Related papers: Students' difficulties with vector calculus in ele…
Undergraduate physics students are known to have difficulties with understanding mathematical tools, and with applying their knowledge of mathematics to physical contexts. Using survey statements based on student interviews and written…
Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and…
An important goal of graduate physics core courses is to help students develop expertise in problem solving and improve their reasoning and meta-cognitive skills. We explore the conceptual difficulties of physics graduate students by…
The theorems of vector analysis (divergence theorem, etc.) are typically first applied in the undergraduate physics curriculum in the context of the electromagnetic field and the differential forms of Maxwell's equations. However, these…
We investigate learning difficulties among second-year students on electromagnetism courses when they apply Amp\`ere-Maxwell's law. Using phenomenography, we analysed written answers from 65 undergraduate physics students to four questions…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
In this paper, we use differential forms to prove a number of theorems of integral vector calculus that are rarely found in textbooks. Two of them, as far as the author knows, have not been published before. Some possible applications to…
Learning vector calculus techniques is one of the major missions to be accomplished by physics undergraduates. However, beginners report various difficulties dealing with the index notation due to its bulkiness. Meanwhile, there have been…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
We investigated how students apply the concept of circulation when faced with problems related to the Ampere-Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed…
Helping students learn why Gauss' law can or cannot be easily applied to determine the strength of the electric field at various points for a particular charge distribution, and then helping them learn to determine the shape of the Gaussian…
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
Formally investigating the sources of students' difficulties around specific subjects is crucial for developing appropriate strategies to help students. We have been studying difficulties in understanding magnetism encountered by students…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a…