Partial Differential Equations: An Essay Towards an Entirely New Method of Integrating Them |
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Page 3
... equa- tion ( 1 ) refers to the fact that there are operations to be performed in that equation in reference to two sets of inde- pendent variables . Had we to write down an equation in which differential and integral operations would ...
... equa- tion ( 1 ) refers to the fact that there are operations to be performed in that equation in reference to two sets of inde- pendent variables . Had we to write down an equation in which differential and integral operations would ...
Page 4
... equa- tion . 8. In determining what shall be the forms of the con- stituent members of a new set of variables , we are at liberty to introduce n arbitrary hypotheses if we use equation ( 1 ) of Art . 4 ; but only ( n − 1 ) arbitrary ...
... equa- tion . 8. In determining what shall be the forms of the con- stituent members of a new set of variables , we are at liberty to introduce n arbitrary hypotheses if we use equation ( 1 ) of Art . 4 ; but only ( n − 1 ) arbitrary ...
Page 16
... equa- tions is equivalent to the proposed equation , D1x = α , Ax = -a , and D.Au + bD ̧u = 0 ...... ( 1 ) . The first two give by integration , x = at + § , x = — at + § ' ; and the third being integrated with St gives △ ̧u + bu = F ...
... equa- tions is equivalent to the proposed equation , D1x = α , Ax = -a , and D.Au + bD ̧u = 0 ...... ( 1 ) . The first two give by integration , x = at + § , x = — at + § ' ; and the third being integrated with St gives △ ̧u + bu = F ...
Page 17
... applies to cases of linear equa- tious with constant or quasi - constant coefficients and when the symbols of operation are commutative . E. 13. It is well known that the integral of any EQUATIONS OF THE HIGHER ORDERS . 17.
... applies to cases of linear equa- tious with constant or quasi - constant coefficients and when the symbols of operation are commutative . E. 13. It is well known that the integral of any EQUATIONS OF THE HIGHER ORDERS . 17.
Page 21
... € ̄1 ¢ ƒ ( x − bt ) . - The part dependent on W may be determined from equa- tion ( 1 ) , which gives = Є ¿ ̄AtΣ ( A - B ) S1 € 1t W. Bt Hence the complete integral of the proposed equation is 4 EQUATIONS OF THE HIGHER ORDERS . 21.
... € ̄1 ¢ ƒ ( x − bt ) . - The part dependent on W may be determined from equa- tion ( 1 ) , which gives = Є ¿ ̄AtΣ ( A - B ) S1 € 1t W. Bt Hence the complete integral of the proposed equation is 4 EQUATIONS OF THE HIGHER ORDERS . 21.
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A₁ ad¸u Algebra arbitrary constants arbitrary functions ARITHMETIC beginners BROOKE FOSS WESTCOTT Cambridge Chapter CLASS-BOOK cloth coefficients commutative complete integral Crown 8vo d¸³u D₁ D₁u D₁x D₂ d³u Differential Calculus EDWARD THRING ELEMENTARY TREATISE English equa equivalent Essay Examination Papers Extra fcap F₁ Fcap final integral finite terms form of H ƒ Dr ƒ dt GEOMETRY gives Grammar Greek ht+kx independent variables integral in finite John's College kx)² Latin liberty to assume Mathematical method MIXED MATHEMATICS Multiply numerous Examples obtained partial differential equation preceding example principle proposed equation quasi-constants render revised root-integral Schools Second Edition second order shew student substitute symbolical integral symbols of operation tion Trigonometry utª write
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