David G. Zeitoun

• Dr.
• Orot College of edeucation

The study of some parametric integrals is presented with a combined approach of analytical development, the usage of a Computed Algebra System (CAS) and of the Online Encyclopedia of Integer Sequences. The methodology for the solution includes a) an analytical investigation for the study of the parametric integral, b) computations with a CAS of the...

A contribution to teaching continuity and discontinuity of a 1-real variable function. Using animations with a Computer Algebra System.

Groundwater pollution is a general concern in countries using pumping wells for water consumption. Also, the determination of protected zone around pumping wells is a practical concern. The delineation of this zone is frequently obtained using numerical models such as MODFLOW and or FEFLOW. In this contribution we derived the equation of the plane...

Students learning towards a degree in a STEM related domain learn quite early a course in Advanced Calculus, i.e. a course where the main object of study are multivariate functions. It happens that students do not see the connection between the properties of the function such as continuity or differentiability and the 3-dimensional graphical repres...

Accurate plots of 2-variable functions: the choice of the mesh

Accurate mesh for plotting 2-variable functions

Non homogeneous stiff ODEs

We describe working session for the study of 1-parameter families of definite integrals in a technology-rich environment. The joint usage of paper-and-pencil work together with a Computer Algebra System and eventually a web based database may lead to closed forms for the integrals, to the derivation of combinatorial identities, and other kinds of o...

The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the implemented algorithms, yielding continuous approximations of the given function by interpolation. This masks often discontinuities of the given function and its curvature at...

We compute closed forms for some parametric integrals. The tools used are MacLaurin developments and other infinite series. Finally, Stirling numbers appear.

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.

We present the rationale of an ongoing project, aimed at the development of a Virtual Reality assistant learning of limits, continuity, and other properties in multivariable Calculus. The Mathematics for which this development is intended is described briefly, together with the psychological and pedagogical elements of the project. What is Virtual...

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very...

This article is concerned with iterative techniques for linear systems of equations arising from a least squares formulation of boundary value problems. In its classical form, the solution of the least squares method is obtained by solving the traditional normal equation. However, for nonsmooth boundary conditions or in the case of refinement at a...

The paper presents a generalization of the classical L2-norm weighted least squares method for the numerical solution of a first-order hyperbolic system. This alternative least squares method consists of the minimization of the weighted sum of the L2 residuals for each equation of the system. The order of accuracy of global conservation of each equ...

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H 1, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.At each time...

In pavement evaluation using non‐destructive testing (NDT), a large amount of deflection bowls are analysed in terms of the elastic moduli of the layers. The results are used to evaluate the material variability, which could serve in an overlay design procedure based on the concept of reliability. The model currently used for interpreting deflectio...

Modeling the transport of groundwater contamination leads generally to problems wherein the continuity equation is coupled with the contaminant transport equation and Darcy's law. Such a system of equations is called the flow-transport system and is difficult to solve numerically. An optimal control, H1, least squares formulation, associated with a...

A stochastic model for flow through inhomogeneous fractured reservoirs of double porosity, based on Barenblattet al.'s continuum approach, is presented. The fractured formation is conceptualized as an interconnected fracture network surrounding porous blocks, and amenable to the continuum approach. The block permeability is negligible in comparison...

A stochastic approach is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation functio...

A stochastic model for flow through inhomogeneous fractured reservoirs, based on Barenblatt et al. continuum approach, is presented. The fractured reservoir inhomogeneity is attributed to the medium of fractures, while the properties of the blocks are considered constant. The model is represented by a coupled system of partial differential random e...

In this paper a least-squares formulation associated with a conjugate gradient algorithm is proposed for the solution of transport problems. In this procedure the advection–diffusion equation is first discretized in time using an implicit scheme. At each time step the resulting partial differential equation is replaced by an optimal control problem...