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Ng, Chiu-king – Physics Education, 2016

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

Descriptors: Problem Solving, Calculus, Motion, Qualitative Research

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

Raychaudhuri, Debasree – International Journal of Mathematical Education in Science and Technology, 2013

There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following…

Descriptors: Undergraduate Students, College Mathematics, Mathematical Concepts, Calculus

Glaister, P. – International Journal of Mathematical Education in Science and Technology, 2008

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

Descriptors: Equations (Mathematics), Calculus, Mathematics Instruction, Matrices

Boucher, Randy – PRIMUS, 2010

This project was used in a mathematical modeling and introduction to differential equations course for first-year college students. The students worked in two-person groups and were given three weeks to complete the project. Students were given this project three weeks into the course, after basic first order linear differential equation and…

Descriptors: Calculus, Mathematical Models, College Mathematics, Mathematics Instruction

Balkew, Teshome Mogessie – ProQuest LLC, 2015

In many control systems changes in the dynamics occur unexpectedly or are applied by a controller as needed. The time at which a controller implements changes is not necessarily known a priori. For example, many manufacturing systems and flight operations have complicated control systems, and changes in the control systems may be automatically…

Descriptors: Self Control, Public Policy, Health Services, Diseases

Tolle, John – PRIMUS, 2011

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Descriptors: Equations (Mathematics), Calculus, Problem Solving, Mathematics Instruction

Brown, Erin; de la Peña, Lisandro Hernández – Journal of Chemical Education, 2018

The quantum mechanics of a simplified Pöschl-Teller potential in one dimension is analyzed at an elementary level. The number of bound states of this potential is determined by a parameter "l" characterizing the depth of the potential energy. The resulting collection of potentials with varying depth, as well as their ground state…

Descriptors: Quantum Mechanics, Mechanics (Physics), Science Instruction, College Science

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

Raychaudhuri, Debasree – International Journal of Mathematical Education in Science and Technology, 2014

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

Descriptors: Abstract Reasoning, Equations (Mathematics), Mathematics Education, Undergraduate Students

Courtney, Elya; Morris, Collin; Courtney, Michael – Physics Teacher, 2018

Undergraduate lab design balances several factors: 1) simple experiments connected with learning objectives, 2) experiments sufficiently accurate for comparisons between theory and measurements without gaps when students ascribe discrepancies to confounding factors (imperfect simplifying assumptions, measurement uncertainties, and "human…

Descriptors: Electronic Equipment, Measurement, Accuracy, Physics

Latulippe, Christine; Latulippe, Joe – International Journal of Mathematical Education in Science and Technology, 2014

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits…

Descriptors: Writing Exercises, Student Attitudes, Calculus, Qualitative Research

Aminifar, Elahe; Alipour, Mohammad – European Journal of Educational Sciences, 2014

Item bank is one of the main components of adaptive tests. In this research, a test was made in order to design and calibrate items for Homogeneous Second Order Differential Equations. The items were designed according to the goal-content's table of the subject and the Bloom's taxonomy learning domain. Validity and reliability of these items was…

Descriptors: Test Items, Calculus, Mathematics Tests, Mathematics Instruction

Decker, Robert – International Journal for Technology in Mathematics Education, 2011

Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

Descriptors: Expertise, Investigations, Discovery Learning, Computer Software

Deakin, Michael A. B. – International Journal of Mathematical Education in Science and Technology, 2011

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

Descriptors: Equations (Mathematics), Calculus, Mathematics Instruction, Mathematics Education