Numerical and Computational Method

Interpolation schemes; the Lagrangian representation; Aitkin algorithm least square fit.

Interpolation schemes; the Lagrangian representation; Aitkin algorithm least square fit; Interactive processes; Solution of linear equations; Gaussian elimination; inversion of matrices; Fourier series and harmonic analysis; Difference equations; Numerical integration and differentiation - Trapezium; Simpson's; limitation of size of grid; Solution of ordinary differential equation; step by step methods; Partial differential equation; simple wave propagation forward difference; backward difference; central difference in time; the implicit scheme; conditions for stability; e.g.; diffusion equation; hyperbolic equation method of relaxation and other interactive schemes applied to simultaneous equations; ill-conditioned equations; Elliptic equations - interactive methods; spectral series method; Functional representation; minimization and telescoping; Computer solution of equations