Branton, Michael

Stetson University

Department of 

Mathematics

DeLand, FL 32720

mgb@thoth.stetson.edu





A Virtual Environment for Exploring Differential Equations





The "text" is meant to create for the student an environment for exploring

differential equations, their uses and relationships to the physical

world.  In particular, the "text" seeks to provide to the student

kinesthetic feedback by allowing direct manipulation of on-screen

"objects" which may represent physical systems or abstract mathematical

representations of those systems. 



The "text" will place an emphasis on visual representation and the direct

manipulation of such representations. For example, the student may

directly interact with the phase portrait of a differential equation, or

the energy surface of a hamiltonian system, and this interaction will

cause the appropriate associated changes in the physical model to occur. 



Support for student and/or instructor creation of animations will be

created. 



   Specific topics to be covered include:

   Solving first order ODE's

   Solving first order linear systems of ODE's

   Eigenvector, eigenvalue analysis 

   Linear approximation of non-linear systems of ODEs

   Fixed points and stability

   Limit Cycles and attractors

   Bifurcation behavior



Graphics and animation of the following will be supported: ODE solutions



   ODE solutions

   Vector fields for systems of ODEs

   Phase portraits of ODEs

   Projections of systems of ODEs having more than 2 equations

   Eigenvalues and eigenvectors of systems of ODEs

   Hamiltonian systems

   Bifurcations in systems of ODEs

   Vector fields for systems of ODEs 

   Phase portraits of ODEs Projections of systems of ODEs having more than

        2 equations

   Eigenvalues and eigenvectors of systems of ODEs

   Hamiltonian systems 

   Bifurcations in systems of ODEs





 









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