Risorse bibliografiche
 Risorsa bibliografica obbligatoria Risorsa bibliografica facoltativa
 Scheda Riassuntiva
 Anno Accademico 2017/2018 Scuola Scuola di Ingegneria Industriale e dell'Informazione Insegnamento 096119 - ADVANCED MATHEMATICAL ANALYSIS Docente Tomarelli Franco Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - MI (422) INGEGNERIA DELLA PREVENZIONE E DELLA SICUREZZA NELL'INDUSTRIA DI PROCESSO*AZZZZ096119 - ADVANCED MATHEMATICAL ANALYSIS
Ing Ind - Inf (Mag.)(ord. 270) - MI (472) CHEMICAL ENGINEERING - INGEGNERIA CHIMICA*AZZZZ096119 - ADVANCED MATHEMATICAL ANALYSIS

 Programma dettagliato e risultati di apprendimento attesi
 Aims and Scope - Problem solving for ordinary and partial differential equations. Prerequisites - Multiple integrals. Integrals on surfaces. Divergence Theorem. Fourier series of periodic functions. Functions of complex variable. Cauchy-Lipschitz Theorem. Linear second order ordinary differential equations. Euler's equation.  PROGRAM Introduction to partial differential equations - Mathematical modeling. Examples of partial differential equations. Well posed problems. Boundary value problems: Dirichlet and Neuman boundary conditions. Initial value problems. Classification of second order linear PDE.  Conservation Laws - Pollution in a channel. Linear transport equation. Distributed source. Decay and localized source. Characteristics. Inflow and outflow. First order quasi-linear equations.  Diffusion - The diffusion equation. Heat conduction. Well posed problems. Separation of variables. Maximum principle and uniqueness. The fundamental solution. The Dirac distribution. The Cauchy problem for the heat equation. Energy estimates. An example of nonlinear diffusion: the porous medium equation. Transforms - Fourier transform. Laplace transform. Fourier series of periodic signals. Function spaces: C^k, L^1, L^2. Distributions. Convolution. Transform-based methods for solving differential equations with initial and/or energy conditions. The Laplace Equation - Well posed problems and uniqueness. Harmonic functions and their properties. Separation of variables. Eigenvalue problems. The fundamental solution: Newtonian potential. Solution of Laplace equation in R^n. Waves and Vibrations - Types of waves. Transverse waves in a string. The one dimensional wave equation. D’Alembert formula. Domain of dependence and range of influence. Huygens principle. Energy conservation.

 Note Sulla Modalità di valutazione
 The final (written) exam consists in solving exercises and answering questions related with the topics of the course.

 Bibliografia
 Filippo Gazzola, Franco Tomarelli & Maurizio Zanotti, Analytic functions, Integral transforms, Differential equations - Second Edition, Editore: Esculapio, Anno edizione: 2015, ISBN: 978-88-7488-889-4Note:English text is also available as an E-book. A printed version in Italian language is available too.

 Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
26.0
esercitazione
22.0
laboratorio informatico
12.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

 Informazioni in lingua inglese a supporto dell'internazionalizzazione
 Insegnamento erogato in lingua Inglese Disponibilità di materiale didattico/slides in lingua inglese Disponibilità di libri di testo/bibliografia in lingua inglese Possibilità di sostenere l'esame in lingua inglese
 schedaincarico v. 1.6.5 / 1.6.5 Area Servizi ICT 23/04/2021