ABSTRACT
Modern numerical mathematics provides a theoretical foundation behind the use of electronic computers for solving applied problems. A mathematical approach to any such problem typically begins with building a model for the phenomenon of interest. The advent of computers in the middle of the twentieth century has drastically increased our capability of performing approximate computations. Computers have essentially transformed approximate computations into a dominant tool for the analysis of mathematical models. Analytical methods have not lost their importance, and have even gained some additional “functionality” as components of combined analytical/computational techniques and as verification tools. Computers provide a capability of storing large arrays of numbers, and performing arithmetic operations with these numbers according to a given program that would run with a fast execution speed. Therefore, computers may only be appropriate for studying those particular models that are described by finite sets of numbers and require no more than finite sequences of arithmetic operations to be performed.
