UNIT 1:
Eigen values and Eigen vectors of a real matrix
Eigen values and Eigen vectors of a real matrix
Eigen values and Eigen vectors of a real matrix
Eigen values and Eigen vectors of a real matrix
Cayley Hamilton Theorem (statement only)-Problems
Cayley Hamilton Theorem –Applications
Eigen value problems arising from population models( Leslie model)
Eigen value problems arising from population models( Leslie model)
Properties of Eigen values and Eigen vectors
UNIT 2:
Diagonalization of a real symmetric matrix
Diagonalization of a real symmetric matrix
Nature of the quadratic form
Reduction of quadratic form to canonical form by orthogonal transformation
Reduction of quadratic form to canonical form by orthogonal transformation
Applications: Stretching of an elastic membrane.
Applications: Stretching of an elastic membrane.
UNIT 3:
UNIT 4:
Homogeneous functions and Euler’s theorem
Applications: Maxima and minima of functions of two variables
Lagrange’s Method of undetermined Multipliers
Lagrange’s Method of undetermined Multipliers
UNIT 5:
Double integration (Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Change of order of integration
Change of order of integration
Applications of double integral(Area)
Applications of double integral(Area)
Triple Integration(Cartesian Coordinates)
Triple Integration(Cartesian Coordinates)
Applications: Volume of solids
