1st Section

Mathematical Analysis

Mathematical Analysis is the subject of the Mathematical Analysis Section and is one of the most extensive and profound branches of Mathematics. Although it is harder today to demarcate this branch than in the past, one could say that Mathematical Analysis begins with the introduction of the concept of the "limit" and the subsequent infinitesimal analytic method, and further expands radially and inexhaustibly in all directions. The mission of the Mathematical Analysis Section is the initiation of all students in the concepts and methods of Mathematical Analysis and at the same time the cultivation and growth of knowledge in the field through the quest of new ideas and methods.

An invaluable contribution of Mathematical Analysis is the supply of creative and effective tools to other fields of Mathematics, from purely theoretical to completely applied fields. Some of the basic and interdependent directions of Mathematical Analysis are the Theory of Real Functions, the Theory of Complex Functions, Topology, Differential Equations, the Theory of Measure and Integration, Functional Analysis, etc.

The exact study of a physical or mechanical and generally of a dynamical system, which describes the development of a phenomenon or the control of a certain population situation, can take place through continuous or Discrete Differential Equations. Such equations can provide information that refers to the general behaviour of solutions, as for example is the description and ascertainment of stability, approximation, periodicity, etc.

As is natural, the closer the theoretical model is to the natural phenomenon, the closer we come to its exact study through the model. For example, we will have a better approach to reality if we take into consideration the phenomenon's history. Thus, we come to the so-called Delay Differential Equations, which constitute an extensive and rather complex class of Functional Differential Equations. In this general case, the study is carried out by examining the convergence of the paths of abstract systems that are observed in general topological spaces. The study of such spaces, which facilitates comprehension of natural problems, is the subject of Functional Analysis, Topology and the Measure Theory.

Personnel of the Mathematical Analysis Section and their scientific interests: