimensional DEC discretization for PC waveguides and demonstrate it with a selection of numerical experiments typical in the application area. …

First-year engineering students’ use of their mathematics textbook - opportunities and constraints

2012

Published version of an article in the journal: Mathematics Education Research Journal. Also available from the publlisher at: http://dx.doi.org/10.1007/s13394-012-0040-9 The role of the mathematics textbook at tertiary level has received limited exposure in previous research although it is likely that students work individually and that some of this work depends on the use of the textbook. The aim of this study was to investigate the process of approaching the textbook from epistemological, cognitive, and didactical perspectives. The focus was on identifying and discussing the opportunities and constraints in the process. The study was an explorative case study and the participants were fi…

Enseñanza de las ciencias : revista de investigación y experiencias didácticas

1996

Resumen basado en el de la publicación Resumen en inglés La evolución histórica del principio de Le Chatelier está relacionada con su uso en el aula de química. La aparente simplicidad en la cual el principio de Le Chatelier fue formulado por primera vez y el éxito logrado en la implementación de algunos procesos industriales importantes le dio un reconocimiento inicial que aún perdura. Sin embargo, desde el comienzo de este siglo, diferentes autores han señalado el carácter limitado de la regla cualitativa y su formulación vaga y ambigua. Además, la termodinámica dada por el Principio de Le Chatelier en algunas formulaciones cuantitativas limitan su aplicabilidad. Sin embargo, la mayoría d…

The use of integrals in Mechanics of Materials textbooks for engineering students: the case of the first moment of an area

2018

International audience; Research has reported on the difficulties engineering students face in relating the content of their mathematics courses to what is taught in their professional courses. One way to address these difficulties is by better understanding how mathematical notions are used in professional engineering courses. This paper analyses how the notion of first moment of an area – which is defined as an integral – is used in civil engineering courses. Basing our analysis on elements from the anthropological theory of the didactic, we are currently analysing a classic Mechanics of Materials book. Our findings indicate that although first moments are introduced as an integral, the t…

The Fractionally-damped Duffing Oscillator under Gaussian white noise

2012

Stochastic response of fractional visco-elastic beams

2012

3D fractional viscoelasticity with applications to structural engineering

The complexity of knowledge construction in a classroom setting

2018

International audience; We study a class of mathematics education MA students in an introductory course on Chaos and Fractals, as they grapple with the Sierpinksi triangle, and in particular with the apparent paradox that its area equals 0, while its perimeter is infinitely long. For this purpose, we network an approach for investigating the construction of knowledge in small groups with one for examining how ideas and ways of reasoning function-as-if-shared in a classroom. Our results show complexities: (i) small group work and whole class discussions mutually influence each other; (ii) ideas may function-as-if-shared in the whole class even if the majority of students have not previously …

Exponentiating derivations of quasi∗-algebras: possible approaches and applications

2005

The problem of exponentiating derivations of quasi∗-algebras is considered in view of applying it to the determination of the time evolution of a physical system. The particular case where observables constitute a properCQ∗-algebra is analyzed.