ﻻ يوجد ملخص باللغة العربية
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games as particular pathways of solutions along resource graphs containing linked procedural and conceptual resources. Using transcript data, we define several procedural resources, show how they can be organized into two facets of a previously described epistemic game, and produce a resource graph that allows visualization of this portion of the epistemic games. By representing two correct mathematical procedures in terms of shared resources, we help clarify the types of thinking in which students engage when learning to apply mathematical reasoning to physics and illustrate how a failure to connect two ideas often hinders students successful problem solving.
While other fields such as statistics and education have examined various issues with quantitative work, few studies in physics education research (PER) have done so. We conducted a two-phase study to identify and to understand the extent of these is
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting and the p
We present a convergence proof for higher order implementations of the projective integration method (PI) for a class of deterministic multi-scale systems in which fast variables quickly settle on a slow manifold. The error is shown to contain contri
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step exponential inte
We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to centre manifold theory. The error is shown to contain contributions associated with the numer