Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti
Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti
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In our eReader you can find the full English version of the book. Read Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti 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 Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti
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125. The conditions that P' v and Q' T be continuous and equal, which insures independence of the path for the line integral of Pdx + Qdy, need to be examined more closely. Consider two examples : First | Pdx + Qdy = I ' - dx -\ dy, J J x- + y- x- + y- where + //" x- + y- cP y 2 — x- dQ y' 2 — x- cy (x 2 + y 2 ) 2 ' ex (x 2 + y 2 ) 2 It appears formally that P' — Q' r . If the integral be calculated around a square of side 2 a surrounding the origin, the result is X + « + adx r + " ady r - a — ...adx r - a — ady _ r + " adx -a x 2 + a 2 J -a a 2 + y 2 J+u x 2 + a 2 «/ + « a 2 + y 2 J- a x 2 + a 2 „ C + a ady . R + " adl- . Ir „ .
+ 2 I — = 4 j — = 4- = 27T5^0.
J -a a 2 + y 2 J -a £- + a- 2 302 INTEGRAL CALCULUS The integral fails to vanish around the closed path. The reason is not far to seek, the derivatives P' y and Q' x are not defined for (0, 0), and cannot be so defined as to be continuous functions of (x, y) near the origin. As a matter of fact r
What to read after Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti?
You can find similar books in the "Read Also" column, or choose other free books by Edwin Bidwell Wilson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
125. The conditions that P' v and Q' T be continuous and equal, which insures independence of the path for the line integral of Pdx + Qdy, need to be examined more closely. Consider two examples : First | Pdx + Qdy = I ' - dx -\ dy, J J x- + y- x- + y- where + //" x- + y- cP y 2 — x- dQ y' 2 — x- cy (x 2 + y 2 ) 2 ' ex (x 2 + y 2 ) 2 It appears formally that P' — Q' r . If the integral be calculated around a square of side 2 a surrounding the origin, the result is X + « + adx r + " ady r - a — ...adx r - a — ady _ r + " adx -a x 2 + a 2 J -a a 2 + y 2 J+u x 2 + a 2 «/ + « a 2 + y 2 J- a x 2 + a 2 „ C + a ady . R + " adl- . Ir „ .
+ 2 I — = 4 j — = 4- = 27T5^0.
J -a a 2 + y 2 J -a £- + a- 2 302 INTEGRAL CALCULUS The integral fails to vanish around the closed path. The reason is not far to seek, the derivatives P' y and Q' x are not defined for (0, 0), and cannot be so defined as to be continuous functions of (x, y) near the origin. As a matter of fact r
What to read after Advanced Calculus a Text Upon Select Parts of Differential Calculus Differenti?
You can find similar books in the "Read Also" column, or choose other free books by Edwin Bidwell Wilson to read onlineMoreLess
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