Search results for "Calculus"

On the fractional integral of Weyl inL p

1994

Regularity of a Degenerated Convolution Semi-Group Without to Use the Poisson Process

2011

We translate in semi-group theory our regularity result for a degenerated convolution semi-group got by the Malliavin Calculus of Bismut type for Poisson processes.

Appendix: Feynman rules

2010

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

2015

We consider the computationally efficient time integration of Maxwell’s equations using discrete exterior calculus (DEC) as the computational framework. With the theory of DEC, we associate the degrees of freedom of the electric and magnetic fields with primal and dual mesh structures, respectively. We concentrate on mesh constructions that imitate the geometry of the close packing in crystal lattices that is typical of elemental metals and intermetallic compounds. This class of computational grids has not been used previously in electromagnetics. For the simulation of wave propagation driven by time-harmonic source terms, we provide an optimized Hodge operator and a novel time discretizati…

From single to multi-variable Calculus: a transition?

2018

International audience; We recently used the notion of praxeology from the Anthropological Theory of the Didactic to model the knowledge that is necessary for students to learn in order to succeed in an undergraduate multivariable Calculus course. We considered the presence and absence of elements of the knowledge to be taught, as proposed by curricular documents, in the knowledge to be learned, as indicated by final exams. Our results indicate that the mathematical activities expected of students at this level align with the activities observed in differential and integral Calculus, where exercise-driven assessments set students' work mainly in the recognition of types of tasks and recolle…

A study of transitions in an undergraduate mathematics program

2018

International audience; In this paper, we introduce an in-progress study of the transitions students face as they advance in their mathematics courses. Previous work has discussed the changes that occur in the transition from high school to university. With regards to the knowledge students are expected to learn, however, significant similarities have been noted: to do well in introductory university courses, students can learn to solve a particular subset of tasks through routinized techniques, with limited awareness of the supporting mathematical theory. In contrast, students in advanced courses are required to work with and on that theory. The first stage of our project aims to better un…

On the Dynamics of Fractional Visco-Elastic Beams

2012

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized …