UNIT 1:
Ch Eigen values and Eigen vectors of a real matrix
Eigen values and Eigen vectors of a real matrix
Properties – Eigen values and Eigen vectors
Statement and applications of Cayley – Hamilton theorem
Diagonalization of Matrices
Reduction of quadratic form to canonical form by orthogonal transformation
Reduction of quadratic form to canonical form by orthogonal transformation
UNIT 2:
Curvature in Cartesian coordinates
Centre and radius of curvature
Centre and radius of curvature
UNIT 3:
Partial derivative and Total derivatives
Differentiation of implicit functions, Jacobian and properties
Taylor series for functions of two variables.
Taylor series for functions of two variables.
Maxima and minima of functions of two variables
Maxima and minima of functions of two variables
UNIT 4:
Higher order linear differential equations with constant coefficients (RHS = eax, sinax(or) cosax)
Method of variation of parameters
Problems on Method of variation of parameters
Eulers(Cauchys) linear equations
UNIT 5:
Double integration in cartesion coordinates
Change of order of integration
Area enclosed by plane of curves
