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unit–i
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–ii
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–iii
Curvature and Evolutes
Introduction - Definition of curvature - Radius of curvature - Length of arc as a function,
Derivative of arc - Radius of curvature - Cartesian equations - Newtonian method -
Centre of curvature - Chord of curvature.
Evolutes: Evolutes and Involutes - Properties of the evolute.
Envelopes: One parameter family of curves - Consider the family of straight lines -
Definition - Determination of envelope.
unit–iV
Lengths of Plane Curves
Introduction - Expression for the lengths 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.