CODE 86966 ACADEMIC YEAR 2022/2023 CREDITS 9 cfu anno 2 INGEGNERIA NAVALE 8722 (L-9) - 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: Naval Architecture and Marine Engineering 8722 (coorte 2021/2022) GEOMETRY 56721 2021 MATHEMATICAL ANALYSIS I 72290 2021 Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: Naval Architecture and Marine Engineering 8722 (coorte 2021/2022) AUTOMATIC CONTROL FOR NAVAL ENGINEERING 66048 TEACHING MATERIALS AULAWEB OVERVIEW The course is aimed at second year students who have acquired the fundamental knowledge related to the functions of one and two variables, to plane analytical geometry and linear algebra. AIMS AND CONTENT LEARNING OUTCOMES The course aims to provide the basics on Integration of functions of multiple variables, Integration on curves and surfaces, Vector fields. Provide algebraic calculation tools and knowledge of 3D analytical geometry AIMS AND LEARNING OUTCOMES ANALYSIS at the end of this activity and after clearing the corresponding exam, the student will be able to - compute integrals of vector fields along curves in space - compute multiple and surface integrals - compute solutions of linear differential equations of the second order GEOMETRY The course aims at providing the necessary theoretical and operative knowledge for the understanding and solving of the problems in the following topics: change of coordinates in the 3-dimensional space, symmetric matrices and their signature, conics and quadrics, curves and surfaces from a differential point of view. At the end of the course the student will be able to recall and present the theoretical notions she will have faced during the lectures. Moreover, by applying the algorithms and the solving technique introducted in the course and justifying every step, she will be able to: - write down and analyse a change of coordinates in the 3-dimensional space given by a rotation and a translation; - evaluate the signature and the positive/negative definition of a symmetric matrix; - identify and study an assigned conic or quadric; - study and characterise the geometry of a parametric curve or surface. ANALYSIS The student will have to know the tools for the calculation of double, triple, curvilinear and surface integrals and the fundamental properties of vector fields in view of the applications. PREREQUISITES Differential calculus for functions of one and two variables. Integration of the functions of one variable. Plane analytic geometry, linear algebra. TEACHING METHODS Lectures and exercise sessions SYLLABUS/CONTENT ANALYSIS double integrals surface integrals integral along curves gauss' and stokes' theorems potential theory differential equations of the second order with constant coefficients GEOMETRY The following topics will be dealt with from both a theorical and operative point of view, withouth a clear subdivision between lectures and exercise sessions. Elements of linear algebra. Change of coordinates, rotations and translations in the 3-dimensional space. Quadratic forms and symmetric matrices. Classification of conics and quadrics. Differential geometry of parametric curves. Differential geometry of parametric surfaces. RECOMMENDED READING/BIBLIOGRAPHY ANALYSIS T. Apostol, vol 3: analisi 2 GEOMETRY Main references: - A.Bernardi, A.Gimigliano, Algebra Lineare e Geometria Analitica, Città Studi Edizioni. - M.V. Catalisano, A. Perelli, Appunti di geometria e calcolo numerico, Lectures notes available on the aulaweb page of the course - M.E. Rossi, Algebra lineare, Lectures notes available on the aulaweb page of the course Further readings: - Silvio Greco, Paolo Valabrega – GEOMETRIA ANALITICA – Levrotto e Bella - Silvana Abeasis - ALGEBRA LINEARE E GEOMETRIA - ZANICHELLI - Marco Abate, Algebra Lineare , ed. McGraw-Hill - E. Sernesi, Geometria vol 1, ed Bollati-Boringhieri TEACHERS AND EXAM BOARD FABIO TANTURRI MICHELE PIANA Ricevimento: Office hours by appointment via email Anna Maria MASSONE Ricevimento: By appointment, to be agreed via email (massone@dima.unige.it) Exam Board Anna Maria MASSONE (President) ALESSIO CAMINATA VICTOR LOZOVANU ELEONORA ANNA ROMANO FRANCESCO VENEZIANO MICHELE PIANA (President Substitute) FABIO TANTURRI (President Substitute) LESSONS LESSONS START TBA Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION ANALYSIS: Written exam followed by an oral exam GEOMETRY: Written exam followed by an oral exam Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools ASSESSMENT METHODS The written part will consist in the resolution of exercises on the topics of the teaching programme (see also the Aims and Learning Outcomes section). Through the resolution of the exercises the student will be evaluted in: - her skills in identifying the theoretical and practical results which are necessary to approach and solve the problems, and general knowledge of the very same results; - her skills in applying the suitable algorithms and procedures to solve the exercises; - her skills in providing the right arguments and justifications for the involved steps she follows. During the oral part the teacher will evaluated the student's knowledge which has not been positively emerged during the written part. At the same time, the teacher will evaluate her knowledge on the topics which have not been covered by the written part. Exam schedule Data appello Orario Luogo Degree type Note 17/01/2023 10:00 GENOVA scritto di geometria 23/01/2023 09:00 GENOVA Scritto + Orale 23/01/2023 09:00 GENOVA Compitino 24/01/2023 10:00 GENOVA orale di geometria 03/02/2023 09:00 GENOVA Scritto 07/02/2023 10:00 GENOVA Orale 17/02/2023 09:00 GENOVA Compitino 17/02/2023 09:00 GENOVA Scritto + Orale 30/05/2023 10:00 GENOVA Scritto 05/06/2023 09:00 GENOVA Orale 14/06/2023 09:00 GENOVA Esame scritto prof. Piana- Massone 22/06/2023 10:00 GENOVA Scritto 29/06/2023 09:00 GENOVA Orale 12/07/2023 09:00 GENOVA Esame scritto prof. Piana- Massone 29/08/2023 09:00 GENOVA Scritto 31/08/2023 10:00 GENOVA Orale 13/09/2023 09:00 GENOVA Esame scritto prof. Piana- Massone 13/09/2023 09:00 GENOVA Scritto + Orale