CODE 101118 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 1 MARITIME SCIENCE AND TECHNOLOGY 10948 (L-28) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/03 LANGUAGE English TEACHING LOCATION GENOVA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW The teaching unit aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry AIMS AND CONTENT LEARNING OUTCOMES The teaching unit aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry. AIMS AND LEARNING OUTCOMES The student must know how to work with complex numbers, vectors and matrices, including their diagonalization, must be able to solve linear systems and to find their number of solutions depending on a real parameter, must know how to work with vector spaces, vector subspaces and linear maps, as well as knowing how to solve simple problems concerning lines, planes and spheres in the space. PREREQUISITES Algebra: factor decomposition, equations and inequalities (first, second degree and fractional); Trigonometry: definitions of sine, cosine, tangent, their graphical representations and main formulas; Euclidean geometry: basic concepts related to lines and circles, and their graphical representations. TEACHING METHODS The teaching unit has a duration of 12 weeks (4 months in total) and consists of 5 hours a week (dedicated to theory and exercises). Working students and students with certified SLD (Specific Learning Disorders), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination arrangements so to take into account individual learning patterns, while respecting the teaching objectives. SYLLABUS/CONTENT Complex Numbers and operations; algebraic, goniometric ed exponential form; representation in the Gauss plane: solution of particular equations. Geometric vectors and operations. Matrices: definitions, operations and properties; determinant of a square matrix; invertible matrices and inverse matrix; rank of a matrix; diagonalization. Linear Systems; Rouché-Capelli’s theorem. Vector Spaces and Subvector spaces: basis, dimension, sum, intersection; definitions and theorems. Linear maps; properties and theorems. Lines and planes in the space: relative positions, parallelism and orthogonality conditions, distances, orthogonal projections and symmetries, lines and planes satisfying some given conditions. Spheres in the space RECOMMENDED READING/BIBLIOGRAPHY Notes and exercises can be found on the website AulaWeb. Suggested books: E. Sernesi, Geometria vol. 1, Bollati-Boringhieri; V. Bertella-A. Damiano, Esercizi su spazi vettoriali e applicazioni lineari, con svolgimento e commenti, Esculapio D. Gallarati, Appunti di Geometria, Di Stefano Editore-Genova; F. Odetti - M. Raimondo, Elementi di Algebra Lineare e Geometria Analitica, ECIG Universitas; M. Abate, Algebra Lineare, McGraw-Hill. TEACHERS AND EXAM BOARD VALENTINA BERTELLA Ricevimento: Write me an e-mail valentina.bertella@gmail.com Exam Board VALENTINA BERTELLA (President) LAURA BAZZOTTI (President Substitute) MASSIMO FIGARI (President Substitute) LESSONS LESSONS START https://corsi.unige.it/10948/p/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The knowledge acquired by the student will be evaluated with a written exam (during 2 hours) and an oral exam. ASSESSMENT METHODS The written exam must be sustained without consulting any documentation and without using any calculator and will consists in solving some exercices. The oral examination, to which the candidate is admitted only if the written test was successful, builds on the results of the written test. Moreover, the knowledge of definitions, propositions and theorems, is required. Exam schedule Data appello Orario Luogo Degree type Note 10/01/2025 11:00 GENOVA Scritto 17/01/2025 15:00 GENOVA Orale 07/02/2025 11:00 GENOVA Scritto 03/06/2025 11:00 GENOVA Scritto 03/06/2025 15:00 GENOVA Orale 26/06/2025 11:00 GENOVA Scritto 26/06/2025 15:00 GENOVA Orale 05/09/2025 11:00 GENOVA Scritto + Orale 11/09/2025 11:00 GENOVA Scritto 11/09/2025 14:00 GENOVA Orale Agenda 2030 - Sustainable Development Goals Quality education Gender equality