Example 5.   Solve  [Graphics:Images/TaylorDEMod_gr_91.gif]  with  [Graphics:Images/TaylorDEMod_gr_92.gif]  over  [Graphics:Images/TaylorDEMod_gr_93.gif].

Solution  5.

[Graphics:../Images/TaylorDEMod_gr_94.gif]


[Graphics:../Images/TaylorDEMod_gr_95.gif]
[Graphics:../Images/TaylorDEMod_gr_96.gif]

First, enter the function  [Graphics:../Images/TaylorDEMod_gr_97.gif]  and create explicit formulas for  [Graphics:../Images/TaylorDEMod_gr_98.gif]  for  [Graphics:../Images/TaylorDEMod_gr_99.gif],  respectively, which will involve  [Graphics:../Images/TaylorDEMod_gr_100.gif].  

[Graphics:../Images/TaylorDEMod_gr_101.gif]


[Graphics:../Images/TaylorDEMod_gr_102.gif]
[Graphics:../Images/TaylorDEMod_gr_103.gif]
[Graphics:../Images/TaylorDEMod_gr_104.gif]
[Graphics:../Images/TaylorDEMod_gr_105.gif]


Second, replace  [Graphics:../Images/TaylorDEMod_gr_106.gif]  with   [Graphics:../Images/TaylorDEMod_gr_107.gif]  and construct the implicit formulas  [Graphics:../Images/TaylorDEMod_gr_108.gif]  for  [Graphics:../Images/TaylorDEMod_gr_109.gif], respectively.  

[Graphics:../Images/TaylorDEMod_gr_110.gif]


[Graphics:../Images/TaylorDEMod_gr_111.gif]
[Graphics:../Images/TaylorDEMod_gr_112.gif]
[Graphics:../Images/TaylorDEMod_gr_113.gif]
[Graphics:../Images/TaylorDEMod_gr_114.gif]


[Graphics:../Images/TaylorDEMod_gr_115.gif]

[Graphics:../Images/TaylorDEMod_gr_116.gif]

[Graphics:../Images/TaylorDEMod_gr_117.gif]
[Graphics:../Images/TaylorDEMod_gr_118.gif]
[Graphics:../Images/TaylorDEMod_gr_119.gif]
[Graphics:../Images/TaylorDEMod_gr_120.gif]
[Graphics:../Images/TaylorDEMod_gr_121.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004