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The present book provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject.


Limit and Continuity of functions of two variables. Partial differentiation. Change of variables. Partial derivation and differentiability of real-valued functions of two variables. Schwartz’s and Young’s Theorem. Statements of Inverse and implicit function theorems and applications. Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two variables. Jacobins. Envelopes. Evolutes. Maxima, Minima and saddle points of functions of two variables. Lagrange’s undetermined multiplier method.

Double and Triple Integrals, Change of variables. Applications to evaluation of areas, Volumes, Surfaces of solid of revolution, Change of order of integration in double integrals.

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