This book provides a comprehensive, through and up-to-date treatment of B.Sc. third Semester (FYUGP) Students Gauhati University. It is intended to introduce students of Mathematics, Physics, computer science, chemistry and related fields to those areas of applied Mathematics that are most relevant for solving practical problems. General Features of the book include: • Simplicity of examples. • General increase in difficulty of material with no jumps or gaps. • Modern standard notations. This book is written according to the latest B.Sc. third Semester (FYUGP) syllabus under NEP-2020 of Gauhati University. A number of worked examples are given in each chapter of the book. The book also contains a set of exercises of the end of each topic. The aim of these exercises is to provide additional material on the subject and also to test the student’s comprehension and abilities. No claim to originality is made but the presentation of the subject is in our own style. We feel indebted to various authors on the subject whose books have been consulted in preparing the present volume. Suggestions for the improvement of the book will be gracefully acknowledge. We are also very thankful to the publishers and printers for their full cooperation and utmost efficiency with which they have brought out the book in the present nice form.