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1. Date despre program

,QVWLWXĠLDGHvQYăĠăPkQW ACADEMIA DE STUDII ECONOMICE
1.2. Facultatea &,%(51(7,&Ă67$7,67,&Ăù,,1)250$7,&Ă(&2120,&Ă
1.3. Departamente (Departament) MATEMATICI APLICATE
1.4. Domeniul de studii &LEHUQHWLFăVWDWLVWLFăúLLQIRUPDWLFăHFRQRPLFă

1.5. Ciclul de studii /,&(1ğĂ

)RUPDGHvQYăĠăPkQW &8)5(&9(1ğĂ

1.7. Programul de studii &LEHUQHWLFăHFRQRPLFă

1.8. Limba de studiu 5RPkQă

1.9. Anul universitar 2018-2019

2. Date despre disciplina

2.1. Denumire $OJHEUă

2.2. Cod 18.0203IF1.1-0002

2.3. Anul de studii 1 2.4. Semestrul 1 2.5. Forma de Examen 2.6. Regimul O 2.7. Nr. credite 5
evaluare disciplinei (Obligato ECTS
riu)
2.8. Titulari C(C) SURIXQLYGU&29(,'5$*2ù3Ă758 dragos.covei@csie.ase.ro
C(C) conf.univ.dr. DEDU Silvia silvia.dedu@csie.ase.ro
C(C) lect.univ.dr. MIRCEA Iulian iulian.mircea@csie.ase.ro
C(C) lect.univ.dr. URECHE Ana Daniela ana.tudorache@csie.ase.ro
C(C) OHFWXQLYGU9(*+(ù2YLGLX Ovidiu.Veghes@csie.ase.ro
S(S) $VRFLDWGU%$5&Ă8$/(;$1'5808*85(/ Alexandru.Barcau@csie.ase.ro
S(S) SURIXQLYGU&29(,'5$*2ù3Ă758 dragos.covei@csie.ase.ro
S(S) conf.univ.dr. DEDU Silvia silvia.dedu@csie.ase.ro
S(S) lect.univ.dr. MIRCEA Iulian iulian.mircea@csie.ase.ro
S(S) lect.univ.dr. NECULAESCU Cristian cristian.neculaescu@csie.ase.ro
S(S) lect.univ.dr. URECHE Ana Daniela ana.tudorache@csie.ase.ro
S(S) OHFWXQLYGU9(*+(ù2YLGLX Ovidiu.Veghes@csie.ase.ro

3. Timp total estimat

1XPăUGHVăSWăPkQL 14.00
1XPăUGHRUHSHVăSWăPkQă 4.00 din care
C(C) 2.00
S(S) 2.00

Pagina 1/6
7RWDORUHGLQSODQXOGHvQYăĠăPkQW 56.00 din care
C(C) 28.00
S(S) 28.00
7RWDORUHGHVWXGLXSHVHPHVWUXQXPăU(&76 RUH 125.00
3.5. Total ore studiu individual 69.00

'LVWULEXĠLDIRQGXOXLGHWLPSSHQWUXVWXGLXLQGLYLGXDO
6WXGLXGXSăPDQXDOVXSRUWGHFXUVELEOLRJUDILHúLQRWLĠH 32.00
'RFXPHQWDUHVXSOLPHQWDUăvQELEOLRWHFăSHSODWIRUPHOHHOHFWURQLFHGHVSHFLDOLWDWHúLSHWHUHQ 20.00
3UHJăWLUHVHPLQDULLODERUDWRDUHWHPHUHIHUDWHSRUWRIROLLúLHVHXUL 14.00
Tutoriat 1.00
([DPLQăUL 2.00
$OWHDFWLYLWăĠL 0.00

3UHFRQGLĠLL
4.1. de curriculum $OJHEUăVXSHULRDUăQXPăUDUHDQDOL]ăPDWHPDWLFăODQLYHOGHOLFHXFHOSXĠLQODQLYHOXOVWDQGDUGXOXLFXUULFXODU0
GHFRPSHWHQĠH Utilizarea conceptelor matematice în rezolvarea de probleme.

