CODE 57048 ACADEMIC YEAR 2016/2017 CREDITS 8 cfu anno 2 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - 12 cfu anno 2 FISICA 8758 (L-30) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italiano TEACHING LOCATION SEMESTER Annual PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: PHYSICS 8758 (coorte 2015/2016) MATHEMATICAL ANALYSIS 1 52474 2015 Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: PHYSICS 8758 (coorte 2015/2016) MATHEMATICAL METHODS IN PHYSICS 1 61734 OVERVIEW The basic topics in calculus of severable variables are covered. The course is split in two semesters. Physics and SMID students need to take the first part devoted to differential calculus, integration theory in two variables. The second semester is mandatory only for Physics students covering integration along curves and surfaces, Gauss and Stokes' theorems and their consequences, and an introduction to systems of differential equations and Fourier series. AIMS AND CONTENT LEARNING OUTCOMES The students will become acquinted with the most important topics regarding functions of several variables and how they are used in practice. The only proof that are presented are those wich illustrate fundamental principles and are free of technicality. Applications to Physics and Probability are emphasised. TEACHING METHODS Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester is 12 weeks with four hours of theory and two hours of exercices each week. The second semester is 12 weeks with three hours of theory and two hours of exercices each week. SYLLABUS/CONTENT This course covers differential, integral and vector calculus for functions of more than one variable. Topics include: Sequences and series of functions. Functions of several variables, continuity, differentiability, derivative. Parametrized curves, arc length, curvature, torsion. Vector fields, gradient, curl, divergence. Multiple integrals, change of variables, line integrals, surface integrals. Stokes' theorem in one, two, and three dimensions. RECOMMENDED READING/BIBLIOGRAPHY Serge Lang - Calculus of Several Variables, Third Edition, Undergraduate Texts in Mathematics, Springer, 1987. TEACHERS AND EXAM BOARD ERNESTO DE VITO ADA ARUFFO Ricevimento: At the end of lectures or by appointment. GIANCARLO MAUCERI Exam Board ERNESTO DE VITO (President) ADA ARUFFO FILIPPO DE MARI CASARETO DAL VERME GIANCARLO MAUCERI LESSONS LESSONS START The class will start according to the accademic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral exam ASSESSMENT METHODS The written examination consists in four/five exercises. The oral exam is optional. If a student does not give it the final mark is the grade of the written exam if less or equal than 24 the final mark is 24 if the grade of the written exam if greater than 24 Exam schedule Data appello Orario Luogo Degree type Note 13/06/2017 09:00 GENOVA Scritto 23/06/2017 09:00 GENOVA Orale 13/07/2017 09:00 GENOVA Scritto 17/07/2017 09:00 GENOVA Orale 11/09/2017 09:00 GENOVA Scritto FURTHER INFORMATION For any further informations, please send a message to devito@dima.unige.it