4 hours/week Credit:
4
Co-ordinate
Geometry:
Transformation of co-ordinates; Pair of straight lines; Circles; System of
circles; Radial axis; Parabola-standard equation Ellipse, Hyperbola in
Cartesian and Polar co-ordinate, Diameter, Conjugate Diameter, Tangent, Normal;
General equation of second degree.
Matrices: Definition of matrix: Algebra of matrices,
Multiplication of matrices. Transpose of matrix and inverse of matrix. Rank and
elementary transformation of matrices. Solution of linear equations. Linear
dependence and independence of vector. Quadratic forms. Matrix polynomials.
Determination of characteristic roots and vectors. Null space and nullity of
matrix. Characteristic subspace of matrix.
Vector Analysis: Scalars and vectors, equality of vectors.
Addition and subtraction of vectors, Multiplication of vectors by scalars, Position
vector of a point. Resolution of vectors. Scalar and vector product of two
vectors and their geometrical interpretation. Triple product and multiple
product. Application to geometry and mechanics. Linear dependence and
independence of vectors. Differentiation and integration of vectors together
with elementary application. Definition of line, surface and volume integral.
Gradient, divergence and curl of point functions. Various formulae. Gauss's
theorem stake's theorem Green's theorem and their applications.