15 Aug 2019 | | Contributor(s):: Lawrence C Udeigwe
The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....
Two competing populations: simulations with differential equations
01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan
Abstract: Suppose two populations are competing with each other. How can they then develop? We offer insights with simulation calculations. In the model is the evolution of the biomass of the two populations described with differential equations. A fundamental building block is the logistic...
01 Dec 2017 | | Contributor(s):: Brian Winkel
Levermore. David. 21012. First-Order Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp/5. First-Order Equations: General Theory5.1. Well-Posed Problems 25.2. Existence and Uniqueness 36. First-Order Equations: Graphical Methods6.1....
Hundley- Local Linear Analysis of Nonlinear Autonomous DEs
10 Sep 2017 | | Contributor(s):: Brian Winkel
Hundley, D. Local Linear Analysis of Nonlinear Autonomous DEs. Notes. 4 pp.. http://people.whitman.edu/~hundledr/courses/M244S14/M244/LinearizationNote.pdf .Accessed 10 September 2017.Thorough and very readable material on linearization issues with rich examples (geometric) and...
08 Sep 2017 | | Contributor(s):: Brian Winkel
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505-519.Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series...
21 Mar 2017 | | Contributor(s):: Mark A. Lau Kwan
This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation. The spreadsheet features a number of dynamic controls that permit the user to alter the parameters of the Van der Pol equation and explore the...