اسلامی اخلاقیات واقدار کے فروغ میں خاندانی ماحول کا کردار؛معاصرانہ چیلنجز اور لائحہ عمل The role of family environment in the development of Islamic ethics and values, Contemporary challenges, and action plan

Islamic rules and moral values are unique in all aspects. The members of Muslim Ummah have always tried to promote them. At the national level, this duty was carried out by people at different levels whether they were teachers, businessmen or lay man of the society. At international level, some rulers, business professionals and religious leaders played their role. Man's first relationship is with family. This relationship is the cornerstone in the development of a personality.  There has been a lot of change taken place in the family system. In the past, due to the limited necessities of life the financial responsibility was limited to a few people. Media was not that advanced and bold and family members were loving and respectful. With the beginning of advance era, human needs were widened and to satisfy them, women started participating in economic activities along with men. Due to which the child was shifted from his home to day care centre, while the media gave birth to the social media, the stories of compassion and care in home became the past. In the present era, there is a dire need to remove these barriers that hinder the development of Islamic values through balance between income and expenditure, positive and moderate use of media and positive attitude in family. These issues will be discussed under the answers to the following questions. What is the role of family in the development of Islamic ethics? What are the problems faced by the family in the development of Islamic moral values? What are the solutions to the present-day problems?  

Transformation Techniques to Find the Analytical and Numerical Solutions of Ordinary Differential Equations Odes

The analytical solutions are very rare in the field of differential equation. However, in Physics and engineering sciences it is always preferred to find analytical solution. Analytical solutions are exact and error free solutions supported with a logical proof. The motivation is to find the analytical solution of second order ordinary differential equations (ODEs). In this thesis we have presented some methods to find the analytical solutions of different forms of differential equations (DEs). The chapter wise summary of this thesis is as under. The first chapter presents brief introduction to the problem of study, its objectives and methodology used to achieve the goal. In the second chapter we have presented a comprehensive form of literature review related to the studying problem understudy. The current literature is discussed in detail and results are summarized to draw conclusions and further directions. The third chapter is preliminaries, showing notions and basic definitions which are associated with this study. In chapter four, we have presented our main results with their proofs for solving ODEs by using a transformation technique. We have implemented the results in the form of solution methods to provide general solutions to practical examples. We have also solved some problems to explain the solution procedure and its implementation. The numerical verification and comparison of each problem is also included in this chapter. In chapter five, we have proposed an idea to solve second order differential equation with polynomial coefficients by using Laplace transformation. The operator form of solution is presented and discussed in this chapter.