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Kose, Emek; Kunze, Jennifer – College Mathematics Journal, 2013

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Descriptors: College Mathematics, Mathematics Instruction, Equations (Mathematics), Climate

Graham, Jeff; Lerch, Michael – PRIMUS, 2007

This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models an electrical circuit. (Contains 2 footnotes.)

Descriptors: Mathematical Models, Equations (Mathematics), Calculus, Mathematics Instruction

Dvoryatkina, Svetlana N.; Melnikov, Roman A. M.; Smirnov, Eugeny I. – European Journal of Contemporary Education, 2017

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

Descriptors: Calculus, Cognitive Ability, Technology Uses in Education, Teaching Methods

van der Hoff, Q.; Harding, A. – International Journal of Mathematical Education in Science and Technology, 2019

It is well-known that the Lotka-Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka-Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit…

Descriptors: Calculus, Mathematical Models, Mathematics, Biology

Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)

Cadeddu, L.; Cauli, A. – International Journal of Mathematical Education in Science and Technology, 2018

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…

Descriptors: Mathematical Applications, Mathematics Activities, Calculus, Science Education History

Buendía, Gabriela; Cordero, Francisco – International Journal of Mathematical Education in Science and Technology, 2013

In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…

Descriptors: Graphs, Calculus, Mathematics Instruction, Epistemology

Budinski, Natalija; Takaci, Djurdjica – International Journal for Technology in Mathematics Education, 2011

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Descriptors: Foreign Countries, World Problems, Mathematics Instruction, Problem Solving

Myers, Joseph; Trubatch, David; Winkel, Brian – PRIMUS, 2008

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Descriptors: Equations (Mathematics), Calculus, Teaching Methods, Mathematical Models

Curtis, Dan – College Mathematics Journal, 2010

This article gives a simple method for determining the maximum interval of existence for a solution of a single, autonomous, first-order differential equation as well as the behavior of the solution as the independent variable approaches the ends of the interval. The methods used are elementary enough to be included in an introductory differential…

Descriptors: Intervals, Predictor Variables, Calculus, Mathematics Instruction

Spayd, Kimberly; Puckett, James – PRIMUS, 2016

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

Descriptors: Mathematics Instruction, Equations (Mathematics), Heat, Teaching Methods

Kovacs, Zoltan – International Journal for Technology in Mathematics Education, 2010

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Descriptors: Equations (Mathematics), Computer Uses in Education, Computer Software, Mathematics Instruction

Seshaiyer, Padmanabhan – PRIMUS, 2017

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

Descriptors: Research Projects, Undergraduate Students, Mathematical Models, Problem Based Learning

Alzabut, Jehad – Journal on Mathematics Education, 2017

In this research, I provide an overview of potentially selected interactive mathematical instructions that help learners-educators identifying the most effective practices for teaching a course on differential equations. Based on my practical experience, positive and negative aspects of the used techniques are discussed. Immediate reactions on the…

Descriptors: Mathematics Instruction, Conventional Instruction, Action Research, Calculus

Suárez, Álvaro; Baccino, Daniel; Martí, Arturo C. – Physics Education, 2019

Simple experiments for which differential equations cannot be solved analytically can be addressed using an effective model that satisfactorily reproduces the experimental data. In this work, the 1D kinematics of a remote-control model (toy) car was studied experimentally and its dynamical equation modelled. In the experiment, maximum power was…

Descriptors: Models, Motion, Video Technology, Equations (Mathematics)