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General


Semester

Autumn 2009 (Monday, October 5 to Friday, December 11)

Timetable

  • Fri 12:05 - 12:55

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


Alexander Movchan
Email abm@liv.ac.uk
Phone (0151) 7944740
Interests Partial differential equations, asymptotic analysis, continuum mechanics
Photo of Alexander Movchan


Students


Photo of Fatih Bribesh
Fatih Bribesh
(Loughborough)
Photo of Steven Eyre
Steven Eyre
(York)
Photo of Matt Ferguson
Matt Ferguson
(York)
Photo of Jan HOLLAND
Jan HOLLAND
(Cardiff)
Photo of Daniel HUGHES
Daniel HUGHES
(Cardiff)
Photo of Imran Khan
Imran Khan
(Manchester)
Photo of Ye Luo
Ye Luo
(Loughborough)
Photo of Samantha Newsham
Samantha Newsham
(Lancaster)
Photo of Heiner Olbermann
Heiner Olbermann
(Cardiff)
Photo of Lavdie Rada
Lavdie Rada
(Liverpool)
Photo of Moritz Reinhard
Moritz Reinhard
(East Anglia)
Photo of Veronika Schreiber
Veronika Schreiber
(Loughborough)
Photo of Kathleen Scott
Kathleen Scott
(Manchester)
Photo of Thomas Shearer
Thomas Shearer
(Manchester)
Photo of Nikola Stoilov
Nikola Stoilov
(Loughborough)
Photo of Desislava Todorova
Desislava Todorova
(Loughborough)
Photo of Yue  Wu
Yue Wu
(Loughborough)
Photo of Tim Yeomans
Tim Yeomans
(Newcastle)


Bibliography


No bibliography has been specified for this course.

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
assignment_1.pdf
assignment_2.pdf
assignment_3.pdf
assignment_4.pdf
LDO0_m.pdf
LDO1.pdf
LDO2.pdf
LDO3.pdf
LDO4.pdf
LDO5.pdf
LDO6.pdf
LDO7.pdf


Recorded Lectures


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