Multiple Product - Scalar triple product, Vector triple Product, Geometrical interpretations . related Problems: vector function of a Scalar Variable interpretation as a space curve; derivative, tangent normal and binormal vectors to a space curve; curvature and Torsion of a space curve; - definitions, derivation and Problems, Servlet Frenet formulae. Scalar field: Gradient of a scalar field, Geometrical meaning, directional derivative, unit normal using Surfaces, - tangents plane and normal to the surface; vector field . divergence and curl of a vector field, geometrical meaning, solenoidal, and irrotational field ; Laplacian of a scalar field; vector identities.
Unut-2 VECTOR INTEGRATION:
Definition and Basic Properties, Vector line integral, surface integral and volume integral; Green's theorem in the plane - Proof and Related Problems, Direct consequences of the theorem; Gauss Divergence theorem - Proof and Related Problems, Direct consequences of the theorem; Stoke's theorem - Proof and Related Problems, Direct Consequences of the theorem.
Unit-3 ANALYTICAL GEOMETRY:
Planes, Straight lines and Spheres planes: Distance of a point from plane, Angle between two planes Pair of planes, Bisectors of angle between two planes; Straight lines: Equation of Straight lines, Distance of a point from a straight line, Distance between two straight lines, Distance between a straight line and a plane: Spheres: Different forms, intersection of two Sphere. orthogonal intersection, Tangents and normal Radical plane, Radical lino, coaxial System of Spheres, pole, polar and conjugancy
Unit -4
Locus, Surfaces, Curves and Conicoid Space outves, Algebraic curves, Ruted surfaces; Some Standard Surfaces, classification of quadratic Surfaces; cone ,, cylinder, central concords Tangent plane, Normal, polar planes and polar Lines.
