·        a curve is a functional map relationship between two factors (i.e. a function - However, the word function is a reserved word).

·        You can use the EO API to create common types of functions, find zeroes and calculate derivatives - currently supports constants, lines, quadratic curves, polynomials and Chebyshev approximations.

·        A function basis is a set of functions that can be combined to form a particular class of functions.

 

·        the abstract base class from which all other curve classes are derived – it provides the following methods:

·        ValueAt(Double) - evaluates the curve at a specific point.

·        SlopeAt(Double) - evaluates the derivative

·        Integral(Double, Double) - evaluates the definite integral over a specified interval.

·        TangentAt(Double) - returns a Line curve that is the tangent to the curve at a specific point.

·        FindRoots() - attempts to find all the roots or zeroes of the curve.

·        A particular type of curve is defined by a Parameters property, of type ParameterCollection

·        defines a curve whose value and, optionally, derivative and integrals, are calculated using arbitrary methods. A general curve has no parameters.

·        Constructor params:  RealFunction delegates – 1 for the function, and optionally another 2 for the derivative and integral

·        If no derivative  or integral function is supplied, they are calculated via the NumericalDifferentiation  and AdaptiveIntegrator classes in the Extreme.Mathematics.Calculus namespace.