Content and idea

See also the presentation of H. Krogstad: Mathematical Modelling – Content and Philosophy.

The course aims to teach simple but general techniques in mathematical modeling. The goal is to provide an analytical/critical approach to practical problem solving and modeling, as opposed to uncritical "cookbook mentality" and the use of ready-made computer software. The methods we will cover will force understanding of what is going on. Be warned that the course differs from traditional mathematic courses in that many problems will not have complete solutions, and therefore we often have be stop reaching only partial solutions. While mathematic courses applies difficult techniques to simple problems, we do the opposite in this course. What is needed here is ingenuity and creativity, which is difficult enough! Unfortunately, we have to spend more time than we would like on analytical techniques not generally known to the students. These topics will be dealt with in a rather brief manner, and will probably require some extra effort on the student's behalf during the semester.

• gives an indication about how reasonable a model is and what it should look like
• reduces the number of variables and parameters to a minimum
• reduces the number of experiments both on computers and in the laboratory
• provides a technique for scaling of physical experiments

• systematic method of problem analysis
• forces one to make estimates and understand what is going on
• tells us what's important and less important
• gives dimensionless equations with large or small parameters
• important to complete before the numerical computations are initiated

• method to find approximate solutions of scaled equations
• complementary to numerical calculations

• very common models
• easy to understand and easy to do numerical simulations

• direct mathematical description of the fundamental laws of nature
• applicable not only for liquids!
• diffusion as a general modeling technique

• Numerical solution of differential equations.
• To apply complete "black box" computer programs.
• Neural networks and expert systems.
• "Blind modeling" with an ARIMA process of sufficiently high order.
• Modeling of geometric shape.