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.