19
SESSION 2014 MPSI007 EPREUVE SPECIFIQUE - FILIERE MP !!!!!!!!!!!!!!!!!!!! SCIENCES INDUSTRIELLES Durée : 3 heures !!!!!!!!!!!!!!!!!!!! N.B. : Le candidat attachera la plus grande importance à la clarté, à la précision et à la concision de la rédaction. Si un candidat est amené à repérer ce qui peut lui sembler être une erreur d’énoncé, il le signalera sur sa copie et devra poursuivre sa composition en expliquant les raisons des initiatives qu’il a été amené à prendre. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! A

SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

  • Upload
    votuyen

  • View
    214

  • Download
    2

Embed Size (px)

Citation preview

Page 1: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

SESSION 2014 MPSI007 !

!!!

EPREUVE SPECIFIQUE - FILIERE MP!!!!!!!!!!!!!!!!!!!!!"

!SCIENCES INDUSTRIELLES

Durée : 3 heures!

!!!!!!!!!!!!!!!!!!!!"

N.B. : Le candidat attachera la plus grande importance à la clarté, à la précision et à la concision de la rédaction. Si un candidat est amené à repérer ce qui peut lui sembler être une erreur d’énoncé, il le signalera sur sa copie et devra poursuivre sa composition en expliquant les raisons des initiatives qu’il a été amené à prendre.!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""!!!!!!!!!!!!!!!!!!!!!!!!!!!

A

Page 2: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw
Page 3: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

• • • •

−⋅−

Page 4: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

η

α

η

λ

ω

ω

ω

Page 5: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw
Page 6: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

η

⋅⋅⋅⋅

⋅ ⋅

η

λ

η

Page 7: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

• ⋅

• ⋅

• ⋅

Page 8: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

( ) ⋅

⋅⋅

( ) ⋅

( ) ⋅

⋅⋅

( )

( ) ( )( )

( )

+

( )

Page 9: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

ΩΩ

τ

( ) +∞→∞ = ( ) =

( ) =

( ) =∞ ( ) =

⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅⋅⋅

( ) +

= ∈

⋅⋅ ⋅⋅

ω⋅

ω⋅

ω⋅

Page 10: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

( ) ( )( )

=

( ) −=

=

Page 11: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw
Page 12: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

−=

=→

−−

−−

Page 13: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

Γ

( )

+

=→

( )

+

=→

( )∈ =

−=

Γ⋅

Γ⋅

Γ

Γ

Page 14: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

Page 15: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

IM

PR

IM

ER

IE

NA

TI

ON

AL

E –

14

1310

– D

’ap

rès

do

cum

ents

fo

urn

is

Page 16: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

B

MPSI007

Page 17: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw
Page 18: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw

−ω ⋅ −

ω ⋅ −

Page 19: SCIENCES INDUSTRIELLES - ccp.scei- · PDF file,,, ,qioxhqfh gx jdlq . vxu ohv shuirupdqfhv gh o dvvhuylvvhphqw . 7hpsv gh upsrqvh j hq vhfrqgh 'psdvvhphqw pd[lpxp hq )dfwhxu gh frqiruw