A Treatise On the Differential And Integral Calculus And On the Calculus of Var
A Treatise On the Differential And Integral Calculus And On the Calculus of Var
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In our eReader you can find the full English version of the book. Read A Treatise On the Differential And Integral Calculus And On the Calculus of Var Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Treatise On the Differential And Integral Calculus And On the Calculus of Var
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Given x -\- y ■\- z i=. <: to="" find="" the="" values="" of="" rr="" y="" and="" z="" when="" cos="" arcos="" a="" maximum.="" regarding="" x="" as="" independent="" variables="" function="" we="" obtain="" by="" differentiating="" t="" with="" respect="" successively.="">+!=«■ ^"^ '+!=« (!)• But since it ■=. Maximum, log u = log cos X -\- log cos y + log cos z = maximum, ((/ locr u\ dz — r- — ) = — tan X — tan 2 -7- = 0, dx I dx (d]o2, u\ dz ^ .
and I — r^— ) =r — tan y — tan 2 -- = 0.
\ dy J ^ dy or, by replacing -- and — by their values derived from equa> tions (1).
— tan x + tan 2 = 0, — tan y + tan g = 0, 1 • . Tan X = tan z = tan y, and x = y=z=-'Jir.
o 3I /'V 1 4. To find the greatest rectangular parallelopipedon which can be inscr...<: to="" find="" the="" values="" of="" rr="" y="" and="" z="" when="" cos="" arcos="" a="" maximum.="" regarding="" x="" as="" independent="" variables="" function="" we="" obtain="" by="" differentiating="" t="" with="" respect="" successively.="">ibed in a given ellipsoid.
Let a, h, and c, be the semi-axes of the ellipsoid, x, y, and z^ tbp co-ordinates of one of the vertices of the parallelopipedon.
136 DIFFERENTIAL CALCULUS.
Then 2x, 2y, and 2z, are the three edges of the parallelopipedon, alid, therefore, 2x .
What to read after A Treatise On the Differential And Integral Calculus And On the Calculus of Var?
You can find similar books in the "Read Also" column, or choose other free books by Edward Courtenay to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Given x -\- y ■\- z i=. <: to="" find="" the="" values="" of="" rr="" y="" and="" z="" when="" cos="" arcos="" a="" maximum.="" regarding="" x="" as="" independent="" variables="" function="" we="" obtain="" by="" differentiating="" t="" with="" respect="" successively.="">+!=«■ ^"^ '+!=« (!)• But since it ■=. Maximum, log u = log cos X -\- log cos y + log cos z = maximum, ((/ locr u\ dz — r- — ) = — tan X — tan 2 -7- = 0, dx I dx (d]o2, u\ dz ^ .
and I — r^— ) =r — tan y — tan 2 -- = 0.
\ dy J ^ dy or, by replacing -- and — by their values derived from equa> tions (1).
— tan x + tan 2 = 0, — tan y + tan g = 0, 1 • . Tan X = tan z = tan y, and x = y=z=-'Jir.
o 3I /'V 1 4. To find the greatest rectangular parallelopipedon which can be inscr...<: to="" find="" the="" values="" of="" rr="" y="" and="" z="" when="" cos="" arcos="" a="" maximum.="" regarding="" x="" as="" independent="" variables="" function="" we="" obtain="" by="" differentiating="" t="" with="" respect="" successively.="">ibed in a given ellipsoid.
Let a, h, and c, be the semi-axes of the ellipsoid, x, y, and z^ tbp co-ordinates of one of the vertices of the parallelopipedon.
136 DIFFERENTIAL CALCULUS.
Then 2x, 2y, and 2z, are the three edges of the parallelopipedon, alid, therefore, 2x .
What to read after A Treatise On the Differential And Integral Calculus And On the Calculus of Var?
You can find similar books in the "Read Also" column, or choose other free books by Edward Courtenay to read onlineMoreLess
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