Partial Differential Equations: An Essay Towards an Entirely New Method of Integrating Them |
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Page 16
... commutative because their equivalents d + ad , de - ad , are so ; consequently the equa- tion ( 1 ) may be written in the form △ ¿ Ð ̧μ + bD¿u = 0 , which being integrated with Σ , gives -bt Du = 16 DETERMINATION OF QUASI - CONSTANTS .
... commutative because their equivalents d + ad , de - ad , are so ; consequently the equa- tion ( 1 ) may be written in the form △ ¿ Ð ̧μ + bD¿u = 0 , which being integrated with Σ , gives -bt Du = 16 DETERMINATION OF QUASI - CONSTANTS .
Page 17
... commutative ) D¿¿ . D¿u + b Dr. D¿u = 0 , Dƒat · A¿u + bD ̧ . △ ¡ μ = 0 , DA . bu + bD1 . bu = 0 ; · . :: Dƒa¿ . ( D¿u + △ u + bu ) + bD1 . ( D1u + A ̧u + bu ) = 0 . This equation is of the same form as ( 1 ) , and we learn from it ...
... commutative ) D¿¿ . D¿u + b Dr. D¿u = 0 , Dƒat · A¿u + bD ̧ . △ ¡ μ = 0 , DA . bu + bD1 . bu = 0 ; · . :: Dƒa¿ . ( D¿u + △ u + bu ) + bD1 . ( D1u + A ̧u + bu ) = 0 . This equation is of the same form as ( 1 ) , and we learn from it ...
Page 19
... commutative in the preceding example . It will be found always necessary to notice whether the symbols of operation in any proposed example are com- mutative , for the commutativeness of the symbols of operation is a property of immense ...
... commutative in the preceding example . It will be found always necessary to notice whether the symbols of operation in any proposed example are com- mutative , for the commutativeness of the symbols of operation is a property of immense ...
Page 43
... that if the operative sym- bols DA , be commutative on x , they will be so on u , i.e. on any function of t , x . The commutativeness of the symbols of operation is of such great utility in the work of ( 43 ) CHAPTER VI. ...
... that if the operative sym- bols DA , be commutative on x , they will be so on u , i.e. on any function of t , x . The commutativeness of the symbols of operation is of such great utility in the work of ( 43 ) CHAPTER VI. ...
Page 44
... commutative on x , then as far as u depends on x , they are commutative on u , any function of the variable . The same may be proved for y , z , ... the remaining variables . Hence the symbols of operation Dt , A , are commutative on u ...
... commutative on x , then as far as u depends on x , they are commutative on u , any function of the variable . The same may be proved for y , z , ... the remaining variables . Hence the symbols of operation Dt , A , are commutative on u ...
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Common terms and phrases
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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