|\^/|     Maple 7 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) 2001 by Waterloo Maple Inc.
 \  MAPLE  /  All rights reserved. Maple is a registered trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
# coord_derivs.maple -- compute derivatives of (mu,nu,phi) wrt (x,y,z)
# $Id: coord_derivs.maple,v 1.1 2002/04/17 14:34:16 jthorn Exp $
> 
> mu  := arctan(y/z);
                               mu := arctan(y/z)

> nu  := arctan(x/z);
                               nu := arctan(x/z)

> phi := arctan(y/x);
                               phi := arctan(y/x)

> 
########################################
> 
> simplify(diff(mu,x));
                                       0

> simplify(diff(mu,y));
                                       z
                                    -------
                                     2    2
                                    z  + y

> simplify(diff(mu,z));
                                        y
                                   - -------
                                      2    2
                                     z  + y

> 
> simplify(diff(nu,x));
                                       z
                                    -------
                                     2    2
                                    z  + x

> simplify(diff(nu,y));
                                       0

> simplify(diff(nu,z));
                                        x
                                   - -------
                                      2    2
                                     z  + x

> 
> simplify(diff(phi,x));
                                        y
                                   - -------
                                      2    2
                                     x  + y

> simplify(diff(phi,y));
                                       x
                                    -------
                                     2    2
                                    x  + y

> simplify(diff(phi,z));
                                       0

> 
########################################
> 
> simplify(diff(mu,x,x));
                                       0

> simplify(diff(mu,x,y));
                                       0

> simplify(diff(mu,x,z));
                                       0

> simplify(diff(mu,y,y));
                                       z y
                                 -2 ----------
                                      2    2 2
                                    (z  + y )

> simplify(diff(mu,y,z));
                                      2    2
                                    -z  + y
                                   ----------
                                     2    2 2
                                   (z  + y )

> simplify(diff(mu,z,z));
                                       z y
                                  2 ----------
                                      2    2 2
                                    (z  + y )

> 
> simplify(diff(nu,x,x));
                                       z x
                                 -2 ----------
                                      2    2 2
                                    (z  + x )

> simplify(diff(nu,x,y));
                                       0

> simplify(diff(nu,x,z));
                                      2    2
                                     z  - x
                                  - ----------
                                      2    2 2
                                    (z  + x )

> simplify(diff(nu,y,y));
                                       0

> simplify(diff(nu,y,z));
                                       0

> simplify(diff(nu,z,z));
                                       z x
                                  2 ----------
                                      2    2 2
                                    (z  + x )

> 
> simplify(diff(phi,x,x));
                                       y x
                                  2 ----------
                                      2    2 2
                                    (x  + y )

> simplify(diff(phi,x,y));
                                      2    2
                                    -x  + y
                                   ----------
                                     2    2 2
                                   (x  + y )

> simplify(diff(phi,x,z));
                                       0

> simplify(diff(phi,y,y));
                                       y x
                                 -2 ----------
                                      2    2 2
                                    (x  + y )

> simplify(diff(phi,y,z));
                                       0

> simplify(diff(phi,z,z));
                                       0

> quit
bytes used=444120, alloc=458668, time=0.04