Course Contents
The aim of this lecture course is to introduce basic concepts for exact and
approximate solution of ordinary and partial differential equations including
the demonstration of applications on material science relevant questions.
In detail, among others the following examples are treated:
Relaxation processes and oscillations in electrical circuits. Ordinary and parametric resonance.
Charge injection in dielectrics and organic semiconductors. Space-charge limited current.
Charge defect migration in ferroelectrics induced by depolarization fields.
Thermostimulated currents in semiconductors with deep defect states.
Normal oscillation modes of small molecules.
Gas diffusion through a membrane.
Diffusion of point defects into rod-shaped or globular precipitates in metals.
Atomic diffusion through a semi-transparent interface.
Solidification in one-, two- or three-dimensional geometry.
Magnetic field diffusion in conductors and superconductors.
Bifurcations and phase transitions in open biological and chemical reaction systems. Self-organization and switching waves in nonlinear active media.
Literature
J.R. Acton, P.T. Squire, "Solving Equations with Physical Understanding",
Adam Hilger, Bristol (1985).
G.B. Arfken, H.J. Weber, "Mathematical Methods for Physicists", Academic
Press, New York (1995).
H.S. Carslaw, J.C. Jaeger, "Conduction of Heat in Solids", Clarendon Press,
Oxford (1993).
J. Crank, "The Mathematics of Diffusion", Clarendon Press, Oxford (1993).
R.E. O'Malley, "Thinking About Ordinary Differential Equations", Cambridge
University Press, Cambridge (1997).
H. Haken, "Synergetics", Springer-Verlag, Heidelberg, 1978
- Lehrende: Yuri Genenko