Start: Tuesday January 21, Time: 13.15-15.00, Room 3418 Math Building, Lindstetdsv. 25

The course will run on Tuesdays: 13.15-15.00

A few classes will be outside this time-window but will be discussed and agreed upon with the participants.

Goal:

To learn about certain problems with origins in industrial applications. The goal is to introduce students to real-world problems and to provide them with tools and techniques for solving such problems. The course can be seen as an introduction to the subject and there are possibilities of further study and "Examensarbete" in mathematics.

Topics:

Basics in Mathematical Analysis:

Several Variable Calculus, Vector Analysis, Ordinary Differential Equations, Fourier Series, Numerics.

New Mathematical Tools:

Harmonic/Caloric functions, Greens function, Poisson/Laplace Equation, Maximum Principle, Calculus of Variation, Discrete Version of these. References will be suggested for each topic.

Industrial Topics:

Crystal Precipitation, Air Quality Modelling, Electron Beam Lithography, Development of Color Film Negative, Catalytic converter. A few other topics will be added as projects.

Prerequisites:

Standard courses in Calculus and Linear Algebra. It is desirable but not necessary to have some knowledge in: Fourier analysis, functions of one complex variable, ordinary differential equations, and some numerics.

Literature:

Industrial Mathematics (A course in solving real world problems) by Avner Friedman and Walter Littman. ISBN 0-89871-324-2.

Any standard basic literature in ODE/PDE.

Numerics: See https://people.maths.ox.ac.uk/suli/nsodes.pdf

Examination

The examination will consist of two parts.

Home work assignments to be announced here: Total 6 separate HW, each containing a few problems both from the book and also general PDE/ODE knowledge. See the Assignment page.
Project, with a presentation to follow: See details here: Projects

Grading policy

The HWs will have 40% weight and Projects 60%

SF2724 VT20-1 Topics in Mathematics IV