Math Help

Archive for the ‘Numerical Analysis’ Category

 

If we divide [a,b] into n equal intervals, each of width: 

 

The first rectangle has area
The second rectangle has area
The ith rectangle has area
The nth rectangle has area

The area under f range [a,b] is therefore: 

Lagrange Theorem

Given numbers x₀ to x_n are distinct and numbers y₀ to y_n, then there exists a unique polynomial P_n (x) of degree n such that:

The Lagrangian polynomial is:

Below are Euler functions and equations often used in college pure math.

Euler Equation (Calculus of Variation)

If then

and x is not explicit.

Then is a constant.

Euler Identity (Series)

Euler-Maclaurin Integration Formula

B_n(s) is the Bernauli function