The Doctrine of Germs Or the Integration of Certain Partial Differential Equat
The Doctrine of Germs Or the Integration of Certain Partial Differential Equat
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To quickly assess the difficulty of the text, read a short excerpt:
-. U = A4* 2 -™*)t+vx cos m (%Mt + x+B).
The minor germs of x and t are in this integral implicitly contained in the arbitrary constants A, B. The form is a major-germ form.
62. To find the integral of ^ 2 = -^7 in a minor-germ form, i. E. In a form which renders the major germ latent in the arbi- trary constants of the integral.
From Art. 34 we learn that the subintegrals obtained by the elimination of a major germ will all be homogeneous and of different dimensions. This therefore suggests th...e following method of obtaining the subintegrals required.
OF TWO INDEPENDENT VARIABLES. 43 Let V be a function of x and t which is of zero dimensions. The general representative of such a function in the case of the proposed example will be V = (— J, for if Moc, MH be written x in this for x, t, the germ M will disappear. Denote -j by v, and then the following general form of homogeneity will represent any one of the subintegrals, P = t p V, the dimensions of this subintegral being p.
This being an integral of the proposed equation must satisfy it, and being substituted therein, the following is the resulting equation for the determination of V, dv* + 2 dv P Now we wish to obtain subintegrals in a finite form, or if that be not possible, then in a form that shall give a finite expression for u.
What to read after The Doctrine of Germs Or the Integration of Certain Partial Differential Equat?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Earnshaw to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
-. U = A4* 2 -™*)t+vx cos m (%Mt + x+B).
The minor germs of x and t are in this integral implicitly contained in the arbitrary constants A, B. The form is a major-germ form.
62. To find the integral of ^ 2 = -^7 in a minor-germ form, i. E. In a form which renders the major germ latent in the arbi- trary constants of the integral.
From Art. 34 we learn that the subintegrals obtained by the elimination of a major germ will all be homogeneous and of different dimensions. This therefore suggests th...e following method of obtaining the subintegrals required.
OF TWO INDEPENDENT VARIABLES. 43 Let V be a function of x and t which is of zero dimensions. The general representative of such a function in the case of the proposed example will be V =
This being an integral of the proposed equation must satisfy it, and being substituted therein, the following is the resulting equation for the determination of V, dv* + 2 dv P Now we wish to obtain subintegrals in a finite form, or if that be not possible, then in a form that shall give a finite expression for u.
What to read after The Doctrine of Germs Or the Integration of Certain Partial Differential Equat?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Earnshaw to read onlineMoreLess
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