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The present book meets the requirements of B.E./B. Tech students. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Special emphasis has been laid on fundamentals for better understanding of the subject. Each chapter begins with definitions followed by important results with proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned and exhaustive exercises have been given in each chapter to provide the students with an opportunity of exhaustive practice. Each exercise has been divided into Short Answer Type Questions and Long Answer Type Questions. Review of the chapter is given at the end of each chapter so that students can revise the chapter at a glance. CONTENTS : Curve Tracing; Curvature. Rectification; Areas bounded by standard curves; Volumes and surfaces of revolution of curves; Centre of gravity and moment of inertia. Partial differentiation; Homogeneous functions and Euler’s theorem; Composite functions; Derivative of an implicit function; Change of variable; Jacobians. Tangent and normal to a surface; Taylor’s and Maclaurin’s series for a function of two variables; Errors and approximations; Maxima and minima of function of several variables; Lagrange’s method of undetermined multipliers. Double and triple integral, change of order of integration, change of variable, Application of double and triple integration to find areas and volumes. Scalar and vector fields, differentiation of vectors, Vector differential operators: Gradient, Divergence and Curl, their physical interpretations. Line, surface and volume integrals. Solenoidal and Irrotational vectors. Gauss Divergence theorem. Green’s theorem in plane, Stoke’s theorem and their applications.