Description
Concavity, convexity, points of inflexion, multiple points, double points and its types for curves in a plane. Tangents at origin, asymptote and its types, methods for finding asymptotes of rational algebraic curves. Special methods for finding oblique asymptotes of rational algebraic curves. Intersection of a curve and its asymptotes.
Introduction to the polar coordinate system, tracing of curves represented by equations in Cartesian coordinates, Polar coordinates, and in parametric forms.
Curvature and radius of curvature at a point of curves in Cartesian and Polar Co-ordinates including parametric forms as well as curves represented by equation f (x, y) = 0 implicitly.
Integral Calculus: Integration of hyperbolic and inverse hyperbolic functions. Reduction Formulae.
Numerical integration: Trapezoidal, Prismoidal and Simpson Rules.
Application of definite integral: Summation of Series, Quadrature, rectification, volumes and surfaces of solids of revolution (Cartesian co-ordinates only)
