Description

The text starts with the concepts of limit, continuity, differentiability and is followed by the study of successive differentiation, tangents and normals, Rolle’s theorem, Lagrange’s mean value theorem, Taylor’s theorem, Taylor’s and Maclaurin’s series, indeterminate forms, partial differentiation, curvature, asymptotes, concavity, convexity and points of inflexion, singular points, tracing of the curves, elementary integration, integration of rational functions, irrational algebraic functions and trigonometric functions, definite integrals, reduction formulae, quadrature, rectification and volumes and surfaces of revolution. Moreover, three Appendices on Beta and Gamma functions, Maxima and Minima, and Practicals with Mathematica have also been presented.

Salient Features:

Presentation of the subject in a natural way

Description of the concepts with justification

Tangents, Normals and Derivative of Arcs

Mean Value Theorems and Expansion of Functions

Indeterminate Forms

Partial Differentiation

Curvature

Asymptotes

Concavity, Convexity and Points of Inflexion

Singular Points

Tracing of the Curves

Elementary Integration

Integration of Rational Functions

Integration of Irrational Algebraic Functions

Integration of Trigonometric Functions

Definite Integrals

Reduction Formulae

Quadrature

Rectification

Volumes and Surfaces of Solids of Revolution