A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 2
... - v k - K = C - v k - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by C. The first member is a vanishing fraction 2 [ CH . XIX . ADDITIONS TO CHAPTER II .
... - v k - K = C - v k - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by C. The first member is a vanishing fraction 2 [ CH . XIX . ADDITIONS TO CHAPTER II .
Σελίδα 3
George Boole Isaac Todhunter. replaced by C. The first member is a vanishing fraction , the limiting value of which is ( du ) , the brackets being used to dk denote that after the differentiation l is to be made equal to x . Hence the ...
George Boole Isaac Todhunter. replaced by C. The first member is a vanishing fraction , the limiting value of which is ( du ) , the brackets being used to dk denote that after the differentiation l is to be made equal to x . Hence the ...
Σελίδα 13
... vanish then if dc dc x2 + y2 — m2 = 0 . This therefore is the singular solution and it satisfies both the tests , as both x and y are contained in its expression . Of the partial tests аф dc = аф 0 , = 8 , dx do = ∞ dy the first is not ...
... vanish then if dc dc x2 + y2 — m2 = 0 . This therefore is the singular solution and it satisfies both the tests , as both x and y are contained in its expression . Of the partial tests аф dc = аф 0 , = 8 , dx do = ∞ dy the first is not ...
Σελίδα 14
... vanish , and the nume- rator of ( 9 ) , instead of being the difference of a finite and an infinite quantity , would be the difference of two infinite and equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be ...
... vanish , and the nume- rator of ( 9 ) , instead of being the difference of a finite and an infinite quantity , would be the difference of two infinite and equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be ...
Σελίδα 23
... vanish with y . We can therefore neither affirm nor deny that the proposed solution is of the envelope species . 8. Before demonstrating a general Rule for the discrimi- nation of solutions of this character , we shall notice certain of ...
... vanish with y . We can therefore neither affirm nor deny that the proposed solution is of the envelope species . 8. Before demonstrating a general Rule for the discrimi- nation of solutions of this character , we shall notice certain of ...
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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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