This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 edition. Excerpt: ...au anti-differential (or integral), relation (li) must be satisfied; conversely, if relation (2) is satisfied, the expression (1) has an integral. Accordingly, relation (2) is called the criterion of inteyrubility for the expression (1). If this criterion is satisfied, the expression (1) is said to be a ...
Read More
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 edition. Excerpt: ...au anti-differential (or integral), relation (li) must be satisfied; conversely, if relation (2) is satisfied, the expression (1) has an integral. Accordingly, relation (2) is called the criterion of inteyrubility for the expression (1). If this criterion is satisfied, the expression (1) is said to be a complete differential, u total differential, and also an exact differential. If test (2) is satisfied, the integral of (1) can easily be found. This integral's partial x-differential, Pdx, can only come from terms containing x (Art. 79). Hence, the integral of Pdx with respect to x. namely. / JPdx + c, (3) must yield all the terms of the required integral that contain x. Also, Qdy can only come from terms containing y. Hence the integral of Qdy with respect to y, namely, -ca (4) must yield all the terms of the required integral that contain y. Some of these terms may contain x; if so, they have already been obtained in (3), and need not be taken this second time. Hence, if the integral of a differential of the form Pdx+Qdy is required, apply the test for integrability, namely, dydx' if this test is satisfied, integrate Pdx with reject to x; then integrate Qdy with respect to y, neglecting terms already obtained in I Pdx; add the results and the arbitrary constant of integration. EXAMPLES. 1. Integrate (2 xy + 2 + 3 ya + 12 x) dx + (ifl + 0 xy + 4 ya) dy. Here P = 2 xy + 2 + 3 y + 12 x, and Q = x + 6 xy + 4 if. 'dy dx Thus the criterion of integrability is satisfied. and f Q dy = xy + 3 xya + y4, in which y' has not been already obtained in ( Pdx. Hence the integral is xy + 2 x + 3 ya + 6 xa + / + e 2. Verify the result in Ex. 1 by differentiation. 3. Find (xdy-ydx). Here QQ = 1, and =-!; hence the test for integrability is not satis ox dy j...
Read Less
Add this copy of A First Course in Infinitesimal Calculus to cart. $23.14, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of A First Course in Infinitesimal Calculus to cart. $34.31, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of A First Course in Infinitesimal Calculus to cart. $56.70, new condition, Sold by Booksplease rated 3.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of A First Course In Infinitesimal Calculus to cart. $64.67, new condition, Sold by Booksplease rated 3.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2010 by Kessinger Publishing.
Add this copy of A First Course In Infinitesimal Calculus to cart. $65.13, new condition, Sold by Booksplease rated 3.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2007 by Kessinger Publishing.
Add this copy of A First Course in Infinitesimal Calculus to cart. $66.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Kessinger Publishing.
