An Undergraduate Student Project on study of differential Equations from dynamical system point of view using MATHEMATICA
Dipendra Chandra Sengupta, Ph.D
dsengpta@umfort.cs.ecsu.edu
Corey Ellis
Department of Mathematics and Computer Science
Elizabeth City State University
U.S.A.
Abstract
In this project we begin the systemic study of "differential equations". This study is not a study of an equation and tricks to 'solve it', but rather of the dynamic 'movement' produced by the differential equation.
A differential equation describes 'how things change', and if we know where we start, we should be able to predict where we go and how fast. The 'systems' we study here are families of initial value value problems (I.V.P.) given by a diffrential equation and a starting position.
One good analogy for a mathematical dynamical system is the 'flow' on the surface of a smoothly moving river. The differential equations corresponds to the velocity vector at each point on the surface, while the collection of paths of all the water particles constitute the solution flow. We study numerical, graphical and symbolic description of mathematical flows determined by a differential equations and its initial conditions.
In this project we explicitly analyze and solve several models which leads to linear and nonlinear differential equations using MATHEMATICA .
© Asian Technology Conference in Mathematics, 1998. |
