# BCA205

Mathematics II
Code:
BCA205
Year / Semester:
2nd Semester
Objective:

To practice basic arithmetic to enhance reasoning and computational capabilities.

Credits:
3

### Matrices

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 Analysis

Vector Algebra : Triple products, reciprocal Vectors, Products of Vectors.

### Vector Differentiation

Ordinary differentiations of vectors, Application to mechanics and geometry , Differential operator , Definition of del, Gradiant , Divergence , Curl

### Vector integration

Gauss’s divergence theorem , Green’s theorem , Stoke’s theorem ( without proof) and their simple applications.

### Determinants

Determinants and their properties.

### Differential Equation

First order and first degree differential equations, separation of variables, Homogeneous, linear, exact differential equations, second order linear equations with constant coefficients, Orthogonal trajectories.