CODE 60235 ACADEMIC YEAR 2017/2018 CREDITS 6 cfu anno 2 INGEGNERIA MECCANICA 8720 (L-9) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION SEMESTER 1° Semester MODULES Questo insegnamento è un modulo di: MATHEMATICAL ANALYSIS 2 AND MATHEMATICAL PHYSICS AIMS AND CONTENT LEARNING OUTCOMES In the Analysis module we provide the tools for the comprehension and computation of double and triple integrals, of curvilinear integrals of scalar and vector functions, and we introduce the related theorems (divergence, Gauss-Green). We show how to deal with linear systems of differential equations (considering in particular the case of constant coefficients). AIMS AND LEARNING OUTCOMES The first goal is the understanding of integral calculus for functions of two or three real variables: double and triple integrals, line and surface integrals of scalar fields. We will discuss the divergence theorem in two and three dimensions. The second objective is a general understanding of systems of ordinary differential equations (with particular emphasis on linear systems in low dimension). We will discuss the convergence properties of sequences and series of functions, in particular of power series expansions. TEACHING METHODS Lectures and practice SYLLABUS/CONTENT Integration theory for functions of several variables. Double and triple integrals, changes of variables in multiple integrals. Polar, cylindrical, spherical coordinates. Parametric curves. Line integrals of scalar functions, length of a curve. Vector fields, line integrals of differential forms, closed and exact forms, potentials. Divergence theorem and Gauss Green formulas in the plane. Parametric surfaces in space, area of a surface, surface integrals. Flow of a field through a surface. Divergence theorem in space. Systems of ordinary differential equations. Existence and uniqueness for the Cauchy problem. Linear systems, fundamental matrix. Solution of systems with constant coefficients. Stability and asymptotic behavior. Sequences and series of functions. Pointwise and uniform convergence of sequences and series of functions. Power series. RECOMMENDED READING/BIBLIOGRAPHY C. Canuto e A. Tabacco, Analisi Matematica II, Springer-Verlag, 2008. TEACHERS AND EXAM BOARD EDOARDO MAININI MANUEL MONTEVERDE Exam Board FRANCO BAMPI (President) EDOARDO MAININI (President) ANDREA BRUNO CARBONARO ROBERTO CIANCI MANUEL MONTEVERDE LESSONS Class schedule MATHEMATICAL ANALYSIS 2 EXAMS Exam schedule Data appello Orario Luogo Degree type Note 25/01/2018 09:00 GENOVA Scritto 15/02/2018 09:00 GENOVA Scritto 05/06/2018 09:00 GENOVA Scritto 19/07/2018 09:00 GENOVA Scritto 10/09/2018 09:00 GENOVA Scritto
