# Numerical Analysis

An equation of the form a$_{0}$x$^{n}$ + a$_{1}$x$^{n-1}$ + a$_{2}$x$^{n-2}$ + .........+ a$_{n}$ = 0 where a$_{0}$ $\neq$ 0 and a$_{1}$, a$_{2}$, ........, a$_{n}$ are constants and n is a positive integer called an algebraic equation of degree n.

If f(x) = a$_{0}$x$^{n}$ + a$_{1}$x$^{n-1}$ + a$_{2}$x$^{n-2}$ + .........+ a$_{n}$ then above equation becomes f(x) = 0

If f(x$_{0}$) = 0 for x = x$_{0}$ then x$_{0}$ is called a root of f(x) = 0

There are various numerical methods to solve algebraic equations like Iteration method, newton raphson method, finite differences, algebraic equations using gauss eliminations and gauss seidel method, rate of convergence, lagrange's method, numerical differentiation and integration etc.

Numerical analysis is the study of algorithms that use numerical approximation based on mathematical analysis. It does not seek answers as it is impossible to obtain in practice. It's applications can be found in all fields of engineering and physical sciences. Numerical weather prediction is feasible.