Applied Mathematics I Sem 1

Matrices:
Minors and Cofactors, Adjoint of a square matrix, Inverse of a matrix.
Rank of a matrix, Solution of Homogeneous and non homogeneous
linear Equations using Matrix method.

Eigen Values and Eigen Vectors:
Vectors, linear combination of vectors, Inner Product of two vectors,
characteristic equation, Eigen Vector, Cayley- Hamilton Theorem,
Similarity of Matrices, Derogatory and Non-derogatory matrices,
Complex Matrices: Hermitian, skew-Hermitian and Unitary matrices
and their properties.

Vector Calculus:
Vector Differentiation: Vector Operator Del, Gradient, and
Geometrical Meaning of gradient, Divergence and Curl.

Differential Equations:
Differential Equations of 1st order and 1st degree and applications

Linear Differential Equations:
Linear Differential equations with constant coefficient, Differential
equations of higher order and applications.

Successive differentiation, Mean Value theorems, Partial
differentiation, Euler’s Theorem, Approximation and errors, Maxima
and Minima