Vector Calculus: Vector Function. Derivative of a Vector function. Gradient of a scalar function. Divergence and curl of vector functions. Directional derivative and calculation of pressure, Kinetic interpretation of energy.Linear Algebra: integral of matrices. Addition and multiplication of matrices. Inverse of square matrix. Orthogonal, Hermition and Unitary matrices. Properties of determinants and expansion of the determinants. Solution of nonhomogeneous linear equations by Cramer’s rule. Elementary operations. Echelons and reduced echelon forms. Rank of a matrix. Equivalent matrices. Gauss-Jordan elimination method. System linear homogeneous and nonhomogeneous equations vector spaces. Subspaces. Linear dependence and independence Span, Basis and Dimension. Eigen value problems Eigen vectors. Cayley - Hamilton theorem.
