CODICE 98219 ANNO ACCADEMICO 2024/2025 CFU 8 cfu anno 1 ENGINEERING TECHNOLOGY FOR STRATEGY (AND SECURITY) 10728 (LM/DS) - GENOVA SETTORE SCIENTIFICO DISCIPLINARE MAT/07 LINGUA Inglese SEDE GENOVA PERIODO Annuale 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 Fondamenti di modellazione e simulazione. Teoria e pratica della simulazione continua e relative metodologie. Teoria e pratica della simulazione discreta e relative metodologie. Simulazione ibrida. OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO Active participation in lectures and individual study will enable the student to: - be able to classify the main partial differential equations; - calculate the analytical solution of partial differential equations of elliptic, parabolic and hyperbolic types; - use the techniques of separation of variables, series and Fourier transform, special functions. PREREQUISITI The course does not require any formal prerequisites, being self-consistent and including all the elements and references necessary for the study; while not formally required, we warmly recommend to brush up the basic knowledge of the theory of partial and ordinary differential equations. MODALITA' DIDATTICHE The module is based on theoretical lessons. PROGRAMMA/CONTENUTO 1. Introduction to partial differential equations (PDE). The elastic string and the transition from discrete systems to continuous systems. Second order partial differential equations. Classification and normal form. Elliptic, hyperbolic and parabolic PDE. 2. Elliptic equations. The harmonic functions. Dirichlet and Neumann boundary conditions, the Poisson formula for the circle. 3. Separation of variables technique. Series and Fourier transform. The Gibbs effect, the analysis of normal modes, the delta Dirac "function”. Bessel functions and problems in polar coordinates. 4. Parabolic differential equations, diffusion and heat equations; descriptions in space and time domain. 5. Hyperbolic equations: the equation of D'Alembert. The method of characteristics, the elastic membrane, the mechanical interpretation of the normal modes. 6. Some concept on PDE of higher order: the biharmonic equation and its Cauchy problem. The vibration of bars and plates. 7. Non homogeneous PDE and Green functions. 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 ROBERTO CIANCI Ricevimento: Students may also take appointment via email sent to roberto.cianci@unige.it LUCA FABBRI Ricevimento: Students may also take appointment via email sent to luca.fabbri@unige.it Commissione d'esame ROBERTO CIANCI (Presidente) AGOSTINO BRUZZONE LUCA FABBRI (Presidente Supplente) LEZIONI INIZIO LEZIONI https://corsi.unige.it/10728/p/studenti-orario Orari delle lezioni L'orario di questo insegnamento è consultabile all'indirizzo: Portale EasyAcademy ESAMI MODALITA' D'ESAME The examination mode consists of an oral or written test to ensure learning of the course content. MODALITA' DI ACCERTAMENTO The written or oral exam focuses on the learning of a few subjects from those discussed in class. Calendario appelli Data appello Orario Luogo Tipologia Note 07/01/2025 14:00 GENOVA Orale 17/01/2025 09:00 GENOVA Orale 31/01/2025 09:00 GENOVA Orale Dead-line for subscriptions: 23rd of January 05/02/2025 14:00 GENOVA Orale 14/02/2025 09:00 GENOVA Orale Dead-line for subscriptions: 7th of February 03/06/2025 14:00 GENOVA Orale 06/06/2025 09:00 GENOVA Orale 01/07/2025 14:00 GENOVA Orale 11/07/2025 09:00 GENOVA Orale 05/09/2025 09:00 GENOVA Orale 11/09/2025 14:00 GENOVA Orale 19/09/2025 09:00 GENOVA Orale