Formulas of this year's [2024] NPTEL Course titled Advanced Computational Techniques
1) Lagrange's Formula for Interpolation
2) Taylor Seriers [ Specifically for the increasing powers of h ]
3) Newton Forward Interpolation
4) Newton Backward Interpolation
5) Hermite Interpolation
6) Spline Interpolation
7) Simpson's 1/3 rule for Numerical Integration
8) Simpson's 3/8 rule for Numerical Integration
9) Trapezoidal rule for Numerical Integration
10) Tri-diagonal System and Thomas Algorithm
11) Gauss Quadrature Rule for Numerical Integration
12) Least Square Approximation for curve fitting
13) Eigen values - Power Method
14) Quadratic form Q(x) of system of linear equations
15) LU Decomposition
16) Gauss Elimination
17) Gauss Jacobi Iteration
18) Gauss Seidal Iteration
19) Gauss Seidal Iteration - Sucessive over relaxation (SOR)
20) Steepest Descent Method
INITIAL VALUE PROBLEMS
21) Euler Method
22) Runge-Kutta Order
23) Milne's Method
BOUNDARY VALUE PROBLEMS
24) Finite Differences
25) Transfer Equations
26) Linear Hyperbolic PDE