An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

Calculus is perhaps the most widely taught and researched upper-secondary/post-secondary mathematics subject the world over. The research literature is amassing greater clarity around students' understandings of calculus, yet calculus instruction tends to be at odds with this literature, maintaining a focus on procedural aspects of the subject.…

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

We use Action-Process-Object-Schema (APOS) theory to study students' geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science,…

Challenge: Courses like introductory calculus are described as "gatekeeper" classes but are required for students across a variety of science, technology, engineering, and mathematics (STEM) majors. Real applications of mathematics subjects are known to have a positive effect on student motivation and retention. Considering the broad and…

All differential equations students have encountered eigenvectors and eigenvalues in their study of systems of linear differential equations. The eigenvectors and phase plane solutions are displayed in a Cartesian plane, yet a geometric understanding can be enhanced, and is arguably better, if the system is represented in polar coordinates. A…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.

This study explores the integration of game play into an inclusive, hands-on computing project in Calculus class. The project is focused on designing and analyzing priority switches for applications competing for computational resources on embedded devices such as smart watches and tablets. By engaging students in real-world problem-solving…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

We examine a group (N = 88) of Swedish first-year engineering students, their motivation, self-efficacy, and beliefs about the nature of mathematics, and how these relate to their task performance in mathematics. In our data, engineering students who emphasized the exact reasoning in their view of mathematics performed significantly better in a…

The paper presents results of two case studies with undergraduate students majoring in applied mathematics and engineering. The first case study deals with students' preferences for and difficulties with application problems and pure mathematics questions in their courses. The students were majoring in applied mathematics and taking a second-year…

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…

Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve nonstandard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the…

This study shows that using authentic contexts for learning differential equations in a differentiation-by-interest setting can enhance students' beliefs about the relevance of mathematics. The students in this study were studying advanced mathematics (wiskunde D) at upper secondary school in the Netherlands. These students are often not aware of…

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…