Mathematical Concepts -II

Matrix algebra, Determinants, matrix inversion, Solving Simultaneous equations using inverse of a matrix, consistency and independence. Simultaneous equations with three unknowns (e.g. spectrophotometry) using Cramer’s rule. Homogeneous linear equations.

Vectors and coordinate systems: Unit vectors (application in solid state), Component of vectors, addition and subtraction of vectors, multiplication of vectors. Vector calculus: differentiation of vectors, Vector derivative operators(Basic concepts of gradient, divergence and curl).Coordinate systems in three dimensions (Cartesian, polar, spherical and their interconversion).

Maximum and minimum values of functions of two variables. Extreme points and stationary points of a function, Euler’s theorem on homogenous function of two variable. Multiple integrals (Basic concepts of double and triple integral). Change of order of double integration.

Differential equations: Order and degree of differential equations, solution of first order and first degree differential equations with separable variables, homogeneous and linear differential equations, partial differential  equation of first order PDE, types of integrals of a PDE, the integral of the Lagranje’s linear equation, solution of first order PDE using Charpit’s method.  

Complex numbers, complex plane, Argand diagram,complex conjugates, modulus of a complex number, square root of a complex number, Euler’s formula and polar form of complex numbers.