الفهرس 
Sturm-liouville boundary value problemOnly 14 pages are availabe for public view
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Abstract
This thesis includes a study of eigen value problems of d i f f e r e n t i a l operator and the numerical solution of Sturm-Liouville equation with Periodic conditions. It i s c l a s s i f i e d into three chapters. The f i r s t chapt e r i s devoted to the study of the baundary value problem of some d i f f e r e n t i a l operators specially Sturm-Liouville one. Also accurate asymptotic solutions of concerned d i f f e r e n t i a l equation are obtaine& chapter contains four sections, the f i r s t section represents the spectra of the operator -d 2 ( + q(x)) , in the secand section the general dx form the Sturm-Liouville boundary value problem i s given , the t h i r d one i s preserved f o r the asymptotic formula of the eigen values and eigen functions -of Sturm-Liouville equation, and the fourth explain how we can obtain the solutions of expansion of Stun-Liouville equation in terms of the set of eigen functions. The second chapter deals with using the inverse s c a t t - ering theory for the problem on the half line and whole l i n e generated by the Sturm-Liouville d i f f e r e n t i a l equation. This chapter consists of two s e c t i o n s , in the first section solutions of a generalized form of Sturm-Liouville d i f f e r e n t i a l equation on the half line and i t s scattering function i s obtained and i t s properties are studied.