# A System of Analytic Mechanics Volume 50,

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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. 1855 edition. Excerpt: ...method of obtaining the functional determinant. 355. In performing the successive eliminations, the operation must not be restricted to any prescribed order of the variables, but one of the variables, remaining in f, -, must occupy the place of x, -. Hence there is not one of the factors of the determinant in the form of 351 which vanishes, unless a function be obtained from which all the variables are explicitly eliminated, or, in other words, unless one of the given functions is included in the others and can be derived from them, so that they are not independent of each other. I/', therefore, the given functions are mzzizzally z'nde_pendent, their functional deternzinant does not vanis/z. 356. If F, F1, ......F, are given functions of _f, f1, ......f, which are themselves functions of the variables 2:, 1'1, ......: v, the derivatives of the functions with respect to the variables (.v, -) are represented by the equation This equation coincides with (18124), if the notation for at" is combined with the notation The remaining notation and conclusions of 346 and 347 may, therefore, be applied to this case.-Hence, by (18218) the functional determinant of the independent functions taken with respect to the same number of variables (: v, -), which enter into only as they are involved in the same number of independent functions ( explicitly involved in is obtained by multiplying the functional determinant of taken with respect to ( f, -) by the functional determinant of ( taken with respect to If the number (p--1) of functions ( exceeds the number (n--l) of functions the complete functional determinant of is by (18211) the sum of all the partial determinants of obtained by every possible combination of (n + 1) of the functions (f, ). If...show more

## Product details

• Paperback | 94 pages
• 189 x 246 x 5mm | 181g
• United States
• English
• black & white illustrations
• 1236954963
• 9781236954961