To practice basic arithmetic to enhance reasoning and computational capabilities.
Symmetric, Skew –symmetric , Hermitian and Skew Hermitian matrices, orthogonal and Unitary matrices, Elementary operation on matrices, Inverse of a matrix , Row rank, Column rank and their equivalence, Rank of a matrix, Eigen Vectors , Eigen values and the Characteristic equation of a matrix , Cayley –Hamilton theorem and its use in findings inverse of a matrices.
Vector Algebra : Triple products, reciprocal Vectors, Products of Vectors.
Ordinary differentiations of vectors, Application to mechanics and geometry , Differential operator , Definition of del, Gradiant , Divergence , Curl
Gauss’s divergence theorem , Green’s theorem , Stoke’s theorem ( without proof) and their simple applications.
Determinants and their properties.
First order and first degree differential equations, separation of variables, Homogeneous, linear, exact differential equations, second order linear equations with constant coefficients, Orthogonal trajectories.
Mathematics By R D Sharma