Determining Eigenvalues and Eigenvectors of a real matrix Properties of Eigenvalues and Eigenvectors Cayley Hamilton Theorem (statement only) Problems Applications: Eigenvalue problems arising from population models (Leslie model).

Diagonalization of a real symmetric matrix Quadratic form Canonical form Nature of the quadratic form Reduction of quadratic form to canonical form by orthogonal transformation Applications: Stretching of an elastic membrane.

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

Partial derivatives – Homogeneous functions and Eulers theorem Jacobians Taylors series for functions of two variables Applications: Maxima and minima of functions of two variables Lagranges method of undetermined multipliers.

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