(Created 2011-09-01.)

MATHEMATICAL METHODS OF NANOTECHNOLOGY | EXTF65 |

*Knowledge and understanding*

For a passing grade the student must

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

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.