# Calculus | Krishna Series

Contents

This book Calculus on has been specially written according to the latest Unified Syllabus to meet the requirements of the B.A. and B.Sc. Part-I Students of all Universities in Uttar Pradesh.

This book is important for UPSC Optional, IIT JEE Mains, Graduation College Students BSC all sem (1st, 2nd, 3rd year), BA (1st, 2nd, 3rd, 4th, 5th, 6th semester), Engineering, Preparing for SSC, Banking And Other Competitive Examination.

The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The proofs of various theorems and examples have been given with minute details. Each chapter of this book contains complete theory and a fairly large number of solved examples. Sufficient problems have also been selected from various university examination papers. At the end of each chapter an exercise containing objective questions has been given.

### Syllabus

Differential Calculus

Unit-1: ε-δdefinition of the limit of a function, Continuous functions and classification of discontinuities, Differentiability, Chain rule of Differentiability, Rolle’s theorem, First and second mean value theorems, Taylor’s theorems with Lagrange’s and Cauchy’s forms of remainder, Successive differentiation and Leibnitz’s theorem.

Unit-2: Expansion of functions (in Taylor’s and Maclaurin’s series), Indeterminate forms, Partial differentiation and Euler’s theorem, Jacobians.

Unit-3: Maxima and Minima (for functions of two variables), Tangents and normals (polar form only), Curvature, Envelopes and evolutes.

Unit-4(a): Asymptotes, Tests for concavity and convexity, Points of inflexion, Multiple points, Tracing of curves in Cartesian and Polar coordinates.

Integral Calculus

Unit- 4(b): Reduction formulae, Beta and Gamma functions.

Unit-5: Quadrature. Rectification. Volumes and surfaces of solids of revolution, Pappus theorem, Double and triple integrals, Change of order of integration, Dirichlet’s and Liouville’s integral formulae.