This book provides a comprehensive, thorough and up to date treatment of mathematics in engineering and sciences. This is intended to introduce students of engineering, physics, mathematics, computer sciences and other related fields to those areas of applied mathematics that are most relevant for solving practical problems. Practice is the key word in the learning process of mathematics . The aim of this book is to provide a vast knowledge of mathematics and its diverse practical use in daily lives. The course contents in this book are the sole pre-requisites. The experience of the author of more than a decade in teaching at under graduate, post graduate level and in the research areas of mathematics in University makes this book useful. In this book all the topics and related concepts have been given in a lucid and simple way filling every gap between students and mathematics. A lot of worked examples are given so as to help the readers understand better.