Types of Matrices– Rank of a matrix - Eigen values and Eigen vectors –Cayley Hamilton theorem –Inverse of a matrix –Physical significance of matrices.

Differential Equation –Geometrical Interpretation –Physical Significance –Order and degree –Differential equations of first order and first degree – Variable separable equations –Homogeneous equation –Linear equations –Exact Differential equations –Equations reducible to homogeneous, linear and exact forms.

Linear and nonlinear second order differential equations – Superposition principle –Homogeneous linear equation with constant coefficients – Initial value and boundary value problems –Inhomogeneous equations – Particular integrals for various forms of inhomogeneity -Cauchy-Euler equation – Method of undetermined Coefficients –Method of variation of parameters –Wronskian and linear dependence of solutions

Wave equation –Solution of homogeneous and inhomogeneous wave equations by method of characteristics – Solution of Laplace equation in one, two and three dimensions by variable seperable method.

Definition of line integral and basic property – Evaluation of line integrals –Definition of double integral –Conversion to iterated integrals – Evaluation of double integral – Change of variables –Surface Areas – Surface integral in cylindrical and polar coordinates -Definition of triple integrals – Evaluation of triple integrals –Volume integrals in spherical polar coordinates.