&RQGLĠLLGHVIăúXUDUHDFWLYLWăĠL
pentru C(C) 3UHOHJHULOHVHGHVIăúRDUăvQVăOLFXPXOWHWDEOHvQVWDUHEXQăGHYL]LELOLWDWH
pentru S(S) 6ăOLFXPDLPXOWHWDEOHúLFXFDOFXODWRDUH

&RPSHWHQĠHVSHFLILFHDFXPXODWH
PROFESIONALE C1 2SHUDUHDFXQRĠLXQLWHKQLFLúLPHWRGHGHWHRULDVLVWHPHORUúLFLEHUQHWLFăHFRQRPLFă

7. Obiectivele disciplinei
7.1. Obiectivul general ÌQYăĠDUHDúLFXQRDúWHUHDQRĠLXQLORUVSHFLILFHFRQĠLQXWXOXLFXUVXOXLúLXWLOL]DUHDDFHVWRUDvQPRGHODUHDIHQRPHQHORU
socio-economice.
7.2. Obiective specifice • Presenting and explaining the theoretical concepts in conjunction with specific economic variables.
• Acquiring of the methods, techniques and knowledge specific to the content of discipline.
• Develop skills of analysis, selection and synthesis of information specific to economic cybernetics.
Creating a positive attitude towards the interdisciplinary approach.

&RQĠLQXWXUL

8.1. C(C) Metode de predare/ lucru 5HFRPDQGăUL

1 2ELHFWLYHOHGLVFLSOLQHLFRPSHWHQĠHOHGREkQGLWHFDUH]XOWDWDOvQYăĠăULLPHWRGHGH Prelegere în sistem clasic,

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Cap.16SDĠLLYHFWRULDOHOLQLDUH VWXGHQĠLL
'HILQLĠLDVSDĠLXOXLYHFWRULDOOLQLDU6XEVSDĠLXYHFWRULDO([HPSOHDOJHEULFH
H[HPSOXGLQWHRULDFRQVXPDWRUXOXL5HJXOLGHFDOFXOvQWUXQVSDĠLXYHFWRULDO
&RPELQDĠLHOLQLDUă$FRSHULUHOLQLDUă6LVWHPHGHJHQHUDWRUL
2 )DPLOLHGHYHFWRULOLQLDULQGHSHQGHQWăOLQLDUGHSHQGHQWă2SHUDĠLLFXIDPLOLLGH Prelegere în sistem clasic,
YHFWRUL%D]ăDXQXLVSDĠLXYHFWRULDOúLUHSHU)DPLOLHOLQLDULQGHSHQGHQWăPD[LPDOă ODWDEOăvQLQWHUDFĠLXQHFX
VLVWHPGHJHQHUDWRULPLQLPDO7HRUHPDGHH[LVWHQĠăDED]HL6SDĠLLYHFWRULDOHGHWLS VWXGHQĠLL
ILQLWH[HPSOH'LPHQVLXQHDXQXLVSDĠLXYHFWRULDO/HPDGHFRPSOHWDUH7HRUHPD
SULYLQGH[LVWHQĠDúLXQLFLWDWHDGHVFRPSXQHULLvQWUXQUHSHU&RRUGRQDWHOHúL
UHSUH]HQWDUHDXQXLYHFWRUvQWUXQUHSHU7HRUHPDUDQJXOXL&RQVHFLQĠH

