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Contents.m

% Numerical Integration Toolbox 
%
% MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration
%
% Edited Version for OCTAVE
% 
% The original 1-D routines were obtained from NETLIB and were 
% written by
%          Howard Wilson
%          Department of Engineering Mechanics
%          University of Alabama
%          Box 870278
%          Tuscaloosa, Alabama 35487-0278
%          Phone 205 348-1617
%          Email address: HWILSON @ UA1VM.UA.EDU
% 
% The rest of the routines were written by
%          Bryce Gardner
%          Ray W. Herrick Laboratories
%          Purdue University
%          West Lafayette, IN 47906
%          Phone: 317-494-0231
%          Fax:  317-494-0787
%          Email:  gardner@ecn.purdue.edu
%
% Easy to use routines:  (these routines iteratively integrate with 
%                   higher order quadratures until the integral has
%                   converged--use these routine unless you want to
%                   specify the order of integration quadrature that
%                   is to be used)
%        quadg.m  -- High accuracy replacement for QUAD and QUAD8 (1-D)
%        quad2dg.m      -- 2-D integration over a rectangular region
%        quad2dggen.m   -- 2-D integration over a general region
%        quadndg.m      -- n-D integration over a n-D hyper-rectangular region
%          README.nit   -- introductory readme file
%
% The 1-D routines:
%          README -- The original readme file by Howard Wilson
%          gquad.m      -- Integrates a 1-D function with input Gauss 
%                    points and weights (modified by Bryce Gardner to
%                    handle an optional parameter in the function to be
%                    integrated and also to calculate the Gauss points
%                    and weights on the fly)
%          gquad6.m     -- Integrates a 1-D function with a 6-point quadrature
%          grule.m      -- Calculates the Gauss points and weights
%          run.log      -- File with examples
%
%    New 1-D routines:
%        quadg.m  -- High accuracy replacement for QUAD and QUAD8
%        quadc.m  -- 1-D Gauss-Chebyshev integration routine
%          crule.m      -- Calculates the Gauss-Chebyshev points and weights
%          ncrule.m     -- Calculates the Newton-Coates points and weights
%
% The 2-D routines:
%        quad2dg.m      -- 2-D integration over a rectangular region
%        quad2dc.m      -- 2-D integration over a rectangular region with
%                    a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity
%          gquad2d.m    -- Integrates a 2-D function over a square region
%          gquad2d6.m   -- Integrates a 2-D function over a square region with
%                    a 6-point quadrature
%        quad2dggen.m   -- 2-D integration over a general region
%        quad2dcgen.m   -- 2-D integration over a general region with
%                    a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity
%          gquad2dgen.m -- Integrates a 2-D function over a variable region
%                    (That is the limits on the inner integration are
%                    defined by a function of the variable of integration
%                    of the outer integral.)
%          grule2d.m    -- Calculates the Gauss points and weights for gquad2d.m
%          grule2dgen.m -- Calculates the Gauss points and weights for 
%                    gquad2dgen.m
%          crule2d.m    -- Calculates the Gauss-Chebyshev points and weights 
%                    for gquad2d.m
%          crule2dgen.m -- Calculates the Gauss-Chebyshev points and weights 
%                    for gquad2dgen.m
%
% The n-D routines:
%          quadndg.m    -- n-D integration over an n-D hyper-rectangular region
%          gquadnd.m    -- Integrates a n-D function over 
%                          an n-D hyper-rectangular 
%                    region using a Gauss quadrature
%          cquadnd.m    -- Integrates a n-D function over 
%                          an n-D hyper-rectangular 
%                    region using a Gauss-Chebyshev quadrature
%          innerfun.m   -- used internally to gquadnd.m and cquadnd.m
%
% Utility routines:
%        count.m  -- routine to count the number of function calls
%        zero_count.m   -- routine to report the number of function calls and
%                    then to reset the counter
%
% Test scripts:
%          run2dtests.m -- 2-D examples and 1-D Gauss-Chebyshev examples
%        tests2d.log  -- output of run2dtests.m -- Matlab 4.1 on a Sparc 10
%        test_ncrule.m-- m-file to check the Newton-Coates quadrature
%        testsnc.log  -- output of test_ncrule.m -- Matlab 4.1 on a Sparc 10
%        test_quadg.m -- m-file to check the quadg routine
%        testsqg.log  -- output of test_quadg.m -- Matlab 4.1 on a Sparc 10
%
% Test functions:
%          xsquar.m     -- xsquar(x)=x.^2
%          xcubed.m     -- xcubed(x)=x.^3
%          x25.m  -- x25(x)=x.^25
%        fxpow.m  -- fxpow(x,y)=x.^y
%          hx.m         -- hx(x)=sum(x.^2)
%          gxy.m  -- gxy(x,y)=x.^2+y.^2
%          gxy1.m -- gxy1(x,y)=ones(size(x))
%          gxy2.m -- gxy2(x,y)=sqrt(x.^2+y.^2)
%          glimh.m      -- glimh(y)=3
%          glimh2.m     -- glimh(y)=y
%          gliml.m      -- gliml(y)=0
%          lcrcl.m      -- lcrcl(y)=-sqrt(4-y.^2)
%          lcrcu.m      -- lcrcu(y)=sqrt(4-y.^2)
%

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