This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...123. In this connection a discovery made by Jacobi (Crelle's Journal, bd. 17, p. 68) is of great use. He showed that with the integration of the differential equation G=o, also that of the differential equation J = o is performed. We are then able to derive the general expression for, and may determine ...
Read More
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...123. In this connection a discovery made by Jacobi (Crelle's Journal, bd. 17, p. 68) is of great use. He showed that with the integration of the differential equation G=o, also that of the differential equation J = o is performed. We are then able to derive the general expression for, and may determine completely whether and when u--O. We shall next derive the general solution of the equation J = o, it being presupposed that the differential equation G=o admits of a general solution. We derived the first variation in the form We may form the second variation by causing in this expression G alone to vary, and then w alone, and by adding the results. It follows that Since the differential equation G=o is supposed satisfied, we dy dAdy'l and also Gi = y'G, G2=-x' G. When in the expression for Gx, the substitutions and if we take into consideration 3), 4), 6) and 7) of the last Chapter, we may write the above result in the form: In an analogous manner, we have When these values are substituted in (), we have Hence from (o) we have By the previous method we found the second variation to be see formula 8) of the last Chapter These two expressions should agree as to a constant term. The difference of the integrals is k to but since it is seen that f r-dw', D=rwF'-dtV The formula (&) is When we compare this with 12) of the preceding Chapter, the differential equation for u, viz.: it is seen that as soon as we find a quantity w for which 8(7=0, we have a corresponding integral of the differential equation for u. 125. The total variation of G is &G=G(x+eg1+, ?+Vi+-ih + + +..../ + Vi +.1h'+...' S'+r"+ Ts +..-.)-G (x, y, x', /,,"/') =e8G + #G+ where 8(7, as found in the preceding article, has the value...
Read Less
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