Pagina 2/6
3 Teorema schimbului - Steinitz. Metoda pivotului (Gauss-Jordan). Lema Prelegere în sistem clasic,
VXEVWLWXĠLHL0DWULFHDGHWUHFHUHGHODXQUHSHUODDOWXO'HILQLĠLDL]RPRUILVPXOXLGH ODWDEOăvQLQWHUDFĠLXQHFX
VSDĠLLYHFWRULDOH6SDĠLLYHFWRULDOHGHWLSILQLWL]RPRUIH6SDĠLXFkW7HRUHPHGH VWXGHQĠLL
izomorfism.
4 6XPDúLLQWHUVHFĠLDDGRXăVXEVSDĠLLYHFWRULDOH7HRUHPDOXL*UDVVPDQQ6XPă Prelegere în sistem clasic,
GLUHFWăGHVXEVSDĠLLYHFWRULDOH7HRUHPDGHFDUDFWHUL]DUHDVXPHLGLUHFWH ODWDEOăvQLQWHUDFĠLXQHFX
Suplement direct. VWXGHQĠLL
Cap. 2. Operatori liniari.
'HILQLĠLDXQXLRSHUDWRUOLQLDU([HPSOH3URSULHWăĠL2SHUDĠLLFXRSHUDWRULOLQLDUL
Operator invers.
5 1XFOHXOúLLPDJLQHDXQXLRSHUDWRUOLQLDU7HRUHPDGLPHQVLXQLLSHQWUXRSHUDWRUL Prelegere în sistem clasic,
OLQLDUL5HSUH]HQWDUHDPDWULFHDOăDRSHUDWRULORUOLQLDULGHILQLĠLSHVSDĠLLYHFWRULDOHGH ODWDEOăvQLQWHUDFĠLXQHFX
WLSILQLW5DQJXOXQXLRSHUDWRUOLQLDUúLGHIHFWXOOXL/HJăWXUDGLQWUHRSHUDĠLLOHFX VWXGHQĠLL
RSHUDWRULOLQLDULúLRSHUDĠLLOHFXPDWULFHOHFRUHVSXQ]ăWRDUHORU0RGLILFDUHDPDWULFHL
unui operator liniar la schimbarea reperelor.
6 9DORULSURSULLúLYHFWRULSURSULLDLXQXLRSHUDWRUOLQLDUFDUHHVWHHQGRPRUILVP Prelegere în sistem clasic,
6XEVSDĠLLSURSULL'LPHQVLXQHDDOJHEULFăúLJHRPHWULFăDXQHLYDORULSURSULL ODWDEOăvQLQWHUDFĠLXQHFX
3ROLQRDPHGHHQGRPRUILVPHVDXGHPDWULFHSăWUDWLFH3ROLQRPFDUDFWHULVWLFDOXQXL VWXGHQĠLL
HQGRPRUILVPVDXDOXQHLPDWULFHSăWUDWLFH7HRUHPD+DPLOWRQ±&D\OH\
&RQVHFLQĠH2SHUDWRUOLQLDUGLDJRQDOL]DELO0DWULFHGLDJRQDOL]DELOă3XWHULOHXQHL
matrice diagonalizabile. Teorema de diagonalizare.
([HPSOHGHVRIWSHQWUXGHWHUPLQDUHDYDORULORUSURSULLúLDYHFWRULORUSURSULL
7 )RUPDGLDJRQDOăIRUPDFDQRQLFă-RUGDQDXQXLHQGRPRUILVP9HFWRULSULQFLSDOLúL Prelegere în sistem clasic,
QXFOHHSULQFLSDOH)RUPDFDQRQLFăDXQXLRSHUDWRUQLOSRWHQW$OJRULWPLGH ODWDEOăvQLQWHUDFĠLXQHFX
jordanizare. Reper Jordan. VWXGHQĠLL
Exemple de soft pentru determinarea formei canonice Jordan.
8 $SOLFDĠLLODIRUPDFDQRQLFD-RUGDQ6LVWHPHGHHFXDWLLGLIHUHQWLDOHOLQLDUHGH Prelegere în sistem clasic,
RUGLQXOLQWDLFXFRHILFLHQĠLFRQVWDQĠLVLVWHPIXQGDPHQWDOGHVROXWLLVROXĠLDJHQHUDOă ODWDEOăvQLQWHUDFĠLXQHFX
(cazul bidimensional). VWXGHQĠLL
9 )XQFĠLRQDOHOLQLDUH'XDOXODOJHEULFDOXQXLVSDĠLXOLQLDU)XQFĠLRQDOHELOLQLDUHúL Prelegere în sistem clasic,
VHVTXLOLQLDUH5HSUH]HQWDUHDPDWULFHDOăúLIRUPDDOJHEULFă)XQFĠLRQDOHELOLQLDUH ODWDEOăvQLQWHUDFĠLXQHFX
simetrice si sesquiliniare hermitiene. VWXGHQĠLL
10 )XQFĠLRQDOHSăWUDWLFHUHDOH'HILQLĠLHúLIXQFĠLRQDODSRODUă5HSUH]HQWDUHD Prelegere în sistem clasic,
PDWULFHDOăúLIRUPDDOJHEULFăDXQHLIXQFĠLRQDOHSăWUDWLFHUHDOH&ODVLILFDUHD ODWDEOăvQLQWHUDFĠLXQHFX
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11 Cap. 36SDĠLLOLQLDUHHXFOLGLHQH Prelegere în sistem clasic,
3URGXVVFDODUUHDO6SDĠLXHXFOLGLDQ3URGXVVFDODUFRPSOH[6SDĠLXXQLWDU1RWLXQHD ODWDEOăvQLQWHUDFĠLXQHFX
de norma, distanta, punct fix, contractie. Teorema de punct fix. Inegalitatea VWXGHQĠLL
Cauchy-Buniakovsky-Schwarz. Vectori ortogonali. Baze ortogonale. Procedeul de
ortogonalizare Gram-Schmidt. Baze ortonormate.
12 6XEVSDĠLLRUWRJRQDOH&RPSOHPHQWRUWRJRQDO7HRUHPDGHGHVFRPSXQHUHvQ Prelegere în sistem clasic,
VXEVSDĠLLRUWRJRQDOH3URLHFĠLDXQXLYHFWRUSHXQVXEVSDĠLX$GMXQFWXOXQXLRSHUDWRU ODWDEOăvQLQWHUDFĠLXQHFX
OLQLDUGHILQLĠLHSURSULHWăĠL VWXGHQĠLL
13 (QGRPRUILVPHDXWRDGMXQFWHGHILQLĠLHSURSULHWăĠL0HWRGDYDORULORUSURSULLSHQWUX Prelegere în sistem clasic,
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HQGRPRUILVPHRUWRJRQDOLGHILQLĠLHSURSULHWăĠL$SOLFDĠLLvQDQDOL]DGDWHORUVDXvQ VWXGHQĠLL
microeconomie.
14 5HFDSLWXODUHDFKHVWLXQLORUWHRUHWLFH&RPHQWDULLúLFRPSOHWăUL3UH]HQWDUHDXQXL Prelegere în sistem clasic,
bilet de examen. ODWDEOăvQLQWHUDFĠLXQHFX
VWXGHQĠLL

