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Instructors: Apl. Prof. Dr. rer. nat. Yuri Genenko
Event type:
Lecture
Org-unit: Dept. 11 - Institute of Materials Science
Displayed in timetable as:
Math.Meth.Mat.Sci.
Subject:
Crediting for:
Hours per week:
2
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Course Contents:
• Linear ordinary differential equations: constant an d variable coefficients
• Relaxation processes and oscillations in electrical circuits, parametric resonance
• Normal vibrational modes of polyatomic molecules: Lagrangian mechanics
• Linear partial differential equations: elliptic, hyperbolic, and parabolic equations
• Method of Fourier and Laplace transforms
• Diffusion in composite media: interface resistance
• Diffusion of foreign atoms to cylindrical and spherical precipitates
• Diffusion of magnetic field in a metal
• Solidification processes in an undercooled melt: Stefan problem
• Injection of electrons into dielectrics and organic semiconductors
• Green’s function technique
• Bifurcations and phase transitions in open biological and chemical systems
• Self-organization in nonlinear active media
Literature:
1. G.B. Arfken, H.J. Weber: Mathematical Methods for Physicists, Academic Press, New York (1995)
2. H.S. Carslaw, J.C. Jaeger: Conduction of Heat in Solids, Clarendon Press, Oxford (1993)
3. J. Crank: The Mathematics of Diffusion, Clarendon Press, Oxford (1994)
4. H. Heuser: Gewöhnliche Differentialgleichungen – Einführung in Lehre und Gebrauch, Teubner, Stuttgart (1995)
5. G. Lehner: Elektromagnetische Feldtheorie für Ingenieure und Physiker, Springer, Berlin (1996)
6. W. Richter: Einführung in Theorie und Praxis der partiellen Differentialgleichungen, Spektrum, Heidelberg (1995)
Preconditions:
Basic knowledge in mathematics, physics, and materials science
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