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Basic Course Descriptions |
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Page 8 of 9
7. Applied analysis,mathematical physics, and dynamical systems.
The two basic courses here provide a thorough introduction to the theory of ordinary differential equations and dynamical systems, and to that of partial differential equations.
Outline of the contents:
• Dynamical systems
◦ flow properties of dynamical systems
◦ omega limit sets
◦ stability of fixed points and periodic orbits
◦ invariant manifolds
◦ examples of local and global bifurcations
◦ chaotic behavior
• Partial differential equations
◦ scalar first order equation
◦ elementary PDEs: heat equation, wave equation, Laplace equation
◦ solutions of linear problems via orthogonal series (separation)
◦ elliptic problems via Lax–Milgrams theory, maximum principles
◦ existence and smoothing properties of parabolic equations
◦ hyperbolic equations in several space dimensions
◦ semilinear equations
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