UNIT 1:
Determining Eigen values and Eigen vectors of a real matrix
Determining 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)
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
Applications: Stretching of an elastic membrane.
UNIT 3:
Radius of curvature in Cartesian Coordinates
UNIT 4:
Homogeneous functions and Euler’s theorem
Taylor’s series for functions of two variables
Applications: Maxima and minima of functions of two variables
Lagrange’s Method of undetermined Multipliers
UNIT 5:
Double integration (Cartesian Coordinates)
Change of order of integration
Applications of double integral(Area)
Triple Integrals(Cartesian Coordinates)
Applications: Volume of solids
