II_lug08 - ω = ± x x 2 + y 2 + log y 2 ² dx + ± 2 x y +...

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CdL in FISICA ANALISI MATEMATICA II 11/07/2008 Cognome . ............................................. Nome. ...................................... Matricola . ............................. Gruppo . ........................................... 1. Determinare l’intervallo di convergenza e studiare la convergenza uniforme della se- guente serie di potenze: + X n =1 1 n n log n ( x + 1) n . Risultato: .................................................................................. 2. Classificare i punti critici della seguente funzione: f ( x,y ) = x 4 - 6 x 2 y 2 + y 4 . Risultato: .................................................................................. 3. Calcolare il seguente integrale doppio: Z Z C ydxdy dove C ` e la regione di piano descritta in coordinate polari da ρ 1 + cos θ, θ [0 ] . Risultato: .................................................................................. 4. Studiare la seguente forma differenziale
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Unformatted text preview: ω = ± x x 2 + y 2 + log y 2 ² dx + ± 2 x y + y x 2 + y 2 ² dy e calcolare l’integrale curvilineo di ω esteso all’arco di curva di equazione y = cos x , x ∈ [-π/ 4 ,π/ 4]. Risultato: .................................................................................. 5. Determinare un’equazione differenziale lineare del second’ordine omogenea a coeffi-cienti costanti avente y ( x ) = xe x come soluzione. Risultato: .................................................................................. 6. Risolvere i seguenti problemi di Cauchy: x 2 y + 2 y = 2 √ ye 1 /x y (1) = 0 , x 2 y + 2 y = 2 √ ye 1 /x y (1) = 9 e 2 . Risultato: .....................................................................................
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This note was uploaded on 10/13/2011 for the course MAT 05 taught by Professor Trombetti during the Spring '10 term at Università DI Napoli "Federico II""".

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II_lug08 - ω = ± x x 2 + y 2 + log y 2 ² dx + ± 2 x y +...

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