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Otarod, Masood – Chemical Engineering Education, 2023
A derivation of the conservation equations for fixed bed tubular reactors in cylindrical coordinates is presented and a differential operator for the substantial derivative in porous beds is introduced. The emphasis on the distinction between the functions of the void and volume fractions in the derivation of the conservation equations sets the…
Descriptors: Equations (Mathematics), Chemistry, Science Instruction, Mathematical Concepts
Chong, Zhiwei; Wu, Zhuoyi; Wei, Yajun – Physics Education, 2022
The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…
Descriptors: Motion, Equations (Mathematics), Physics, Science Instruction
Tu, Tao; Li, Chuan-Feng; Zhou, Zong-Quan; Guo, Guang-Can – Physical Review Physics Education Research, 2020
Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students' solutions to midterm exam questions and utilized think-aloud interviews. We also applied a framework that organizes students'…
Descriptors: Science Instruction, Physics, Equations (Mathematics), Quantum Mechanics
Tu, Tao; Li, Chuan-Feng; Xu, Jin-Shi; Guo, Guang-Can – Physical Review Physics Education Research, 2021
In quantum mechanics courses, students are often asked to solve bound and scattering state problems. The use of an ordinary differential equation is a standard technique to solve these questions. Here, we investigated students' problem-solving processes for two typical problems of a single particle in one spatial dimension: a bound state problem…
Descriptors: Quantum Mechanics, Science Instruction, Problem Solving, Barriers
Tisdell, C. C. – International Journal of Mathematical Education in Science and Technology, 2017
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
Descriptors: Calculus, Mathematics Instruction, Mathematical Models, Biology
Norton, Douglas E. – PRIMUS, 2022
This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model…
Descriptors: Undergraduate Study, College Mathematics, Mathematical Models, Biological Sciences
Bollen, Laurens; van Kampen, Paul; De Cock, Mieke – Physical Review Physics Education Research, 2018
We have developed, implemented, and assessed a teaching-learning sequence that aims to enhance students' understanding of the divergence and curl of electromagnetic fields. We designed guided-inquiry worksheets based on student difficulties we identified during semiquantitative and qualitative studies and discussions in the literature. A multiple…
Descriptors: Energy, Magnets, Teaching Methods, Concept Formation
Dayal, Vikram – International Journal of Mathematical Education in Science and Technology, 2023
Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of…
Descriptors: Biology, Visual Aids, Epidemiology, Science Instruction
Fisher, Robert J. – Chemical Engineering Education, 2019
Our exponentially increasing knowledge base creates many new technology challenges. Academia must therefore respond emphatically. Educating rising professionals to successfully confront these future difficulties requires innovative curricula challenges. A successful adaptation integrates STEM program protocols into core courses. Embracing…
Descriptors: Science Instruction, Teaching Methods, Mathematical Concepts, Engineering Education
Barzykina, Irina – Journal of Chemical Education, 2020
Chemical reactions far from equilibrium can exhibit oscillatory behavior. Full understanding of this phenomenon is outside of the school curriculum. However, the importance of such processes in life sciences and peculiar spatial and temporal patterns accompanying the reactions can attract the attention of IB Diploma science students. They will…
Descriptors: Science Instruction, Chemistry, College Science, Undergraduate Study
Rubin, Scott – Physics Teacher, 2019
The stereotypical situation of a snowball picking up both mass and speed as it rolls without slipping down a hill provides an opportunity to explore the general form of both translational and rotational versions of Newton's second law through multivariable differential equations. With a few reasonable assumptions, it can be shown that the snowball…
Descriptors: Science Instruction, Physics, Motion, Scientific Concepts
Forest Mannan – International Journal of Mathematical Education in Science and Technology, 2024
This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon…
Descriptors: Calculus, Mathematical Models, Programming, Heat
Gojkovic, Ljubomir; Malijevic, Stefan; Armakovic, Stevan – Physics Education, 2020
In this work three examples of textbook circuits (resistor-capacitor, resistor-inductor and resistor-inductor-capacitor) have been modeled by employing the Euler method for the approximate solution of differential equations using algorithms implemented in the "Python" programming language. The aim of this work was to demonstrate how…
Descriptors: Science Instruction, Programming Languages, Teaching Methods, Mathematics
Bollen, Laurens; van Kampen, Paul; Baily, Charles; De Cock, Mieke – Physical Review Physics Education Research, 2016
Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector…
Descriptors: Science Instruction, Magnets, Energy, Semi Structured Interviews
Rizcallah, Joseph A. – Physics Education, 2018
At the introductory level, projectile motion is usually considered under the assumption of the absence of air resistance. Even the simplest case of linear drag might be beyond the students, as it requires some familiarity with differential equations. This leaves many students wondering about the effect of air resistance on the motion and the way…
Descriptors: Introductory Courses, Motion, Physics, Science Instruction