Rank of a matrix, Eigen values, Eigen vectors of a Matrix, Cayley Hamilton theorem, Consistency of equations, Matrix invertion, Gaussian elimination scheme, Cholesky factorization, Jacobi and Gauss-Seidal iterative methods for solving simultaneous equations, Eigen value solution using forward iteration, Inverse itrration, Hermitian and skew Hermitian forms, Unitary Matrix, Functions of a Matrix, Quadratic forms and conical forms

Differential Equations of First Order and its Applications

Formation of differential equation, Solution of a differential equation, Geometrical meaning, Equations of the first order and first degree, Variables separable, Homogeneous equations, Linear equations, Bernoulli s equation, Exact equations, Equation reducible to exact equations, Equations of the first order and higher degree, Calirut s equation, Geometric applications, Orthogonal trajectories, Physical applications, Simple electric circuits, Heat flow, Chemical applications, Newton s law of cooling

Frobenis method, Special function as solution from series, Bessel equation, Bessel functions of first and second kind, Equation reducible to Bessel s equations, Legender s equations, Legender polynomial, Rodrigues formula, Generating functions, Recurrence relation, Orthonogolity relation for Bessel functions and Legendre polynomial

Transforms of elementary functions, Properties of Laplace transforms, Existence conditions, Inverse transforms, Transform of derivatives, Transform of Integrals, Multiplication s by t division by t , Convolution theorem, Application to ordinary differential equations and simultaneous linear equations with constant coefficients, Unit step function, Impulse functions and periodic functions