CODE 60241 ACADEMIC YEAR 2018/2019 CREDITS 6 cfu anno 2 INGEGNERIA CHIMICA E DI PROCESSO 10375 (L-9) - GENOVA 6 cfu anno 2 INGEGNERIA ELETTRICA 8716 (L-9) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: Chemical Engineering 8714 (coorte 2017/2018) MATHEMATICAL ANALYSIS I 56594 2017 Electrical Engineering 8716 (coorte 2017/2018) MATHEMATICAL ANALYSIS I 56594 2017 GEOMETRY 56716 2017 FUNDAMENTAL OF PHYSICS 72360 2017 TEACHING MATERIALS AULAWEB OVERVIEW The course is aimed at sophomore students and needs basic skills in Calculus, Linear Algebra and Geometry. AIMS AND CONTENT LEARNING OUTCOMES The course provides basic notions about multiple integrals, line integrals, surface integrals and vector fields. It provides also basic skills about holomorphoic functions, Laplace transforms together with some appplications to ODE's. AIMS AND LEARNING OUTCOMES At the end of the course students will be required to -calculate double or triple integrals by using reduction formulae or by changing variables. In particular students will be required to calculate the area, the volume, the coordinates of the center of mass or the components of the tensor of inertia. -calculate line and surface integrals by using the Divergence Theorem and the Gauss-Green formula. -calculate the potentials of conservative vector fields; -calculate the integral of functions of a complex variable by using the Residue theorem -solve ODE's by using Laplace transform. PREREQUISITES Basic Calculus, Linear algebra and Geometry. TEACHING METHODS Frontal lessons. Examination mode: written and oral examination. SYLLABUS/CONTENT Riemann integral in R^n. Fubini' s theorem in 2D and 3D: applications. Change of variables. Curves in R^n: lenght of a curve, line integrals. Parametric surfaces in R^3, area, surface integrals. Divergence Theorem. Vector fields: irrotational vector fields and conservative vector fields. Gauss- Green formula and Stokes Theorem. Functions of a complex variable, holomorphic functions, Laplace transform. Applications RECOMMENDED READING/BIBLIOGRAPHY Analisi Matematica M. Bertsch, R. Dal Passo, L. Giacomelli Mc Graw Hill TEACHERS AND EXAM BOARD DANILO PERCIVALE ANNA ONETO Ricevimento: Besides the hours of exercises in the afternoon, every student can fix an appointment. LESSONS Class schedule MATHEMATICAL ANALYSIS II EXAMS Exam schedule Data appello Orario Luogo Degree type Note 09/01/2019 14:30 GENOVA Scritto 09/01/2019 14:30 GENOVA Scritto 29/01/2019 14:30 GENOVA Scritto 14/02/2019 14:30 GENOVA Scritto 14/02/2019 14:30 GENOVA Scritto 14/02/2019 14:30 GENOVA Scritto 18/06/2019 09:30 GENOVA Scritto 04/07/2019 09:30 GENOVA Scritto + Orale 19/09/2019 09:00 GENOVA Scritto