The Fourth Edition of this well-received book continues to serve as a basic text for beginning students of engineering of all branches. The new edition is largely revised and rewritten keeping in mind the recent changes in the Engineering Mathematics curriculum. What distinguishes the new edition is the addition of many new examples and exercises drawn from the AMIE and IIT-JEE papers. The book begins with a detailed discussion on higher algebra, geometry, vectors and complex numbers. The text then goes on to give an indepth analysis of geometry, vectors and complex numbers; applications of differential calculus; integration; and ordinary differential equations of the first order. The book concludes with a thorough treatment of numerical methods -- a significant area of engineering mathematics. What's New to This Edition : A new Chapter (Chapter 5) on Ordinary differential equations of the First Order. Two sections on Diagonalisation by Orthogonal Transformation, and Quadratic Forms (Chapter 1). Sections on Analytical Geometry of Three Dimensions (Chapter 2). Section on Numerical Methods for First Order Differential Equations (Chapter 5). Provides Answers to more exercises, which are now given at the end of each chapter. With these additions and revisions, the book should appeal not only to students of engineering but also to practising engineers and scientists.