The Fourth Edition of this accessible and student-friendly book continues to serve as a basic text for engineering students as part of their course in engineering mathematics. The new edition has substantial revisions and modifications, in light of the recent changes in the mathematics syllabi of various universities/engineering institutes. Volume 2 focuses on differential equations of the second order, Laplace transforms, and inverse Laplace transforms and their applications to differential equations. It provides an in-depth analysis of functions of several variables and presents, in an easy-to-understand style, double, triple and improper integrals. The book also covers in detail vector analysis and the functions of a complex variable besides having a fairly detailed discussion on advanced numerical methods. New to This Edition 1 Two new chapters (Chapters 3 and 4) on Functions of Several Variables and Multiple Integrals 2 Three new sections on Elastic Curves, Electric Circuits, and Matrix Methods for Systems of Linear Differential Equations (Chapter 1) 3 New sections on Jacobians (Chapter 3) and Green’s Theorem in a Plane (Chapter 5) 4 Answers to more exercises, given at the end of each chapter 5 Several new illustrative examples and exercises. With these additions, including the many pedagogic features — both existing and new ones — the text should prove to be highly useful to students of engineering and should also benefit practising engineers and scientists.