Download - CURS AM
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Calcul integral 2013-2014
Marina Gorunescu
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Integrala Riemann
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Funcţie integrabilă Riemann
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1. Exemplu
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Clase de funcţii integrabile Riemann
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Proprietăţile integralei Riemann
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Teorema de medie
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3. Exemplu
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4. Exemplu
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Rezolvarea in Matlab a exemplului nr 4.
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Transfer de integrabilitate
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5.Exemplu
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6-7. Exemple
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De reţinut • Funcţie integrabilă Riemann • Clase de functii integrabile • Proprietăţile funcţiilor integrabile • Teorema de medie • O primitivă a unei funcţii integrabile Riemann • Transfer de integrabilitate
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Integrale improprii
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Integrale pe intervale nemărginite
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8. Exemple
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Rezolvarea in Matlab a exemplului nr 8
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Criteriu de convergenţă
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9. Exemplu
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Consecinţă
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10.Exemplu
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Rezolvarea in Matlab a exemplului nr 10
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Integrală absolut convergentă
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11. Exemplu
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Rezolvarea in Matlab a exemplului nr 11
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Integrale definite de funcţii nemărginite
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12. Exemple
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Rezolvarea in Matlab a exemplelor nr 12
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Criteriu de convergenţă
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13. Exemplu
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Rezolvarea in Matlab a exemplelor nr 13
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De reţinut • Integrale pe intervale nemărginite • Criteriul de convergenţă şi consecinţă • Integrală improprie absolut convergentă • Integrala definită de funcţii nemărginite • Criteriu de convergenţă
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Integrale multiple
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Integrale duble
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Funcţie reală de două variabile reale, integrabilă
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Calculul prin iterare al integralei duble
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14. Exemplu
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Calculul integralelor duble in Matlab
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Rezolvarea in Matlab a exemplului nr 14
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15. Exemplu
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Rezolvarea in Matlab a exemplului nr 15
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16. Exemplu
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17. Exemplu
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18. Exemplu
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Calculul integralei duble ca succesiune de integrale simple
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19. Exemplu
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Rezolvarea in Matlab a exemplului nr 19
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20. Exemplu
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Rezolvarea in Matlab a exemplului nr 20
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21 Exemplu
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Rezolvarea in Matlab a exemplului nr 21
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Proprietăţile integralei duble
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22. Exemplu - aditivitatea integralei duble
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Rezolvarea in Matlab a exemplului nr 22
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Calculul ariei unei multimi cu integrala dubla
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23. Exemplu
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Rezolvarea in Matlab a exemplului nr 23
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Schimbare de variabile în integrala dublă
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24. Exemplu
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Rezolvarea in Matlab a exemplului nr 24
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25. Exemplu
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Rezolvarea in Matlab a exemplului nr 25
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Coordonate polare generalizate
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26. Exemplu
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Rezolvarea in Matlab a exemplului nr 26
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27. Exemplu
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De retinut • Funcţie reală de două variabile reale, integrabilă • Calculul integralei duble ca succesiune de
integrale simple • Aditivitatea integralei duble • Aplicaţii ale integralei duble. • Schimbarea de variabile
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Integrale triple
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28.Exemplu
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Rezolvarea in Matlab a exemplului nr 28
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29. Exemplu
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Rezolvarea in Matlab a exemplului nr 29
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30. Exemplu
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Rezolvarea in Matlab a exemplului nr 30
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Interpretare geometrica a integralei triple
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31. Exemplu
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Rezolvarea in Matlab a exemplului nr 31
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32. Exemplu
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Rezolvarea in Matlab a exemplului nr 32
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33. Exemplu
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Rezolvarea in Matlab a exemplului nr 33
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Coordonate sferice generalizate
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34.Exemplu
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Rezolvarea in Matlab a exemplului nr 34
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De retinut • Calculul integralei triple ca succesiune de
integrale
• Schimbarea de variabile în integrala triplă
• Aplicaţie a integralei triple