MATEMATIKChalmers 0pt

kurskod= TMA371

Engelska namn= Partial Differential Equations

Ges av= md

Svenska namn= Partiella Differentialekvationer TM3 (för KfKbEIKMVZ)

Antal poäng= 4

Beskrivning= The course is dealing with basic differential equations of science and engineering. It covers the following topics: Polynomial approximation, polynomial interpolation, quadrature rules, variational methods, iterative solution of linear system of equations. Existence and regularity of solutions of linear partial differential equations (PDEs) of elliptic, parabolic and hyperbolic type. Introduction to Galerkin's finite element method. A priori, a posteriori and adaptive error analysis. Some potential theory and integral equations of physics and mechanics. Applications to problems in, e.g., solid mechanics, heat trasfer, fluid mechanics, electromagnetism, acoustics and quantum mechanics. Two point boundary value problems, initial value problems. Poisson equation, heat equation, wave equation, convection-diffusion problems. Lax-Milgram Lemma.

Förkunskaper= The participant is presumed to have

(i) a solid background in calculus of one and several variables,

(ii) knowledge of the elementary theory of linear ordinary differential equations,

(iii) an acquaintance with the complex number system and the complex exponential function.

(iv) a solid background in Fourier analysis (especially method of separation of variables for solving PDEs and also Fourier and Laplace transform techniques to solve PDEs).

Mål= This course gives an introduction to the modern theory of partial differential equations (PDEs) with applications in science and engineering. It also presents an introduction to the finite element method as a general tool for numerical solution of PDEs.

Språk= depends on audience (swedish or english)

Bok= Computational Differential Equations, K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Studentlitteratur, 1996.

Obligatorisk= Compulsary for TM studies

Teaching staff=

Examiner and Lecturer: Mohammad Asadzadeh, mohammad@math.chalmers.se

TA and Tutor: Rikard Bergström, ribe@math.chalmers.se

TA and Tutor: Klas Samuelsson, klassam@math.chalmers.se

Termin= Period II in Fall

Bedömning= Home and computer assignments combined with written exam

Limited number of places.