The present book is designed for the course in Applied Mathematics to meet the requirements of the first year Diploma courses for all the engineering branches of different Technical Boards of Education in India. The objective of this book is to provide a simple presentation of the concepts, emphasizing understanding without sacrificing mathematical rigour. The book is composed of eighteen chapters. Each chapter presents illustrative solved examples and exercises. The problems given in exercises would develop interest and encourage the students to explore new ideas. The book presents an exhaustive coverage of the theory, formulae and a large number of solved examples to make the underlying principles more comprehensive: