This very nicely written paper is the enlarged version of a four-hour seminar talk given by Professor Jacovkis during the Second Congress on Applied, Computational and Industrial Mathematics held in Rosario, Argentina, during December 14‒16, 2009. The author provides an overview of several fundamental steps in mathematical modeling including formulation of a model, calibration of parameters, analysis of initial and boundary conditions and sensitivity issues. A number of important mathematical models are discussed: ordinary differential equations, delay differential equations, and difference equations arising in population dynamics, partial differential equations that model traffic problems and dynamics of shallow water.

Reviewer:

Svitlana P. Rogovchenko (Umeå)