Related papers: "Pulling out" as a procedural resource when solvin…
Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including…
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…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
The prediction of academic dropout, with the aim of preventing it, is one of the current challenges of higher education institutions. Machine learning techniques are a great ally in this task. However, attention is needed in the way that…
We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem…
Partial derivatives are used in a variety of different ways within physics. Most notably, thermodynamics uses partial derivatives in ways that students often find confusing. As part of a collaboration with mathematics faculty, we are at the…
Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving…
Despite the prevalence of physics education research literature related to problem solving, recent studies have illustrated that opportunities for ``authentic'' problem solving -- conceptualized as making decisions with limited information…
We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the Time Dependent…
One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…
The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…