Eigenvalues and Eigenvectors of real matrix-Properties of Eigenvalues and Eigenvectors- Cayley Hamilton Theorem (statement only) and its applications. Diagonalization of a real symmetric matrix- Quadratic forms - Reduction of quadratic form to canonical form by orthogonal transformation- Nature of the quadratic form.

Curvature-Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co- ordinates – Evolutes – Envelopes.

Partial derivatives –Total derivatives – Jacobians – Taylor’s series of functions of two variables –Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers.

Homogeneous Linear ODEs with constant coefficients – Linear ODE with variable coefficients - Cauchy’s and Legendre’s Equations – Method of variation of parameters –- Applications: Modelling of Free Oscillations of a Mass-Spring system

Double integration (Cartesian co-ordinates) – Change of order of integration – Applications of double integral (Area) – Triple Integration (Cartesian co-ordinates) – Applications: Volume of solids.