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