MAGIC018: Linear Differential Operators in Mathematical Physics

Course details

Semester

Autumn 2009
Monday, October 5th to Friday, December 11th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Fridays
12:05 - 12:55

Description

Prerequisites

No prerequisites information is available yet.

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.

Lecturer

  • AM

    Prof Alexander Movchan

    University
    University of Liverpool

Bibliography

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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