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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.
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CategoriesArts and Science
Format EPUB
TypeeBook