Analytical and Approximate Solutions for Volterra Integro-Differential Equations and It’s Applications

       The  main objective of this thesis is to study and solve the Volterra integral and integro-differential equation and some  scientific models for real life problems. This objective may be divided into three sub objectives, as follows:
         The first one  is to classify and study the subject of the integral equations and to supply the basic definitions related to the Volterra integral and integrodifferential equations. In the second  sub objective  we used the " dafterdar-jafari method " to solve Volterra integral and integro-differential equations. The third  sub objective is to introduce another  iterative method which is called  the power series method  to provide a solution of the Volterra integral and integro-differential equations. Finally,  the application of  the  dafterdar-jafari method and the power series method are presented for finding the analytic and approximate  solution for some real  life scientific problems, namely, Volterra’s population  model, the hybrid selection model,  Riccati equation and the logistic model. Also, it is important to remark that the computer programs are coded using the computer software Mathematica.8.