Precize Advanced Calculus (Pbi. U.)

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The entire subject matter in the book 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. Well-planned and exhaustive exercises have been given in each chapter.


Limit and continuity of functions of two and three variables. Partial differentiation. Change of variables. Partial derivation and differentiability of real-valued functions of two and three variables. Schwarz and Young’s theorem. Statements of Inverse and implicit function theorems and applications.

Vector differentiation, Gradient, divergence and curl with their properties and application.

Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two and three variables. Jacobians. Envelopes. Evolutes. Maxima, minima and saddle points of functions of two and three variables. Lagrange’s multiplier method.

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