Eigen values and Eigenvectors of real matrix-Properties of Eigen values 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

Sequences: Definition and examples – Series: Types and Convergence – Series of positive terms – Tests of convergence: Comparison test, Integral test and D’Alembert’s ratio test – Alternating series – Leibnitz’s test.

Basics-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 – Errors and Approximations – 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.