CODE 90600 ACADEMIC YEAR 2016/2017 CREDITS 5 cfu anno 1 INGEGNERIA CIVILE E AMBIENTALE (LM-23) - 5 cfu anno 1 INGEGNERIA CIVILE E AMBIENTALE (LM-35) - SCIENTIFIC DISCIPLINARY SECTOR MAT/07 LANGUAGE Italiano TEACHING LOCATION SEMESTER 1° Semester MODULES Questo insegnamento è un modulo di: MATHEMATICAL PHYSICS II AND NUMERICAL ANALYSIS OVERVIEW The course aims to provide the student knowledge about numerical methods for mechanical engineering problems, particularly with regard to the solution of ordinary and partial differential equations. AIMS AND CONTENT TEACHING METHODS The time-schedule of the course is four hours per week in the second semester. The module consists of a theoretical part complemented by laboratory exercises carried out in Matlab. SYLLABUS/CONTENT The module aims to provide the basic elements of numerical analysis. The main part concerns numerical methods for solving ordinary differential equations (ODE) and partial differential equations (PDE). The purpose is to acquire a knowledge of numerical methods and their implementation, with a focus on stability analysis, accuracy and convergence of the methods. The lectures are complemented by laboratory exercises carried out using Matlab, one of the most used programming languages for scientific computing. 1. Numerical methods for solving systems of nonlinear equations. Polynomial interpolation, data fitting and least squares method. 2. Numerical solution of ordinary differential equations. 3. Numerical methods for partial differential equation: elliptic, parabolic and hyperbolic. Choice of the most suitable type of method depending on the type of PDE. 4. Finite Difference Method for problems in smooth domains: Poisson and diffusion equation. 5. Finite Element Method for elliptic and parabolic equations. Advection-diffusion equation and stabilization techniques. 6. Finite Volume Method for elliptic, parabolic and first-order hyperbolic (nonlinear conservation laws). The Riemann problem: characteristics, shock waves, rarefaction, contact discontinuities. RECOMMENDED READING/BIBLIOGRAPHY • Lecture notes of the course are available in aulaweb; • Quarteroni, F. Saleri, Introduzione al Calcolo Scientifico, Sprinter-Verlag 2006; • Quarteroni, Modellistica Numerica per Problemi Differenziali, Springer-Verlag 2008; • S. Chapra, R.Canale, Metodi numerici per l’Ingegneria, McGraw-Hill 1988; • S. Chapra, R. Canale, Numerical methods for Engineers, McGraw-Hill 2009 (edizione più recente); • R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press 2002. TEACHERS AND EXAM BOARD PATRIZIA BAGNERINI Ricevimento: The teacher will remain in computer room an hour later at the end of the lesson to provide students with explanations on the exercises or theoretical part. Students may also take appointment at other times via email to bagnerini@dime.unige.it. There are also modes for remote explanations via Skype. Exam Board PATRIZIA BAGNERINI (President) ROBERTO CIANCI (President) LESSONS LESSONS START Second semester. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The examination mode consists of an oral test to ensure learning of the course content. ASSESSMENT METHODS The oral exam focuses on the learning of one or two subjects from those discussed in class. Exam schedule Data appello Orario Luogo Degree type Note 06/06/2017 14:30 GENOVA Orale FURTHER INFORMATION See the aulaweb page for more information and details.