A Treatise on Differential Equations. Supplementary Volume |
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Page vi
... independent essays or memoirs which lose nothing by being separated from the other volume ; and indeed no indications had been left by Professor Boole of the place which such Chapters were to occupy in the enlarged edition . I have ...
... independent essays or memoirs which lose nothing by being separated from the other volume ; and indeed no indications had been left by Professor Boole of the place which such Chapters were to occupy in the enlarged edition . I have ...
Page 18
... independent of that of x . If from the complete primitive we seek the singular solution dy by the condition = 0 , we get the two equations dc εcx - c2 = 0 , х - - 2c = 0 . The second of these determines c as a function of x , and leads ...
... independent of that of x . If from the complete primitive we seek the singular solution dy by the condition = 0 , we get the two equations dc εcx - c2 = 0 , х - - 2c = 0 . The second of these determines c as a function of x , and leads ...
Page 33
... independent , we may perform the integration with respect to u as if x were constant . The resulting equa- tion cannot be free from x unless C be infinite , and then it B. D. E. II . 3 du I will evidently not be satisfied unless ( x ART ...
... independent , we may perform the integration with respect to u as if x were constant . The resulting equa- tion cannot be free from x unless C be infinite , and then it B. D. E. II . 3 du I will evidently not be satisfied unless ( x ART ...
Page 56
... independent , then , adopting the notation of determinants , the condition du1 ཙུ ། ུ་ du , du , dx , dx , ' du2 du2 du dx ' dx dxn = 0 ........ ( 2 ) , dun dun du dx " dx dxn is identically satisfied . Conversely , if the above ...
... independent , then , adopting the notation of determinants , the condition du1 ཙུ ། ུ་ du , du , dx , dx , ' du2 du2 du dx ' dx dxn = 0 ........ ( 2 ) , dun dun du dx " dx dxn is identically satisfied . Conversely , if the above ...
Page 58
... independent , and therefore by the theory of linear equations the determinant of the system vanishes identically ... independent . n - 1 First , the n - 1 functions u1 , u ,, ... U are either mutually independent or not mutually ...
... independent , and therefore by the theory of linear equations the determinant of the system vanishes identically ... independent . n - 1 First , the n - 1 functions u1 , u ,, ... U are either mutually independent or not mutually ...
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Common terms and phrases
Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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