Numerical Methods and Transform Techniques

Solutions of algebraic and transcendental equations: bisection, secant, false position and iteration methods; Newton-Raphson method (including simultaneous equations); Interpolation: Newton's forward and backward formulae; Interpolation with unequal intervals; Lagrange's interpolation formula

Trapezoidal rule; Simpson's 1/3 and 3/8 rules; Solution of initial value problems by Taylor's series and Picard's method; Euler's method; Runge-Kutta method (second and fourth order); Milne's predictor-corrector method

Definition, Laplace transforms of standard functions, properties and shifting theorems; Transforms of derivatives and integrals; unit step and Dirac delta functions; Inverse Laplace transforms; convolution theorem (without proof); Applications: solving ODEs (initial value problems) and integro-differential equations

Periodic functions; Fourier series of periodic functions; Dirichlet's conditions; Even and odd functions; change of interval; Half-range sine and cosine series

Fourier integral theorem (without proof); Fourier sine and cosine integrals; Infinite Fourier transforms; sine and cosine transforms; Properties and inverse transforms; convolution theorem (without proof); Finite Fourier transforms