Mathematics BSc
Course description
2013.
Borromean Rings
Partial differential equations
Hours
lect+pc		 Credits
lect+pc		 Assessment Specialization Course code
lect/pc		 Semester Status
2 + 2 2 + 3 exam +
term grade		 pure math. mm1c1pd6m
mm1c2pd6m		 6 optional
applied math. mm1c1pd6a
mm1c2pd6a		 6 compulsory
Strong Weak Prerequisites
Practice class
Strong:
Analysis3L-p (mm1c1an3m) or
Analysis3L-a (mm1c1an3a)
Lecture
Weak:
practice class
Weak:
Differential equationsL-p (mm1c1de5m) or
Differential equationsL-a (mm1c1de5a)
Weak:
Functional analysis1L-p (mm1c1fa5m) or
Functional analysisL-a (mm1c1fa5a)
Literature
  • V. S. Vladimirov: The equations of mathematical physics. 1967.
Syllabus
  • Notion and types of partial differential equations, examples in physics.
  • Classification of second order linear partial differential equations.
  • Distributions.
  • Fundamental solutions.
  • Cauchy problems for parabolic and hyperbolic equations.
  • Elliptic problems, Green formula, Green's functions.
  • Sobolev spaces, embeddings, trace.
  • Weak solution of elliptic boundary value problems.
  • Eigenvalues, eigenfunctions and applications.
  • Initial-boundary value problems for parabolic and hyperbolic equations, Fourier's method.
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