#finite differences

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A blog about mathematics.

Finished Chapter 4: Numerical Differentiation and Integration!

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Finite Difference Method

When given a table of values, you can determine if a polynomial function is linear, quadratic, or cubic by using the finite difference method. To use the finite difference method, you use the y-values and subtract them from each other, two at a time, starting from the bottom. Once all pairs have been subtracted, and the differences are not the same, continue to subtract these differences from one another until the differences are the same. Once the differences are the same, count the amount of columns of differences, including the same difference column. That is the degree of your polynomial function. *Note: It would not matter the pattern of which the x-values are in. Use the finite difference method to find the degree of the polynomial function:

Starting from the bottom, subtracting each pair of y-values:

The first column has the same difference of 2, therefore, the table of values represents a linear polynomial, degree 1. Use the finite difference method to find the degree of the polynomial function:

Starting from the bottom, subtracting each pair of y-values:

The second column has the same difference of 4, therefore, the table of values represents a quadratic polynomial, degree 2. Use the finite difference method to find the degree of the polynomial function:

Starting from the bottom, subtracting each pair of y-values:

The third column has the same difference of 6, therefore, the table of values represents a cubic polynomial, degree 3.