Matrices Vector & Differential Equations

SYLLABUS- MATRICES VECTOR & DIFFERENTIAL EQUATIONS, Unit-I: Type of Matrices, Elementary operation on matrices, Inverse of a matrix by
elementary operations, rank of a matrix, Echelon and normal form, Eigen values,
eigenvectors and characteristic equation of a matrix, Cayley-Hamilton theorem and
its use in finding inverse of a matrix, system of linear homogeneous and non
homogeneous equations, theorems on consistency of a system of linear equations.
Unit-II: Vector Differentiation, Gradient, Divergence and Curl, Vector Integration,
Theorems of Gauss, Green, Stokes and related problems.
Unit-III: Formation of a differential equation, geometrical meaning of a differential
equation, Equation of first order and first degree, Equations in which the variables
are separable, Homogeneous equation, Linear equations Exact differential
equations and equations reducible to the exact form, First order higher degree
equations solvable for x, y, p.
Unit-IV: Clairaut's equation and singular solutions, orthogonal trajectories, linear
differential equation with constant coefficients, homogeneous linear differential
equations.