Syllabus academic year 2011/2012
(Created 2011-09-01.)
 MATHEMATICAL METHODS OF NANOTECHNOLOGY EXTF65
Credits: 7,5. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. EXTF65 overlaps following cours/es: EXTF20 and FFF155. Compulsory for: N2. Course coordinator: Peter Samuelsson, Department of Physics. Recommended prerequisits: FMA430 Calculus in Severable Variables, FAFA05 Physics - Waves, Thermodynamics and Atom Physics, Matlab. Assessment: Oral or written exam. Accepted laboratory work reports. Accepted computer laboratory work reports. Accepted excersise hand-ins. Home page: http://www.teorfys.lu.se/FFF155/.

Knowledge and understanding
For a passing grade the student must

1) Explain and describe basic properties of fourier series, fourier integrals and laplace transforms.

2) Qualitatively describe and explain applications based on fourier analysis such as image processing, heat conduction and analysis of linear mechanical and electrical systems.

3) Derive and describe Maxwells equations and explain their basic properties.

Skills and abilities
For a passing grade the student must

4) Solve simpler exercises related to the central concepts of the course.

5) With the help of computer simulations, analyze and visualize basic properties of models which are discussed during the course and present the analysis in a written report.

6) Carry out, analyze and present in a written report experimental laboratory work in central areas of the course.

Contents
From applications of physics and other parts of science, different mathematical and computational tools are introduced. Starting with specific problems, the methods are generalised and their universality is emphasized.

Mathematical tools that will be introduced are Fourier series and integrals, the Fourier transform, partial differential equations, equations of diffusion, linear systems, wave equation, Maxwell's equations, vector analysis and Laplace transform.

Applications of these tools are introduced through a number of projects. These could involve e.g. electrical circuits, networks, filters, harmonic signals, feedback systems, impedance, electromagnetism, diffusion, acoustics, musical instruments and mechanical systems.

Literature
The projects will be based on instructions produced at the department, L.Gislén.
Jönsson, P.: Matlab, Studentlitteratur.