A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 20
... obtain developed expressions for the nth differ- ence of the product of two functions u , and v . Since △ UxVx = Ux + 1 • Vx + 1 — UxVx = Du2.D'v2 - uz Vz where D applies to u alone , and D ' to v , alone , we have and generally ...
... obtain developed expressions for the nth differ- ence of the product of two functions u , and v . Since △ UxVx = Ux + 1 • Vx + 1 — UxVx = Du2.D'v2 - uz Vz where D applies to u alone , and D ' to v , alone , we have and generally ...
Side 47
... obtained by adding to any par- ticular value v the complete value of what y would be , were u , equal to 0. Hence ..... Σux = vx + C1 € TM 1 * + С2 € TM 2 * + & c . ..... ( 7 ) , C , C , & c . being arbitrary constants , and m ,, m ...
... obtained by adding to any par- ticular value v the complete value of what y would be , were u , equal to 0. Hence ..... Σux = vx + C1 € TM 1 * + С2 € TM 2 * + & c . ..... ( 7 ) , C , C , & c . being arbitrary constants , and m ,, m ...
Side 52
... obtained in finite terms . But the symbolical method above referred to leads to the same result by a single operation . By a known theorem But a d mx mx d ƒ ( 1 ) cm2 p ( x ) = cm2 ƒ ( 1 + m ) & ( x ) . f dx loga . Hence , changing in ...
... obtained in finite terms . But the symbolical method above referred to leads to the same result by a single operation . By a known theorem But a d mx mx d ƒ ( 1 ) cm2 p ( x ) = cm2 ƒ ( 1 + m ) & ( x ) . f dx loga . Hence , changing in ...
Side 54
... obtained , either by integration by parts , or by expressing the trigonometrical functions in their exponential forms , applying the general theorem ( 8 ) , and reducing the re- sults to a rational form . Thus also we might integrate ...
... obtained , either by integration by parts , or by expressing the trigonometrical functions in their exponential forms , applying the general theorem ( 8 ) , and reducing the re- sults to a rational form . Thus also we might integrate ...
Side 56
... obtaining the sum of the preceding terms , and then to add the last term to the result . Thus in the above example we should have 12 + 22 + 32 ... + x2 = Σx2 + x2 x ( x - 1 ) x ( x - 1 ) ( x - = + 2 ) 2 + ac2 3 on determining the ...
... obtaining the sum of the preceding terms , and then to add the last term to the result . Thus in the above example we should have 12 + 22 + 32 ... + x2 = Σx2 + x2 x ( x - 1 ) x ( x - 1 ) ( x - = + 2 ) 2 + ac2 3 on determining the ...
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A₁ A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ c₂ Calculus of Finite Cambridge CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive CONIC SECTIONS convergent Crown 8vo curve deduce denoted determine Differential Calculus differential equation divergent English Notes equation of differences expression Fcap Fellow of St Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral John's College limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates P. G. TAIT particular value periodical function rational and integral reduced result Schools second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux+1 Ux+2 v₂ Vx+1 Vx+2 whence Их
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