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General
Semester
Autumn 2009 (Monday, October 5 to Friday, December 11)
Timetable
Prerequisites
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Syllabus
- Generalised derivatives: Definition and simple properties of generalised derivatives. Limits and generalised derivatives.
- Sobolev spaces: Definition of Sobolev spaces. Imbedding theorems. Equivalent norms.
- Laplace's equation: Laplace's equation and harmonic functions. Dirichlet and Neumann boundary value problems. Elements of the potential theory.
- Generalised solutions of differential equations.
- Singular solutions of Laplace's equation, wave equation and heat conduction equation.
- Variational method.
- Weak Solutions.
- The energy space.
- Green's formula.
- Weak solutions of the Dirichlet and Neumann boundary value problems.
- Spectral analysis for the Dirichlet and Neumann problems for finite domains.
- Heat conduction equation.
- Maximum principle.
- Uniqueness theorem.
- Weak solutions.
- Wave equation.
- Weak solutions.
- Wave propagation and the characteristic cone.
- Cauchy problems for the wave equation and the heat conduction equation.
Bibliography
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Assessment
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