TABLE OF CONTENTS Let
The values, which the independent variable x takes, are called arguments and the corresponding values of f( x) are called entries. The difference between consecutive values of x is called the interval of differencing.
If the interval of differencing is h and the first argument is a, then
| Arguments x: | a, | a + h, | a + 2 h, | a + 3 h, |
|
| Entries f(x): | f( a), | f( a + h), | f( a + 2 h), | f( a + 3 h), |
|
For brevity, these entries are denoted by
y 1 y 0 = f( a + h) f( a) is called the first forward difference of y 0 and is denoted by ? y 0 or ? f( a). Thus
Similarly,
In general,
The differences of the first forward differences are called second forward differences.
Thus
? ( ? y 0) = ? ( y 1 y 0) or ? 2 y 0 = ? y 1 ? y 0 is called the second forward difference of y 0.
Similarly,
In general,
Similarly, we can define differences of higher order.
The table showing the various forward...
