Course syllabus
Partiella differentialekvationer med distributionsteori
Partial Differential Equations with Distribution Theory
FMAN75, 7,5 credits, A (Second Cycle)
Valid for: 2017/18
Decided by: PLED F/Pi
Date of Decision: 2017-04-06
General Information
Language of instruction: The course will be given in English on demand
Aim
- The probably largest class of mathematical models among
technichal systems is based on partial differential equations
(PDE). An indispensable tool in the modern theory for these
equations is distribution theory.
- The aim of the course is on the one hand to give a more stable
theoretical foundation for concepts and methods for PDEs that
have been introduced in earlier courses, and a greater ability to
independently use these, and on the other hand to develop the
theory further. Moreover, the course aims to give the analytical
background to some frequently used numerical solution
methods.
Learning outcomes
Knowledge and understanding
For a passing grade the student must
- be able to explain the foundations of the theory at an
oral examination.
- be able to explain the concept of a weak solution to a PDE, and
its connection to distribution theory.
Competences and skills
For a passing grade the student must
- with access to literature independenly be able to integrate
methods and views from different parts of the course in order to
solve problems and answer questions within the framework of the
course.
- in writing and orally, with proper terminology and clear logic
be able to explain the solution to a mathematical problem within
the course.
Contents
Distribution theory: derivatives, convergence,
fundamental solutions, Green's functions, the Fourier transform,
the Laplace and the wave operators.
Partial differential equations: spectral methods,
eigenfunction expansions, weak solutions. Approximation methods.
Integral equations, finite element methods. Geometrical methods.
Characteristics. The study of some model equations.
Examination details
Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written and/or oral test, to be decided by the examiner. Written assignments.
The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
Admission
Required prior knowledge: FMAN55 Applied Mathematics, first part of FMAN80 Functional Analysis and Harmonic Analysis.
The number of participants is limited to: No
The course overlaps following course/s: FMA250
Reading list
- Renardy & Rogers: An Introduction to Partial Differential Equations. Springer, 2004, ISBN: 0-387-00444-0.
- Material distributed by the department.
Contact and other information
Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Course homepage: http://www.ctr.maths.lu.se/course/partdiff/