Variational methods have proved to be very important in the study of optimal shape, time, velocity, volume or energy. Laws existing in mechanics, physics, astronomy, economics and other fields of natural sciences and engineering obey variational principles. The main objective of variational method is to obtain the solutions governed by these principles. Fermat postulated that light follows a part of least possible time, this is a subject in finding minimizers of a given functional. It is important to note that we are in this book concerned about solution of Boudary Value Problem of some Partial Differential Equations arising from the fields of Sciences and Engineering. This explains why this book is very usefull for Mathematics, Physics, Engineering students and tutors in these areas of descipline.