Sturm-liouville problemleri ve boolean diferansiyel denklemleri

This thesis consists of five sections. In the first section, the important points of subject which we studied are introduced. In the second section, the biological diffusion process is examined with mathematical model and the solution by method of separation variables. Formulation of the general Sturm-Liouville problem is given in the third section. In the fourth section, main results on Sturm-Liouville problem is given with important properties. In addition to the properties, boundary value problem and Green?s function is introduced and relation between Green?s function and regular Sturm-Liouville problem via eigenfunction expansion is given. After giving the important theorems, completeness of eigenfunctions of Sturm-Liouville problems are investigated in the fourth section of the thesis. In the final section, Boolean Differential Equations which are very important in Mathematical Logic are introduced. The purpose of this section is to start to investigate getting Boolean form of Sturm-Liouville problems if it is possible.