Precize CALCULUS I (P.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.


Properties of Real Numbers :Order property of real numbers, bounds, l.u.b. and g.l.b. order completeness property of real numbers, Archimedian property of real numbers.

Limits :    e–d definition of the limit of a function, basic properties of limits, infinite limits, indeterminate forms.

Continuity : Continuous functions, types of discontinuities, continuity of composite functions, continuity of | f (x) |, sign of a function in a neighborhood of a point of continuity, intermediate value theorem, maximum and minimum value theorem.

Mean Value Theorems : Rolle’s Theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, their geometric interpretation and applications, Taylor’s theorem, Maclaurin’s theorem with various form of remainders and their applications.

Hyperbolic, inverse hyperbolic functions of a real variable and their derivatives, successive differentiations, Leibnitz’s theorem.

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