Bibliografie
- Halmos, Paul Richard, Finite-Dimensional Vector Spaces, Springer, Berlin, 1978, Germania

- Roman, Steven, Advanced Linear Algebra, 3ed, Springer, Berlin, 2008, Germania
- Golan, Jonathan, S., The Linear Algebra - a Beginning Graduate Student Ought to Know, Springer, Berlin, 2007, Germania

- &HQXúă*KúLFROHFWLYFDWHGUă0DWHPDWLFLSHQWUXHFRQRPLúWL&,621%XFXUHúWL5RPkQLD

- &ROHFWLY&DWHGUă$6(0DWHPDWLFLDSOLFDWHvQHFRQRPLH&,621%XFXUHúWL5RPkQLD

Pagina 3/6
- 1HFXOăHVFX&9HJKHú2,QWURGXFHUHvQDOJHEUDOLQLDUă$6(%XFXUHúWL5RPkQLD

- Covei Dragos-Patru, Elemente de algebra liniara, ASE, Bucuresti, 2015, România

- ùHUEDQ5DGX,MDFX'DQLHOD0LUFHD,XOLDQ$OJHEUăúLDQDOL]ăPDWHPDWLFă&RULQW%XFXUHúWL5RPkQLD

- Connan, Guillaume; Grognet, Stéphane, Guide Du Calcul Avec Les Logiciels Libres: XCAS, Scilab, Bc, Gp, GnuPlot, Maxima, MuPAD,
'XQRG3DULV)UDQĠD
- Friedberg S.H., Insel A.J., Linear Algebra, Prentice Hall, Englewood Cliffs, 2003, Statele Unite ale Americii
- Strang, Gilbert, Linear Algebra and its applications, 4ed, Brooks Cole, Pacific Grove, 2005, Statele Unite ale Americii
- Strang, Gilbert, 18.06SC Linear Algebra. (Massachusetts Institute of Technology: MIT OpenCourseWare), Cambridge, 2011,
http://ocw.mit.edu (Accesat Septembrie 20, 2012), Statele Unite ale Americii

Pagina 4/6
8.2. S(S) Metode de predare/ lucru 5HFRPDQGăUL

1 0DWULFH5DQJXOXQHLPDWULFH6LVWHPHGHHFXDĠLLOLQLDUHLQYHQWDUXOPHWRGHORUGH $SOLFDĠLLODWDEOăvQ
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2 6SDĠLLúLVXEVSDĠLLYHFWRULDOH'LPHQVLXQHDXQXLVSDĠLXYHFWRULDO&RPSOH[LILFDWXO $SOLFDĠLLODWDEOăvQ
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GLQWUXQVXEVSDĠLXYHFWRULDOúLvQVSDĠLXOFkW dialog continuu cu
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4 2SHUDĠLLFXVXEVSDĠLLYHFWRULDOH $SOLFDĠLLODWDEOăvQ
dialog continuu cu
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5 2SHUDWRULOLQLDUL3URSULHWăĠLJHQHUDOH2SHUDWRULGHSURLHFĠLHREOLFă $SOLFDĠLLODWDEOăvQ
dialog continuu cu
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6 0DWULFHDVRFLDWHRSHUDWRULORUOLQLDUL2SHUDĠLLFXRSHUDWRULOLQLDUL1XFOHXOúL $SOLFDĠLLODWDEOăvQ
imaginea unui operator liniar. dialog continuu cu
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7 (QGRPRUILVPH9HFWRULúLYDORULSURSULLYHFWRULSULQFLSDOL$OJRULWPGH $SOLFDĠLLODWDEOăvQ
Jordanizare. Caz particular: algoritmul de diagonalizare. dialog continuu cu
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8 6LVWHPHGHHFXDĠLLGLIHUHQĠLDOHGHRUGLQXOvQWkLFXFRHILFLHQĠLFRQVWDQĠL $SOLFDĠLLODWDEOăvQ
dialog continuu cu
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9 (YDOXDUHDFXQRúWLQĠHORUGREkQGLWH Test scris

