Course Syllabus for

Introduction to Partial Differential Equations
Kontinuerliga system

FMA022F, 7.5 credits

Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-01-27

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMA021
Teaching language: Swedish


Within the engineering sciences the term "continuous system" means a system whose state space is described by a continuous family of parameters. Continuous systems occur frequently in physics and other natural sciences, in mechanics, electricity and other engineering sciences, in economic sciences, etc. To describe a continuous system one is in general led to partial differential equations (PDE). One aim of the course is to provide mathematical tools, and the ability to use them, for the whole chain model building - analysis - interpretation av solutions to PDE:s appearing for such systems. Another aim is the converse: to lay a foundation for a general competence in mathematics, useful in further studies as well as in professional activities, by showing how abstract mathematical concepts, such as Hilbert spaces, may be used in concrete applications. A further aim is that the doctoral student should become acquainted with the use and usability of software packages for computation and simulation.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Physical models. Fourier's method, series expansions and integral transforms. Green functions. Wave propagation. Function spaces and function norms. Hilbert spaces. Sturm-Liouville operators and their eigenvalues and eigenfunctions. Special functions, e.g., Bessel, Legendre, spherical harmonics. Distributions. The Fourier and Laplace transforms. Something about the numerical solution of partial differential equations.

Course Literature

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination formats: Written exam, miscellaneous. Computer sessions. A voluntary written test at the middle of the course provides an opportunity to collect credits for the final exam.Any credits acquired by passing the voluntary written test at the middle of the course expire after a year. Thereafter it is possible to participate in the voluntary test the following year in order to try to acquire new credits.
Grading scale: Failed, pass

Admission Details

Course Occasion Information

Contact and Other Information

Course coordinators:

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