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| Joubert, Stephan V. | 1 |
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Direct linkFay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2009
We report on a study of the forced van der Pol equation x + [epsilon](x[superscript 2] - 1)x + x = F cos[omega]t, by solving numerically the differential equation for a variety of values of the parameters [epsilon], F and [omega]. In doing so, many striking and interesting trajectories can be discovered and phenomena such as frequency entrainment,…
Descriptors: Student Research, Calculus, Equations (Mathematics), Mathematics Instruction
Fay, Temple H.; Joubert, Stephan V. – International Journal of Mathematical Education in Science and Technology, 2009
We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [second derivative of]x + x + epsilonx[superscript 2] = Fcoswt and the [second derivative of]x + x + epsilonx[superscript 3] = Fcoswt and report the results of a systematic numerical investigation on the global stability of…
Descriptors: Equations (Mathematics), Mathematics Instruction, Mathematical Models, Mathematical Concepts
Fay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2003
The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…
Descriptors: Equations (Mathematics), Calculus, Error of Measurement, Problem Solving
Fay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2002
Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…
Descriptors: Geometric Concepts, Mathematics Instruction, Geometry, Generalization
Fay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2003
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Descriptors: Undergraduate Study, Equations (Mathematics), Problem Solving, Mathematical Formulas
Fay, Temple H. – International Journal of Mathematical Education in Science & Technology, 2006
This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation. For fixed initial conditions and fixed parameter [epsilon] results are reported of a systematic numerical investigation on the global stability of solutions to the initial value problem as the parameters F and…
Descriptors: Student Research, Computer Uses in Education, Equations (Mathematics), Mathematics Instruction
