The main aspects of writing this book are to present the basic requirements of the students as per the Ph.D. Students of all Indian Universities and all over the world Universities in the most simple manner. Each unit is prepared in a systematic and logical presentation of solved examples followed by an Theorems and Example sections. The book is designed as a self - contained comprehensive & friendly from students point of view. Both theorems and examples have been explained by using elegant diagrams. Author's Achievements and Awards in Abroad: As Young Scientist (DST), International Conference on Mathematics and Statistics held at Kuala-Lumpur, Malaysia on 3-5 Nov. 2010-11. Selected as Senior Scientist from DST Delhi, to attend IAENG conference London UK on July 6-9, 2011-12 (DST). Abroad Presentation & Publication: Presented & Published 42 (Forty Two) Papers in various National & International Conference & Reputed Journals. Presently guiding to 6 Ph.D. Research scholars

Dr. Sadanand N. Patil is a working as Asst. Prof. & HOD in the Dept. of Mathematics KLS's, VDRIT Haliyal. Affiliated to VTU, Belgaum. Karnatala. India. He is teaching from last 5 years to UG (BE) and PG (M.Tech.). presently guiding to 6 Ph.D. Research Scholars and Published 42 papers in International Journals. He has attended conference abroad.