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- University
- Politecnico di Milano
- Degree programme
- Computer Engineering
- Subject
- Analisi Matematica 2
- Academic year
- 2012-2013
- Classification
- Exam · Second midterm
- Content
- Exam paper only
- Original format
- Text
- Searchable text
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ExamSecond midtermExam paper only
04 02 2013
Study material for Analisi Matematica 2, shared by the Studwiz community and reviewed by moderators.
Analisi Matematica 2Second midterm
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ANALISI MATEMATICA 2 2 prova in itinere 04/02/2013 domanda 1 2 3 4 5 6 7 totale punteggio 1 3 5 5 5 3 2 2 1 4 31 voto Cognome............................................ .................Nome.............................. ............ n.di matricola...................................... .............. Firma................................ ............. n.d’iscrizione............................ 1) Sia y f(x) la funzione 2 periodica definita in [ , da f(x)x( |x| a) disegnare il grafico qualitativo di f(x) in [-3 , 3 b) scrivere la serie di Fourier associata a f, calcolando i co efficienti b) f(x) 8 sen 2k1x 2k13 Calcoli bn 2 0 x xsennxdx 2 x x cos nx n 0 x cos nx n dx 2 x x sennx n2 0 2 sennx n2 2 2 sennx n2 2 cos nx n2 8/n3 n dispari 0 n pari 2) Risolvere il seguente problema di Cauchy yx 1 6 1senx senx yx cos xe senx 3 y2 y/4 0 y(x) (e senx senx 2 /21/3 y’y2 1 6 1senx senx y3 cos xe senx 3 y3 t 3y’y2 t t’- 1 2 cos x senx t cos xe senx 3 te senx senx c y(e senx senx c1/3 y/4 0 per c- 2 /2 3)Risolvere il seguente problema di Cauchy x2yx 5xyx 4yx 1 x2 y1 0 y1 1 yx 1 t2 log t 1 2t2 log 2t Cal col i Equazione di Eulero x et y”4y’4ye2t yAte 2t Be 2t yCt 2e2t C 1/2 yA log x x B 1 x2 1 2x2 log 2x per il pb. di Cauchy A 1, B0 4) Risolvere la seguente equazione y’(t) t2 ty t ty t y2t yt t2 1/C21/2 Eq. omogenea y(t)tz(t) l eq . diventa ztz’ 1z z 1 z2 dz dt t 1 2 log 1 z2 log Cx yt t2 1/C21/2 5) Calcolare per serie il seguente integrale: I 0 1 x2/3 cos xdx con E102 I 51/110 calcoli x 2/3 cos x 1n…
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