Industrial mathematics is formally defined as a branch of applied mathematics dealing with real problems coming from industry and practice in general. Such problems are usually not mathematically formulated, require original thinking, highly developed common sense, mathematical knowledge and culture, a lot of work and … thick skin.

The seminar starts with a presentation of some real industry mathematical problems’ solutions, followed by a short introduction to the application area of the modern sliding-mode control. Examples include automatic page layout, numeric aesthetic criteria, lip motion capture and identification, real-time advertisement in sport TV broadcast. The introduction course includes aircraft control design, real-time robust exact differentiation, image edge detection, control without a mathematical model, glucose level control in blood. The theoretical material to be covered includes differential equations with discontinuous right-hand sides and differential inclusions, normal forms of nonlinear dynamic systems.

Each student is expected to prepare his own presentation. A number of subjects and corresponding literature are proposed to the students, although each student is welcome to suggest a subject based on real-life mathematical applications of his choice. An alternative way of participation, available when the number of participants is high, is to perform the computer simulation of the real-time noisy-signal differentiation. This will require some programming skills (MatLab, C++, C, Java, etc).

The seminar homepage: http://www.tau.ac.il/~levant/mathappl/index.html

The needed background: standard courses of calculus, linear algebra, and differential equations.