Definition of Calculus Analysis

 

Calculus helps you perform the deferential or integral function on the data in any curve.

 

Differential

Differential numerically differentiates the curve data.

 

     Linear

The N points img69.gif  are given. The differential of points is defined as,

img70.gif

 

     Smooth

The smoothing differential evaluates the derivative by fitting a Cspline(cubic spline) to the curve data and analytically forming the derivative. Given a tabulated function img71.gif , focus attention on particular interval, between  img72.gif and img73.gif .  The cubic spline interpolation in that interval gives the interpolation formula img75.gifwhere,

img76.gif

The first derivative of Cspline is obtained as,

img77.gif

 

Integral

Integral numerically integrates the curve data.

 

     Linear

The N points  img78.gif are given. The integral of points is defined as,

img79.gif

 

     Smooth

The smoothing integral evaluates the integral by fitting a Cspline(cubic spline) to the curve data and analytically forming the integral. Given a tabulated function img80.gif , focus attention on particular interval, between img81.gif  and img82.gif .  The cubic spline interpolation in that interval gives the interpolation formula

img83.gif where,

img84.gif

The integral of Cspline is obtained as,

img85.gif