M.Sc.

This work is oriented towards two objectives:

The first objective is to classify and study the generalized one-dimensional integral equations that contain n one-dimensional integral operators. This study includes the existence of a unique solution for special types of these integral equations and their solutions by using some quadrature methods, namely the trapezoidal rule, the modified trapezoidal rule and Simpson's rule.

This thesis consider the normal distribution with its important appearance in many statistical fields of applications. Some mathematical and statistical properties of the distribution have been collected and illustrated with moments and higher moments. Six related theorems have been studied in the applications of this type of distribution.  The estimation manner and its properties have been illustrated throughout two methods (Moment and Maximum Likelihood methods) which are used to estimate the distribution parameters theoretically.

This work has three objectives:

 The first objective is to study fuzzy set theory including definitions, notations and examples. The second objective is to study and proof the existence and uniqueness theorem of fuzzy boundary value problems directly without transforming the problem into fuzzy initial value problem. The third objective is to study the numerical solution of fuzzy boundary value problems.