CODE 57048 ACADEMIC YEAR 2019/2020 CREDITS 12 cfu anno 2 FISICA 8758 (L-30) - GENOVA 8 cfu anno 2 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER Annual PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: PHYSICS 8758 (coorte 2018/2019) MATHEMATICAL ANALYSIS 1 52474 2018 Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: PHYSICS 8758 (coorte 2018/2019) MATHEMATICAL METHODS IN PHYSICS 1 61734 TEACHING MATERIALS AULAWEB OVERVIEW Basic topics in calculus of severable variables are treated. The course is split into two semesters. The first part is devoted to differential calculus, integration theory in two (or several) variables and function series. The second part deals with integration along curves and surfaces, Gauss and Stokes' theorems and their consequences, and an introduction to systems of differential equations. SMID students need to take only part I (first semester - 8 credits). Both semesters are mandatory for Physics students. AIMS AND CONTENT LEARNING OUTCOMES Students will become acquinted with the most important topics regarding functions of several variables and how they are used in practice. We only present proofs that illustrate fundamental principles and are free of technicalities. Applications to Physics and Probability are emphasised. AIMS AND LEARNING OUTCOMES Students will be able to manipulate functions of several variables and solve basic optimization problems. Moreover they will be at their ease with mean and conditional expectation. PREREQUISITES First year calculus (derivatives and integrals for functions of a single variable). Vector spaces, eigevalues and eigenvectors are frequently used. TEACHING METHODS Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester consists of 12 weeks with four hours of theory and two hours of exercises per week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises per week. SYLLABUS/CONTENT This course covers differential, integral and vector calculus for functions of several variables. Topics include: Sequences and series (numerical, function series, power series,...) Functions of several variables: continuity, partial derivatives, differentiability, local maxima and minima, implicit functions, optimization. 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. Solutions to systems of constant coefficient linear ordinary differential equations RECOMMENDED READING/BIBLIOGRAPHY Serge Lang - Calculus of Several Variables, Third Edition, Undergraduate Texts in Mathematics, Springer, 1987. TEACHERS AND EXAM BOARD FRANCESCA ASTENGO Ricevimento: At the end of lectures or by appointment. MARCO BENINI Exam Board FRANCESCA ASTENGO (President) ADA ARUFFO MARCO BENINI LESSONS LESSONS START Classes 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 solving four/five exercises covering the topics of the course. It is approved with grade at least 15/30. If your written exam is approved with grade at least 18/30, then the oral exam is optional. In case you do not want to take the oral part the final mark is the grade of the written exam if less than or equal to 24 the final mark is 24 if the grade of the written exam is greater than 24 If you take also the oral part, the final mark is a weighted average of the written and oral tests. Exam schedule Data appello Orario Luogo Degree type Note 16/01/2020 09:00 GENOVA Scritto 16/01/2020 09:00 GENOVA Scritto 16/01/2020 09:00 GENOVA Compitino 07/02/2020 09:00 GENOVA Scritto 10/02/2020 09:00 GENOVA Scritto 10/02/2020 09:00 GENOVA Compitino 17/06/2020 09:00 GENOVA Scritto 17/06/2020 09:00 GENOVA Scritto 06/07/2020 09:00 GENOVA Scritto 06/07/2020 09:00 GENOVA Scritto 17/09/2020 09:00 GENOVA Scritto 17/09/2020 09:00 GENOVA Scritto FURTHER INFORMATION For further information, please send a message to astengo@dima.unige.it