Integration and Differentiation

UNIVARIATE QUADRATURE

ROUTINE DESCRIPTION
QDAGS Integrates a function (which may have endpoint singularities).
QDAG Integrates a function using a globally adaptive scheme based on Gauss-Kronrod rules.
QDAGP Integrates a function with singularity points given.
QDAG1D Integrates a function with a possible internal or endpoint singularity.
QDAGI Integrates a function over an infinite or semi-infinite interval.
QDAWO Integrates a function containing a sine or a cosine.
QDAWF Computes a Fourier integral.
QDAWS Integrates a function with algebraic logarithmic singularities.
QDAWC Integrates a function F(X)/(X – C) in the Cauchy principal value sense.
QDNG Integrates a smooth function using a nonadaptive rule.
 

MULTIDIMENSIONAL QUADRATURE

ROUTINE DESCRIPTION
TWODQ Computes a two-dimensional iterated integral.
QDAG2D Integrates a function of two variables with a possible internal or end point singularity.
QDAG3D Integrates a function of three variables with a possible internal or endpoint singularity.
QAND Integrates a function on a hyper-rectangle.
QMC Integrates a function over a hyper-rectangle using a quasi-Monte Carlo method.
 

GAUSS RULES AND THREE-TERM RECURRENCES

ROUTINE DESCRIPTION
GQRUL Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.
GQRCF Computes a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule given the recurrence coefficients for the monic polynomials orthogonal with respect to the weight function.
RECCF Computes recurrence coefficients for various monic polynomials.
RECQR Computes recurrence coefficients for monic polynomials given a quadrature rule.
FQRUL Computes a Fejér quadrature rule with various classical weight functions.
 

DIFFERENTIATION

ROUTINE DESCRIPTION
DERIV Computes the first, second or third derivative of a user-supplied function.