void minimal_surface_catenoid_exact ( int n, double X[], double Y[], double a, 
  double U[], double Ux[], double Uy[], double Uxx[], double Uxy[], 
  double Uyy[] );
double *minimal_surface_catenoid_residual ( int n, double X[], double Y[], 
  double a );
void minimal_surface_helicoid_exact ( int n, double X[], double Y[], double U[], 
  double Ux[], double Uy[], double Uxx[], double Uxy[], double Uyy[] );
double *minimal_surface_helicoid_residual ( int n, double X[], double Y[] );
void minimal_surface_linear_exact ( int n, double X[], double Y[], double a, 
  double b, double c, double U[], double Ux[], double Uy[], double Uxx[], 
  double Uxy[], double Uyy[] );
double *minimal_surface_linear_residual ( int n, double X[], double Y[], 
  double a, double b, double c );
void minimal_surface_scherk_exact ( int n, double X[], double Y[], double a, 
  double U[], double Ux[], double Uy[], double Uxx[], double Uxy[], 
  double Uyy[] );
double *minimal_surface_scherk_residual ( int n, double X[], double Y[], 
  double a );