Partial differential equations: an essay towards an entirely new method of integrating them1871 |
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Page 1
... variables , the work of integra- tion is at once reduced to the use of one independent vari- able only . Quasi - constants . 1. If t , x , y , z ... be n independent variables , and u the dependent variable , it is understood that du ...
... variables , the work of integra- tion is at once reduced to the use of one independent vari- able only . Quasi - constants . 1. If t , x , y , z ... be n independent variables , and u the dependent variable , it is understood that du ...
Page 2
... quasi - constant . Thus in refer- ence to the use of the symbol d , we shall denominate x , y , z , ... and any functions of them quasi - constants : the use of d will imply that ... quasi - constants E , 2 GENERAL PRINCIPLES OF THE ESSAY .
... quasi - constant . Thus in refer- ence to the use of the symbol d , we shall denominate x , y , z , ... and any functions of them quasi - constants : the use of d will imply that ... quasi - constants E , 2 GENERAL PRINCIPLES OF THE ESSAY .
Page 3
Samuel Earnshaw. assigning proper forms for the quasi - constants E , n ,, ... in terms of t , x , y , z , ... the original independent variables will be best learned from the examples which will be given . Distinctive Symbols of ...
Samuel Earnshaw. assigning proper forms for the quasi - constants E , n ,, ... in terms of t , x , y , z , ... the original independent variables will be best learned from the examples which will be given . Distinctive Symbols of ...
Page 4
... equation , which will always be known from the occurrence of the symbol D , or St , we must remember that there remain only ( n - 1 ) new independent variables ( the quasi - constants ) of the set to be determined , one of them ( t ) ...
... equation , which will always be known from the occurrence of the symbol D , or St , we must remember that there remain only ( n - 1 ) new independent variables ( the quasi - constants ) of the set to be determined , one of them ( t ) ...
Page 5
Samuel Earnshaw. ( 5 ) CHAPTER II . DETERMINATION OF QUASI - CONSTANTS . FIRST ORDER . EQUATIONS OF THE Ex . 1. To integrate du + ad ̧u = bu . Let us change the independent variables to t , § . Then the formula of Art . 7 becomes for ...
Samuel Earnshaw. ( 5 ) CHAPTER II . DETERMINATION OF QUASI - CONSTANTS . FIRST ORDER . EQUATIONS OF THE Ex . 1. To integrate du + ad ̧u = bu . Let us change the independent variables to t , § . Then the formula of Art . 7 becomes for ...
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Common terms and phrases
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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