FY505: Physical mathematics (5 ECTS)

STADS: 07000501

Level
Bachelor course

Teaching period
The course is offered in the spring semester.
3nd quarter.

Teacher responsible
Email: paolo.sibani@sdu.dk
Email: pica@cp3.sdu.dk

Additional teachers
marco@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Samlæses med FF505

Ubegrænset deltagerantal. 3. kvartal.

Prerequisites:
None

Academic preconditions:
FY520 Understanding Basic Physics, MM501 Calculus I and MM502 Calculus II must be known.

Course introduction
To introduce the students to fundamental concepts of linear algebra and to show how to use them in modelling selected physical systems.

Qualifications
General qualifications: ability to use fundamental techniques and principles in linear algebra and numeric software for solving dynamic problems, e.g. coupled linear differential equations and boundary value problems in simple geometries. Personal qualifications: the ability of collaborate with others, to use abstract ideas in a specific connection, and to present the results in a well-planned and convincing way.

Expected learning outcome
After completing the course the student should be able to:

• Be able to use basic methods and results from linear algebra to solve systems of linear coupled differential equations and partial differential equations describing physical models.
• Use software packages e.g. matlab to treat specific physical models.
• Assess the quality of the results obtained and the applicability of the underlying model to the phenomena the model is meant to describe.
• Write a report where the results obtained are described in a clear, concise and understandable way.

Subject overview
The course is offered jointly by IFK and IMADA.

Structure:
1st week: Introduction and problem formulation by IFK
2nd-4th week: Mathematics - IMADA
5th-7th. week: Numeric project work – IFK

Topics in Physics:

1. Linearisation as a physical modelling tool.
2. Coupled ordinary differential equations and normal modes.
3. Partial differential equations (diffusion equation, Schrödinger’s equation) in simple geometries.
4. Fourier transformation as a tool for data analysis and as a solving technique.

Topics in Mathemathics:

1. Basic theory of linear vector spaces: vectors, linear independence, basis, dimension, the Euclidean vector spaces Rn and Cn. E.g. vector spaces of functions: Fourier series.
2. Linear mappings between vector spaces: rank and kernel, matrix representation, eigenvalues and eigenvectors, diagonalisation of symmetric (or hermitic) n x n matrix, solution of boundary value problems by expansion in eigenfunctions.

Projects:
The project is based on physical models and is solved by using software packages e.g. Maple or Matlab. The results must be presented in a report written using LaTeX.

Literature

Meddeles ved kursets start

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. 1 project report. Internal examination by lecturer. Marks according to the 7-scale. (5 ECTS). (07000502).

Re-examination after 4th quarter.
The mode of exam at the re-examination may differ from the mode of exam at the ordinary exam.

Expected working hours
The teaching method is based on three phase model.

Ved Institut for Matematik og Datalogi:
Forelæsninger 12 timer
Eksaminatorier 12 timer

Ved Institut for Fysik og kemi:
Forelæsninger 4 timer
Lab.øvelser 24 timer

Educational activities

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.