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InterpolatingFunction

InterpolatingFunction[domain, table]
represents an approximate function whose values are found by interpolation.

InterpolatingFunction[...][x] finds the value of an approximate function with a particular argument x.

In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <>. »

domain specifies the domain of the data from which the InterpolatingFunction was constructed.

If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.

InterpolatingFunction objects that take any number of real arguments may be constructed.

You can take derivatives of InterpolatingFunction objects using D and Derivative.

Make an InterpolatingFunction object that will go through the given points:

Only the domain is shown in standard output format:

Evaluate the function at a point in the domain:

Plot the function over its domain, showing the interpolation points:

Get an InterpolatingFunction object approximating the solution of a differential equation:

Plot the function and its derivative:

Find the indefinite integral of the solution: