Fourier Series and method of separation of variables (Boundary value problems)
Expansion of simple functions in Fourier series, half range series, change of interval, Harmonic analysis.
Application to the solution of wave equation and diffusion equation in one dimension and Laplace’s
equation in two dimensions by method of separation of variable
Units: II
Laplace Transform
Laplace Transform with its simple properties . Inverse Laplace transform convolution Theorem ( without
proof) solution of ordinary differential equation with constant coefficient
Units: III
Special functions.
Bessel’s function of first kind, simple recurrence relations, orthogonal property. Legendre’s function of first
kind simple recurrence relations, orthogonal property , Rodrigue’s formula.
Units: IV
Numerical Analysis
Finite differences , Difference operators , forward, Backward, central & average operators. Newton’s forward
and backward interpolation formula, Stirling’s central difference formula Lagrange’s interpolation formula for
unequal interval. Solution of non linear equations in one variable by Newton Raphson’s and Regula falsi’s
method .
Units: V
Numerical Analysis
Numerical solution of simultaneous algebric equation by Gauss elimination and Gauss seidel method.
Numerical differentiation , Numerical integration trapezoidal rule , Simpson’s one third and three eight rule.
Numerical solution of ordinary differential equation of first order: Picards method, Euler’s , and modified
Euler’s ,method, Milne’s methods and Runga Kutta fourth order method..