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Syllabus for

Academic year
TMA372 - Partial differential equations
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: B
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   18 Dec 2006 am V,  10 Apr 2007 am V,  29 Aug 2007 am V

In programs

CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, Year 1 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Algorithms, Year 4 (elective)
TELTA ELECTRICAL ENGINEERING, Year 4 (elective)
TITEA SOFTWARE ENGINEERING, Year 3 (elective)
TM Teknisk matematik, Year 1 (compulsory)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)

Examiner:

Bitr professor  Mohammad Asadzadeh



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The participant is presumed to have
(i) a solid background in modern linear algebra and calculus of one and several variables,
(ii) knowledge of the elementary theory of linear ordinary differential equations,
(iii) an acquantaince 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).

Aim

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. Iteration procedures and interpolation techniques are also employed to derive a priori and a posteriori error estimates.

Content

The course is dealing with basic differential equa-tions of science and engineering. It covers the following topics: Polynomial approximation, poly-nomial 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 transfer, fluid mechanics, electro-magnetism, acoustics and quantum mechanics. Two point boundary value problems, initial value problems. Poisson equation, heat equation, wave equation, convection-diffusion problems. Lax-Mil-gram Lemma.

Literature

Computational Differential Equations, K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Student-litteratur 1996

Examination

Home and computer assignments combined with written exam


Page manager Published: Thu 03 Nov 2022.