Page 191 - Excel for Scientists and Engineers: Numerical Methods
P. 191

168                                        EXCEL: NUMERICAL METHODS





                                                                                  (8-23)




                                                  as     aR
                                                R--S-
                                                  84     34
                                          Aq =                                    (8-24)
                                               aR as  as aR
                                               aP  84  aP  a4
                   To  find  the  partial  derivatives  6R/6p, etc,  we  could  follow  the  usual
               procedure of making a small change in p  to find the corresponding change in b.
               Instead,  we  will  calculate  the  partial  derivatives  using  analytical  expressions.
               Differentiating  the  expressions  8-11  to  8-14  with  respect  to  p  yields  the
               following:
                                                    abn
                                                cn =-                             (8-25)
                                                     aP


                                                                                  (8-26)



                                                                                  (8-27)



                                                                                  (8-28)



                                                                                  (8-29)
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