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Detaljer för kursplan för kurs FMAN76F giltig från och med HT 2025

Utskriftsvänlig visning

Allmänt
  • Engelska
  • Varje vårtermin
Syfte
  • The overall purpose of the course is that PhD students after completing the course should have deepened the knowledge about the theory partial differential equations that they acquired during the course FMAN55 Applied Mathematics, in particular concerning general geometries and semilinear equations. The purpose is also that the PhD students should have further developed their ability to solve problems and communicate mathematical reasoning.
Innehåll
  • *The method of characteristics and nonlinear equations of the first order.

    *Laplace’s equation. The heat equation. The wave equation.

    *The Cauchy-Kovalevskaya Theorem.

    *Sobolev spaces.

    *Existence, uniqueness and regularity for weak solutions to linear second order elliptic, parabolic and hyperbolic equations.

    *Maximum principles for elliptic and parabolic equations.
Kunskap och förståelse
  • För godkänd kurs skall doktoranden
  • be able to explain in depth the concepts, theorems and methods included in the course,

    be able to identify and prove the most important theorems in the course.
Färdighet och förmåga
  • För godkänd kurs skall doktoranden
  • be able to apply and integrate knowledge from the different parts of the course in connection with problem solving,

    be able to identify problems that can be solved by methods that are part of the course and use an appropriate solution method,

    be able to describe the solution to a mathematical problem within the course framework in speech and writing, logically coherent and with adequate terminology.
Värderingsförmåga och förhållningssätt
  • För godkänd kurs skall doktoranden
Undervisningsformer
  • Föreläsningar
  • Seminarier
Examinationsformer
  • Skriftlig tentamen
  • Muntlig tentamen
  • Underkänd, godkänd
Förkunskapskrav
Förutsatta förkunskaper
  • FMAF01 Analytic Functions, FMAF05 Systems and Transforms, and FMAN55 Applied Mathematics.
Urvalskriterier
Litteratur
  • Evans, Lawrence C.: Partial Differential Equations. American Mathematical Soc., 2010. ISBN 9780821849743.
Övrig information
Kurskod
  • FMAN76F
Administrativ information
  • 2025-01-10
  • Maria Sandsten

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Utskriftsvänlig visning