Bir jinsli integral Reja

M i s o l : qatorni tekshiring.


Echimi:
(31)

Oxirgi qator yakinlashishini integral belgisi orkali tekshiramiz.

Xosmas integral uzoklashuvchi, demak zaruriy shart bajarilgan bulsa xam , garmonik qator deb atalmish (31) qator uzoklashuvchi ekan.
Lekin ma’ruzamizni 1-punktida
. (32)
qator yakinlashuvchanligi kursatilgan edi.Bundan,(32) qator shartli yakinlashishi kelib chikadi.


TEOREMA: Agar (28) – qator absolyut yakinlashsa, uning xadlarining urinlari ixtiyoriy ravishda almashtirilganda xam u absolyut yakinlashuvchanligicha koladi.
Bu va yukorida ta’riflangan teoremalar isbotsiz kabul kilinadi.

S a v o l l a r :

1.Leybnits teoremasini ta’riflang.
2.Uzgaruvchan ishorali qatorlarni ta’riflang.
3.Absalyut va shartli yakinlashishlar nima?

1^ Gerd Baumann,Mathematics for Engineers.II.pp.72-108

1¹ Gerd Baumann,Mathematics for Engineers.II.pp.72-108

1¹ Gerd Baumann,Mathematics for Engineers.II.pp.72-108

2^ C.Canuto , A.Tabacco, Mathematical Analisis I. Springer-Verlag, Milan , 2008.

1¹ C.Canuto , A.Tabacco, Mathematical Analisis I. Springer-Verlag, Milan , 2008.