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dialog continuu cu
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dialog continuu cu
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14 1RUPH&RQVWUXLUHDXQXLSURGXVVFDODUFRPSDWLELOFXQRUPD3UREOHPHvQVSDĠLL $SOLFDĠLLODWDEOăvQ
liniare normate. dialog continuu cu
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Bibliografie
- &HQXúă*KúLFROHFWLYFDWHGUă0DWHPDWLFLSHQWUXHFRQRPLúWL&XOHJHUHGHSUREOHPH&,621%XFXUHúWL5RPkQLD

- ùHUEDQ5DGXFRRGRQDWRU&XOHJHUHGHSUREOHPHGHDOJHEUăOLQLDUă$6(%XFXUHúWL5RPkQLD

- 7RPD$LGD$OJHEUDOLQLDUD&XOHJHUHGHSUREOHPH(FRQRPLFD%XFXUHúWL5RPkQLD

- &KLULĠă6WDQ3UREOHPHGHPDWHPDWLFLVXSHULRDUH'LGDFWLFăúL3HGDJRJLFă%XFXUHúWL5RPkQLD

- 5DLVFKL&RQVWDQWLQFRRGRQDWRU$QDOL]DPDWHPDWLFDFXOHJHUHGHSUREOHPHSHQWUXDQXOOO$6(%XFXUHúWL5RPkQLD

- ùHUEDQ5DGX,MDFX'DQLHOD0LUFHD,XOLDQ$OJHEUăúLDQDOL]ăPDWHPDWLFă&RULQW%XFXUHúWL5RPkQLD

- Covei Dragos-Patru, Elemente de algebra liniara, ASE, Bucuresti, 2015

- Halmos, Paul Richard, Linear Algebra Problem Book, The Mathematical Association of America, Washington, 1995, Statele Unite ale
Americii
- Zhang, Fuzhen, Linear Algebra - Challenging Problems for Students, Johns Hopkins University Press, Baltimore, 1996, Statele Unite ale
Americii

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angajatori reprezentativi din domeniul aferent programului

10. Evaluare
Pondere în
Activitatea Criterii de evaluare Metode de evaluare
QRWDILQDOă
10.1. S(S)
10.2. S(S) *UDGXOGHDVLPLODUHDQRĠLXQLORUPHWRGHORU 3UH]HQĠDFRQWULEXWLDDFWLYăOD 30.00
WHKQLFLORUúLFXQRúWLQĠHORUSUH]HQWDWHSUHFXPúL rezolvarea problemelor prezentate,
aplicarea lor în rezolvarea de probleme. SUHFXPúLXQWHVWVFULVSHSDUFXUVXO
semestrului.
(YDOXDUHILQDOă *UDGXOGHDVLPLODUHDQRĠLXQLORUPHWRGHORU (YDOXDUHILQDOăH[DPHQVFULV 70.00
WHKQLFLORUúLFXQRúWLQĠHORUSUH]HQWDWHSUHFXPúL
aplicarea lor în rezolvarea de probleme.
10.4. Modalitatea de notare Note întregi 1-10
6WDQGDUGPLQLPGHSHUIRUPDQĠă 1RWDODH[DPHQXOVFULVVHREĠLQHSULQURWXQMLUHDSXQFWDMXOXLREĠLQXWGLQEDUHPXOGHFRUHFWDUH1RWD
ILQDOăVHFDOFXOHD]ăFDPHGLHSRQGHUDWăvQWUHQRWDGHODVHPLQDU30%úLSXQFWDMXOREĠLQXWOD
examenul scris (70%QXPDLGDFăQRWDODH[DPHQXOVFULVHVWHPLQLP5'DFăQRWDREĠLQXWăOD
H[DPHQXOVFULVHVWHPDLPLFăGHFDW5DWXQFLDFHDVWDGHYLQHQRWDILQDOă1RWDILQDOăVHREĠLQHSULQ
URWXQMLUH([DPHQXOVHSURPRYHD]ăFXQRWDILQDOăFHOSXĠLQ5.

'DWDOLVWăULL Titulari,
20/11/2018

'DWDDYL]ăULLvQGHSDUWDPHQW Director departament,

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