Partial differential equations: an essay towards an entirely new method of integrating them1871 |
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Page 17
... contain the requisite number of arbitrary functions , it is a complete integral of the proposed equation , and being so we may write u for it . We shall find this principle of great use hereafter ; but it must be noticed that it only ...
... contain the requisite number of arbitrary functions , it is a complete integral of the proposed equation , and being so we may write u for it . We shall find this principle of great use hereafter ; but it must be noticed that it only ...
Page 19
... contains m + n + p arbitrary functions , viz . m corresponding to the symbol s , n to the symbol S " , and p to the symbol ; and consequently it is the com- plete integral of the proposed equation , which is a differential equation of ...
... contains m + n + p arbitrary functions , viz . m corresponding to the symbol s , n to the symbol S " , and p to the symbol ; and consequently it is the com- plete integral of the proposed equation , which is a differential equation of ...
Page 36
... contain an arbitrary function of έ . To obtain this we put the equation in the form Au = Da C u ; . * . u = εc .Di $ ( § ' ) . The complete integral will be obtained by adding this to the above . 27. But now we come upon a difficulty ...
... contain an arbitrary function of έ . To obtain this we put the equation in the form Au = Da C u ; . * . u = εc .Di $ ( § ' ) . The complete integral will be obtained by adding this to the above . 27. But now we come upon a difficulty ...
Page 64
... contain t , and divide the remaining portion by t ; and : . Þ2 ( dı ) . ƒ ' ' ( dr ) + $ 1 ( di ) · ƒ ' ( dr ) + $。( dr ) · ƒ ( di ) = 0 , tf ( d . ) 4 , ( d ) u + { 2ƒ ' ( dr ) ⋅ & 2 ( dı ) + ƒ ( d1 ) 4 , ( di ) } u = t'f ( d . ) 0 ...
... contain t , and divide the remaining portion by t ; and : . Þ2 ( dı ) . ƒ ' ' ( dr ) + $ 1 ( di ) · ƒ ' ( dr ) + $。( dr ) · ƒ ( di ) = 0 , tf ( d . ) 4 , ( d ) u + { 2ƒ ' ( dr ) ⋅ & 2 ( dı ) + ƒ ( d1 ) 4 , ( di ) } u = t'f ( d . ) 0 ...
Page 65
... contain u ; f'dt fde = A de + B B or = > dt + a : . f ( di ) = ( dr + B ) 4 , or ( d , + a ) B . If now either A or B be an integer , we may take the corresponding form for f ( d ) . Suppose A an integer ; :: ƒ ( dt ) = ( dt + B ) 4 ...
... contain u ; f'dt fde = A de + B B or = > dt + a : . f ( di ) = ( dr + B ) 4 , or ( d , + a ) B . If now either A or B be an integer , we may take the corresponding form for f ( d ) . Suppose A an integer ; :: ƒ ( dt ) = ( dt + B ) 4 ...
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A₁ ad¸u Algebra arbitrary constants arbitrary functions ARITHMETIC beginners brackets BROOKE FOSS WESTCOTT C₁ Cambridge Chapter CLASS-BOOK cloth coefficients commutative complete integral Crown 8vo d¸³u D₁ D₁u D₁x d₂ d³u Differential Calculus Dudu ELEMENTARY TREATISE English equa equivalent Essay Examination Papers Extra fcap F₁ Fcap final integral finite terms form of ƒ formula of Art GEOMETRY gives Grammar Greek h+ka Hence ht+kx independent variables integral in finite John's College kx)² liberty to assume Mathematical method MIXED MATHEMATICS obtained partial differential equation pendent variables preceding example principle proposed equation quasi-constants reference render root-integral Ruled Surfaces Schools Second Edition second order set of independent shew student substitute symbolical integral symbols of operation tion Trigonometry write
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