Differential Calculus: With Applications and Numerous Examples; an Elementary TreatiseMacmillan, 1886 - 439 páginas |
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Página xi
... Function , 146-150 Order of Partial Differentiations Commutative , PAGES . 135 135-138 151-152 Second Differential Coefficient of an Implicit Function ... Homogeneous Functions . Euler's Theorems , 143-145 145-152 APPLICATIONS TO PLANE CURVES ...
... Function , 146-150 Order of Partial Differentiations Commutative , PAGES . 135 135-138 151-152 Second Differential Coefficient of an Implicit Function ... Homogeneous Functions . Euler's Theorems , 143-145 145-152 APPLICATIONS TO PLANE CURVES ...
Página 146
... homogeneous functions of the nth degree . 162. We now put the same theorem in a more general form . DEF . A homogeneous function of the nth degree is one which can be put in the form xn F y 2 \ x ' x ' ... xn u = x F ( x , ... ) y_Y ...
... homogeneous functions of the nth degree . 162. We now put the same theorem in a more general form . DEF . A homogeneous function of the nth degree is one which can be put in the form xn F y 2 \ x ' x ' ... xn u = x F ( x , ... ) y_Y ...
Página 147
... homogeneous function of x and y of the ди ди nth degree , Əx ' dy will be homogeneous functions of the ( n - 1 ) th degree , and applying the result of Art . 162 to ди these we have д Әди · + y . = дх дх ( n - 1 ) ди = = ( n − 1 ) ...
... homogeneous function of x and y of the ди ди nth degree , Əx ' dy will be homogeneous functions of the ( n - 1 ) th degree , and applying the result of Art . 162 to ди these we have д Әди · + y . = дх дх ( n - 1 ) ди = = ( n − 1 ) ...
Página 149
... homogeneous , and in cases of homogeneity verify Euler's Theorem of the first degree : ( a ) xe- ( B ) ye y . ye . - ( v ) ( x − y ) ( log x − log y ) . - ( 8 ) sin - 1√x2 ... homogeneous function of the nth PARTIAL differenTIATION . 149.
... homogeneous , and in cases of homogeneity verify Euler's Theorem of the first degree : ( a ) xe- ( B ) ye y . ye . - ( v ) ( x − y ) ( log x − log y ) . - ( 8 ) sin - 1√x2 ... homogeneous function of the nth PARTIAL differenTIATION . 149.
Página 150
... homogeneous function of the nth degree of any number of variables , prove that Эх Ә Ә + y + ду m = nmu . 11. If u = p ( x , y ) and 4 ( x , y ) = 0 , prove that Эф ду ду эф du_dx dy dx dy dx 24 ду 166. General Proof of Euler's Theorems ...
... homogeneous function of the nth degree of any number of variables , prove that Эх Ә Ә + y + ду m = nmu . 11. If u = p ( x , y ) and 4 ( x , y ) = 0 , prove that Эф ду ду эф du_dx dy dx dy dx 24 ду 166. General Proof of Euler's Theorems ...
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Differential Calculus With Applications and Numerous Examples: An Elementary ... Joseph Edwards Sin vista previa disponible - 2006 |
Términos y frases comunes
ALGEBRA angle Assistant-Master asymptote axis Cambridge cardioide centre chord circle co-ordinates coincident points conic Crown 8vo cusp cuts the curve cycloid denote differential coefficient dx dx dx dy dy dx ELEMENTARY ellipse envelope EXAMPLES Extra fcap fcap Fellow of Trinity Find function Globe 8vo Hence independent variable infinite intersection intrinsic equation inverse John's College late Fellow limit LL.D locus MACMILLAN'S EDUCATIONAL CATALOGUE maxima and minima minimum value negative normal ordinate origin Owens College p(x+h parabola parallel pedal equation perpendicular point of contact point of inflexion polar positive pedal PRIMER Professor prove quantity radius of curvature revised School Show straight line tangent Taylor's Theorem Trace the curve Trinity College ultimately coincident vanish whence zero ди ди ду дх
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