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SYLLABUS

UNIT-1

Partial Differentiation: Introduction-Functions of two variables-Neighbourhood of a

point (a; b) - Continuity of a Function of two variables, Continuity at a point - Limit

of a Function of two variables - Partial Derivatives - Geometrical representation of a

Function of two Variables - Homogeneous Functions.

UNIT-2

Theorem on Total Differentials – Composite Functions – Differentiation of Composite

Functions - Implicit Functions-Equality of fxy(a; b) and fyx(a; b) -Taylor’s theorem for a

function of two Variables-Maxima and Minima of functions of two variables Lagrange’s

Method of undetermined multipliers.

UNIT-3

Curvature and Evolutes : Introduction-Definition of Curvature - Radius of curvature –

Lenth of Arc as a fuction, Derivative or arc - Radius of curvature - Certesian equations

- Newtonian method - Centre of curvature - Chord of curvature.

Evolutes: Evolutes and Involutes-Properties of the evolutes:

Envelopes: One Parameter Family of Curves-Consider the family of straight lines -

Definition - Determination of envelope.

UNIT-4

Lengths of Plane Curves: Introduction - Expression for the length of curves y = f(x) -

Expressions for the length of arcs x = f(y); x = f(t), y = f(t), r = f(q)

Volumes and Surfaces of Revolution: Introduction-Expression for the volume

obtained by revolving about either axis-Expression for the volume obtained by revolving

about any line- Area of the surface of the frustum of a cone-Expression for the surface

of revolution-Pappus Theorems -Surface of revolution.