A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 1
... relations equivalent to the following , viz .: The quantities m1 , m , are roots of the quadratic am2 − ( b + a ' ) m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , C + C ' = c ...
... relations equivalent to the following , viz .: The quantities m1 , m , are roots of the quadratic am2 − ( b + a ' ) m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , C + C ' = c ...
Σελίδα 4
... relation between y and x is regarded as one of pure magnitude , and the interpreta- tion of the differential equation becomes a limiting case of that of the equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we ...
... relation between y and x is regarded as one of pure magnitude , and the interpreta- tion of the differential equation becomes a limiting case of that of the equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we ...
Σελίδα 5
... relation connecting x and y may be shewn thus . Let y = $ ( X 。, Y。, x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x ...
... relation connecting x and y may be shewn thus . Let y = $ ( X 。, Y。, x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x ...
Σελίδα 7
... relations between y and x which are deducible from the original primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . To the expression of the complete ...
... relations between y and x which are deducible from the original primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . To the expression of the complete ...
Σελίδα 10
... relation obtained would involve x only , while it is a condition accompanying the use of co that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a ...
... relation obtained would involve x only , while it is a condition accompanying the use of co that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a ...
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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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