A Treatise On the Differential And Integral Calculus: And On the Calculus of ...
A Treatise On the Differential And Integral Calculus: And On the Calculus of ...
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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 ... 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 ...
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— = — sind, -r^r = — cosd = — or, ad ao* dy dy _ d& _ dx "" dx ~* 1 cfy sin 6 d6 d6 . Digitized by Google CHANGE OF THE INDEPENDENT VARIABLE. 189 dhf dx cPx dy dS dd^ dd 1 d^y dd'i cos a sin 3a ^y dx-^" dx^ " sin 2a <^a rfd3 nee by substitution in the given equation, 1 sin 2j cosd dy sin 3a * cW "^ ^y+y. cos a sin 3a = 0. dB ^ y sin^a" = or This example illustrates the important fact, that a change of the independent variable will sometimes simplify the form of the differ ential equation. dhi d^u 2. Transform -7^ + -r^ = 0, so as to render r the independent yariable, where r^ = aj3 + y\ rr « « « dx r d^x d / r\ Here .2 = ,3 ^y. ..._=._..._ = ^(^j T « x^ dr "^ X «3 "" 0?^ And similiirly - = -, -^ = - _. d^u ^ dr^ dr dr^ dr x^ d^u y* ^|^ •'' ^"" ^[ '^72'"5r2''"'r3* rfr" rf/-3 . - d^u y^ d^u , x^ du And _ = _._ + _._. d^u d^u . • . B7 substitution in the given relation -7-^ + -t-j = ^j ^i^d d^u 1 (^u reduction, — r-z + - • -r- = 0. rfr* r dr 104. Prop. Having given u = F {x, y) when a?
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You can find similar books in the "Read Also" column, or choose other free books by Edward Henry Courtenay to read online
To quickly assess the difficulty of the text, read a short excerpt:
— = — sind, -r^r = — cosd = — or, ad ao* dy dy _ d& _ dx "" dx ~* 1 cfy sin 6 d6 d6 . Digitized by Google CHANGE OF THE INDEPENDENT VARIABLE. 189 dhf dx cPx dy dS dd^ dd 1 d^y dd'i cos a sin 3a ^y dx-^" dx^ " sin 2a <^a rfd3 nee by substitution in the given equation, 1 sin 2j cosd dy sin 3a * cW "^ ^y+y. cos a sin 3a = 0. dB ^ y sin^a" = or This example illustrates the important fact, that a change of the independent variable will sometimes simplify the form of the differ ential equation. dhi d^u 2. Transform -7^ + -r^ = 0, so as to render r the independent yariable, where r^ = aj3 + y\ rr « « « dx r d^x d / r\ Here .2 = ,3 ^y. ..._=._..._ = ^(^j T « x^ dr "^ X «3 "" 0?^ And similiirly - = -, -^ = - _. d^u ^ dr^ dr dr^ dr x^ d^u y* ^|^ •'' ^"" ^[ '^72'"5r2''"'r3* rfr" rf/-3 . - d^u y^ d^u , x^ du And _ = _._ + _._. d^u d^u . • . B7 substitution in the given relation -7-^ + -t-j = ^j ^i^d d^u 1 (^u reduction, — r-z + - • -r- = 0. rfr* r dr 104. Prop. Having given u = F {x, y) when a?
What to read after A Treatise On the Differential And Integral Calculus: And On the Calculus of ...?
You can find similar books in the "Read Also" column, or choose other free books by Edward Henry Courtenay to read online
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