Arbeitsbuch Mathematik fuer Ingenieure - download pdf or read online

By Finckenstein, Lehn, Schellhaas, Wegmann

ISBN-10: 3835100343

ISBN-13: 9783835100343

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Example text

34) D ( 0 ) = 1, &(k)u(k"l) = -6, the 0 D(1) = 20. 35) D(k) = 1 16 (18k+1 -2k+7 . 32). 8. 36) over the rectangle 0 5 z 5 CY,0 5 y 5 p. We shall assume that the values of u ( x , y ) are specified on thc bourldary of the rectangle. If we 21 Preliminaries I I I ~ ~ 1K< e, < L where X = h,:/hz. 15 Let us define the K+2 vectors u(k) of order L x 1 by u(k) = ( u k , ~ ) , L 5 L . j), 4 13; ' = W e also define vectors where r(k) = rk,p u(K C, { (2+2X) if i = j otherwise. ), if Xll,k,L+l 0 where if Ii -jl = 1 -X 0 = d.

Then, there exists an integer m , 0 5 'm, odd for An,u,(k)5 0 or n + ' m . even for A n , u ( k ) 2 0 and such that m 5 n-l implies (-l)m,+iAiu,(k)> 0 for all IC E IN(a), m 5i5 n-i 32 Proof. Chapter 1 There arc two c:ascs to considcr. Case 1. A n u ( k ) 5 0 on JN(a). ). If not, then there exists some kl 2 a in N ( a ) such that A"-lw,(kl) 5 0. -,m u ( k ) = - m which is a contradiction to w,(k) > 0. 11) Next let 'rrt >1 ~ ( o . ) ,' m 5 5 n,-I. 11) ~~ >0 011 N(a). (k) > 0 on lN(a), m -2 5i 5n -1 which is a contradiction to the definition of m .

M An-j-' u(k)> 0 and limk+m Aiu(k) = CO, 0 5 i 5 n -j -2. (ii) there is an odd integer j , 1 5 j Proof. 13. 9. 1. 2. 4. 5. Show that t,hc nth forward as well as backward difference of a polynornial of n,th degree is a constant. 7. that Let t,he functions ~ ( k and ) ~ ( k be ) defined on IN(1). 1) is called Abel's trun,sformation. 8. Let ~ ( k bc ) defined on Usc it to show that + 2. /,(lc) = i=l Prove u(k)). 9. Show that u(k) = q(k)! + +(k)! C+l)k(k)! 10. , k E W. Let u ( k ) be defined on IN(a).

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Arbeitsbuch Mathematik fuer Ingenieure by Finckenstein, Lehn, Schellhaas, Wegmann


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