CODICE 66176 ANNO ACCADEMICO 2018/2019 CFU 6 cfu anno 1 YACHT DESIGN 9268 (LM-34) - LA SPEZIA SETTORE SCIENTIFICO DISCIPLINARE MAT/07 LINGUA Inglese SEDE LA SPEZIA PERIODO 2° Semestre MATERIALE DIDATTICO AULAWEB PRESENTAZIONE The course aims to provide a presentation of the most common partial differential equations (PDE) and their solution techniques through an analysis of various applications. The emphasis is devoted to second order PDE and the understanding of the specific techniques for elliptic, parabolic and hyperbolic cases. OBIETTIVI E CONTENUTI OBIETTIVI FORMATIVI The unit deals with the most important partial differential equations through their most important mathematical physical in the pleasure of craft sector. MODALITA' DIDATTICHE The unit is organised with for hours a week: a part of this course takes place in the laboratory to teach Matlab (matrix laboratory) PROGRAMMA/CONTENUTO Introduction to partial differential equations (PDE). The elastic string and the transition from discrete systems to continuous systems . 2 . The differential equations of the second order. The classification and the normal form; elliptic , hyperbolic and parabolic PDE. 3 . Elliptic equations. The harmonic functions. The problems of Dirichelet and Neuman , The Poisson formula for the circle. 4 . The variable separation technique. The series and the Fourier transform . The Gibbs effect, the analysis of normal modes , the delta Dirac "function”. 5 . The Bessel functions, the problems in polar coordinates. 6 . The parabolic differential equations, diffusion and heat equations; descriptions in the domain of space and time. 7 . The hyperbolic equations: the equation of D' Alembert. The method of characteristics, the elastic membrane, the mechanical interpretation of the normal modes 8 . PDE of higher order: the biharmonic equation, its Cauchy problem. The vibration of bars and plates. TESTI/BIBLIOGRAFIA A.N.Tichonov, A.A.Samarskij: Equazioni della Fisica matematica, Problemi della fisica matematica, Mosca,1982; R. Courant, D. Hilbert, Methods of Mathematical Phisics vol I e II, Interscience, NY, 1973; R. Bracewell, The Fourier Transform and Its Applications, New York: McGraw-Hill, 1999; P. V. O’ Neil, Advanced engineering mathematica, Brooks Cole, 2003; H. Goldstein, Meccanica Classica, Zanichelli, Bologna, 1985; V. I. Smirnov. Corso di Matematica superiore, Vol. 3. MIR (1978). DOCENTI E COMMISSIONI GIOVANNI RESTA ROBERTO CIANCI Ricevimento: Students may also take appointment via email sent to cianci@dime.unige.it. Commissione d'esame ROBERTO CIANCI (Presidente) GIOVANNI RESTA (Presidente) LEZIONI INIZIO LEZIONI Come da Calendario didattico Second semester. Orari delle lezioni L'orario di questo insegnamento è consultabile all'indirizzo: Portale EasyAcademy ESAMI MODALITA' D'ESAME Examinations are oral . Some mandatory exercizes can be requested. Calendario appelli Data appello Orario Luogo Tipologia Note 11/01/2019 10:30 LA SPEZIA Orale 06/02/2019 10:30 LA SPEZIA Orale 10/06/2019 10:30 LA SPEZIA Orale 11/07/2019 10:30 LA SPEZIA Orale 11/09/2019 10:30 LA SPEZIA Orale