Mathematics is an essential ingredient in the training of those seeking careers in science and engineering. No matter what the specialization, it is absolutely essential for scientists, physicists and engineers to not only develop an understanding of basic techniques of mathematics but also extend their manipulative skills to apply those techniques in their fields. The choice of mathematical topics in this book is evolved from the lectures given by the authors to undergraduate and postgraduate students in physics and engineering at IIT, New Delhi and at the National University of Singapore. Throughout the book, the authors have followed a style of presentation emphasizing the derivation of techniques from the first principles. The illustrative material, solved examples and problems have been chosen for their value in applications of interest to scientists and engineers. This book should meet the requirements of students of engineering and physical sciences at the undergraduate and postgraduate levels. Large number of solved and unsolved numericals make the text also ideal for self-study.