«05 - • • . 8o6 



SBtc woüm bk 53ctratt'i'n8«n/ ^<« «^f" i^^" Functionen von sinn ^n&nbivUd)tn gsmacfit wccJc«, auf gunctioncn 

 von jvrcy? 5Qcränbcrlid)cn x uiib y anpeilen, t»cOcp luttr eine SJelation j\vifcf)en x, y annehmen, \o 6ag man x aii IIb: 

 fciffe, y al8 Oibinntc einet (Tucoe unb F (x, y) nlu Jf'nd^enin^alt bct (luioen 6etca^ten fann: 



F ( X + A X , y + A y) = F (-^- , >0 + y) + F' (x , y) A X + F" (x, y) A_x_^ ^ 



+ F'" (X. y) A x^ 4. 



[aUeö in ^cjugaufxunöybiffcrenjiert, ferner tlxconflant gefeit, eu6Iicf;dy,d2 y, d'y,.. .. banndy, Jy=, dy', .... fturc^ 



X unb dx ou^ficbcürft, fo ba^ in F' ("x , y), F" (x , y) feine 2)i|Tecenjialicn me^r voifommcn]. Sa()er s|l 



X = «, y = j3 

 [x = ß unb y = |S äufammen scf)6ti9] F (« + A x, /J + A y) "= F («, /3) + F"(x7~y) A x + 

 x = a,y = ^ x=«,y=:/3 



+T^(x77) ~A x' + F (x , yj A x^ + 



2 2.3 



= B + B' A X + B" A x' + B'" A x^ +..-.... 



2 s . 3 



©e^en tt)ir a + A x = x, unb j3 + A y = y, otfo A x = x — «, fo i(l F (x, y) = B +B' (x — u) + 

 + B' (x — cO ^ + ]i"' (X — ay -^ H. f. »., alfo -r \ «;-r 



2 2.3 



F (x, y) = (B — B' ß + B" «* — ; + 



+ (B' — B" 2 ß + B"' 30''— ) X + 



+ <B"-B"'3«+ )x»+u. f. ». 



X = o , y = h 



v.,^ / 



3nfo [wenn bem x = o cnifpcic^t y = h] F (x, y) = B — B' x + B" «' — pjjp 



x = o,y = h x=a,y=ß x = K,y=j3 x = ß,y = ^ x=:ß,y = |3 



F (X, y; = F (X, y)" — F- ( x , y) « + 'F^i~J) 'a' — V" (x,7)'^x ^ + 



2 2.3 



.^iet finb « unb ß Oetieöige iufammenge^ätfge SDBett^e itv Soorbinaten, wie x unb y, o(fo 

 x = o , y := h 



F(x,y) = F (X, y) — P (x, yj x + F^' (x, y) x' — F'" (x . y ) x' + 



2 a . 3 



hieraus ift [wenn dx Eeltnnbig] 



x = o, y=h ' ' 



9.)F(x,y-) = F(x,y) + P(x,y)x- 



— F^' (X, y) X* + F"' (X, y) X ' — F"" (x , y) x< + 



2 2.5 2.3.4 



G6en fo i|t [wenn man dy als befTi^nbige« tfiuKincrementum nimmt] 



F (x + A X, y + A y) = F (x^, y) + d F (x, y) A y + J' F (x. y) A y ' + 



-' ^ ^ dy dy» 3 



u. f. tt). 3(lfo [wenn für y = o baä x = k i(!] 



y = o,x = k 



10.) F (x, y) ='"Fl^7y)'+ F' (x, y) y — F" (x . y) y« + F'" (x , y) y ^ - . . 



2 2.3 



un( fo weiter. 



