FMA021, 7,5 credits, A (Second Cycle)
Valid for: 2014/15
Decided by: Education Board B
Date of Decision: 2014-04-08
Main field: Technology.
Compulsory for: F2, Pi2
Elective for: D4, E4, M4
Language of instruction: The course will be given in 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
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 student
should become acquainted with the use and usability of software
packages for computation and simulation.
Knowledge and understanding
For a passing grade the student must
- be able to demonstrate an ability to formulate mathematical
models for phenomena in heat conduction, diffusion, wave
propagation and electrostatics.
- be able to demonstrate an ability to physically interpret
mathematical models with different boundary conditions for the
three basic types of pde:s: the heat equation, the wave equation
and the Laplace/Poisson equation, and to understand the
characteristics of their solutions.
- be able to demonstrate an ability to use spectral methods
(Fourier) and source function methods (Green) to solve problems for
the three basic equations in simple geometries.
- be able to demonstrate an ability to interpret functions as
abstract vectors in a Hilbert space, and to use for functions
concepts such as norm, distance, scalar product.
- be able to demonstrate an ability to decide whether an
operator is symmetric, and an ability to identify Sturm-Liouville
- be able to demonstrate an ability to find eigenfunctions and
eigenvalues for some types of Sturm-Liouville operators, in
particular those associated with the Laplace operator in one, two
and three dimensions.
- be able to demonstrate an ability to explain the projection
formula and to use it to solve least squares problems.
- have some experience and understanding of the use of
mathematical and numerical software in order to solve problems
related to the course.
Competences and skills
For a passing grade the student must
- be able to demonstrate an ability to independently choose
appropriate methods to solve the three basic types of partial
differential equations, och to carry out the solution essentially
- be able to demonstrate an ability to use theoretical tools from
areas such as Hilbert space theory, special functions, distribution
theory, Fourier and Laplace transforms, and Green functions
to solve the three basic pde:s in simple geometries.
- in connection with problem solving, be able to demonstrate an
ability to integrate knowledge from the different parts of the
- \with proper terminology, in a well structured way and with
clear logic be able to explain the solution of a mathematical
problem within the course.
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.
Grading scale: TH
Assessment: Written test comprising theory and problem solving. Computer sessions. A voluntary test at the middle of the course provides an opportunity to collect credits for the final exam.
Code: 0198. Name: Applied Mathematics.
Credits: 7,5. Grading scale: TH.
Code: 0298. Name: Laboratory work.
Credits: 0. Grading scale: UG.
- FMA430 Flerdimensionell analys
Required prior knowledge: FMAF05 Systems and Transforms.
The number of participants is limited to: No
The course overlaps following course/s: FMAF15, FMA020, FMA022, FMFF15
- Sparr, G & Sparr, A: Kontinuerliga system. Studentlitteratur, 2000, ISBN: 91-44-01355-8.
- Sparr, G & Sparr, A: Kontinuerliga system., Övningsbok. Studentlitteratur, 2000, ISBN: 91-44-01234-9. Preferably the printing from 2006.
Contact and other information
Director of studies: Studierektor Anders Holst, Studierektor@math.lth.se
Course homepage: http://www.maths.lth.se/course/kontsys/
Further information: 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.
The credits may only be used to raise a failing grade to a pass, but not
to raise a pass to a higher mark.