Capitolul 1 Ecuatii diferentiale de ordinul ˆıntâi rezolvabile prin ...

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252 CAPITOLUL 7 p8 := pds2:-plot(t=1/2): p9 := pds2:-plot(t=1): p10 := pds2:-plot(t=2): plots[display]({p6,p7,p8,p9,p10}, title=‘Heat profile at t=0,0.1,0.5,1,2‘); Figura 32 > pds2:-plot3d(t=0..1,x=0..1,axes=boxed); Figura 33
Calculul simbolic ¸si numeric pentru ecuat¸ii parabolice 253 Exemplul 3: ⎧ ⎪⎨ ⎪⎩ ∂u ∂t (x, t) = ∂2u ∂x2(x, t) + t · cosx u(0, t) = t, u(π, t) = 0 u(x, 0) = cos 2x + cos 3x Heat equation > PDE3 := diff(u(x,t),t)=diff(u(x,t),x,x)+t*cos(x); PDE3 := ∂ ∂t u (x, t) = ∂2 ∂x 2u (x, t) + t cos (x) > IBC3 := {u(0,t)=t,u(Pi,t)=0,u(x,0)=cos(2*x)+cos(3*x)}; IBC3 := {u (π, t) = 0, u (0, t) = t, u (x, 0) = cos (2 x) + cos (3 x)} > pds3 := pdsolve(PDE3,IBC3,numeric); pds1 := module () local INFO; export plot, plot3d, animate, value, settings; option ‘Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.‘; end module > q1 := pds3:-plot(t=0): q2 := pds3:-plot(t=1/10): q3 := pds3:-plot(t=1/2): q4 := pds3:-plot(t=1): q5 := pds3:-plot(t=2): plots[display]({q1,pq2,q3,q4,q5}, title=‘Heat profile at t=0,0.1,0.5,1,2‘);
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Capitolul 1 Ecuat¸ii diferent¸ial
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Problema primitivei. Ecuat¸ii dife
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Problema primitivei. Ecuat¸ii dife
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Ecuat¸ii diferent¸iale autonome
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Ecuat¸ii diferent¸iale autonome
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Ecuat¸ii diferent¸iale cu variabi
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Ecuat¸ii omogene în sens Euler 17
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Ecuat¸ii omogene generalizate 19 1
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Ecuat¸ii diferent¸iale liniare de
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Ecuat¸ia diferent¸ialǎ a lui Ber
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Ecuat¸ia diferent¸ialǎ a lui Ber
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Ecuat¸ia diferent¸ialǎ a lui Ric
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Ecuat¸ii cu diferent¸ialǎ total
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Ecuat¸ii cu diferent¸ialǎ total
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Calculul simbolic al solut¸iilor e
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Capitolul 2 Ecuat¸ii diferent¸ial
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Ecuat¸ii diferent¸iale de ordinul
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Reducerea ecuat¸iei diferent¸iale
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Capitolul 3 Sisteme de ecuat¸ii di
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Sisteme de ecuat¸ii diferent¸iale
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Reducerea ecuat¸iilor diferent¸ia
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Calculul simbolic al solut¸iilor s
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Teoreme de existent¸ǎ ¸si unicit
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Proprietǎt¸i calitative ale solut
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Metode numerice 131 4.4 Metode nume
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Metode numerice 133 Sǎ presupunem
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Metode numerice 135 ceea ce demonst
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Metode numerice 137 Pentru a compar
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Metode numerice 139 eval(sol_x1(t),
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Metode numerice 141 > end if; > end
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Metode numerice 143 eval(sol_x1(t),
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Metode numerice 145 178.44235533234
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Metode numerice 147 Figura 19 > wit
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Metode numerice 149 Figura 23 Un al
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Metode numerice 151 Figura 26 Portr
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Metode numerice 153 care aratǎ cǎ
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Integrale prime 155 Întrucât (t0,
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Integrale prime 157 Teorema 4.5.2 D
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Integrale prime 159 3. Arǎtat¸i c
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Integrale prime 161 Exercit¸ii: 1.
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Capitolul 5 Ecuat¸ii cu derivate p
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Ecuat¸ii cu derivate part¸iale de
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Clasificarea ecuat¸iilor cu deriva
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Formulele lui Green ¸si formule de
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Page 201 and 202: Probleme la limitǎ pentru ecuat¸i
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Page 279 and 280: Bibliografie [1] V.I. Arnold, Ecuat
Page 281: BIBLIOGRAFIE 281 [26] M.Stoka, Cule
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