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## GEOMETRY

CODE 105937 2022/2023 12 cfu during the 1st year of 11431 DESIGN DEL PRODOTTO NAUTICO (L-4) - LA SPEZIA MAT/03 Italian LA SPEZIA 1° Semester This unit is a module of: AULAWEB

## OVERVIEW

The course provides an introduction to linear algebra and analytic geometry, with particular focus on matrix computations, on vector spaces and on solving linear systems and analitical geometry problems in 2 and 3 dimensions

## AIMS AND CONTENT

### AIMS AND LEARNING OUTCOMES

The course  will give to the students basic tools of linear algebra and analytic geometry. A goal of the course is to train the student to follow logical deductive arguments, and to use the proper formal language. The student will learn to solve some linear algebra problems, that generally occur as intermediate steps in the solution of more complex mathematical models for engineering problems

### PREREQUISITES

Elementary knowledge of arithmetic, algebra, trigonometry, set theory.

### TEACHING METHODS

Frontal Lectures (52 hours)

### SYLLABUS/CONTENT

Sets and maps. Complex numbers and polynomials. Linear systems and gaussian elimination. Matrices, determinants, rank. Vector spaces. Vectors in geometry. Subspaces, bases, dimension. Linear maps. Matrices related to a linear map. Eigenvalues, eigenvectors. The diagonal form of a matrix. Quadratic forms. Systems of cartesian coordinates, linear changes of coordinates. Points, lines and planes: cartesian and parametric equations, parallelism, angles, distances, orthogonal projections. Conics.

• Lecture notes (Perelli-Catalisano) (see http://www.diptem.unige.it/catalisano/ )
• E.Carlini, M.V.Catalisano, F.Odetti, A.Oneto, M.E.Serpico, GEOMETRIA PER INGEGNERIA - Una raccolta di temi d'esame risolti, ProgettoLeonardo - Editore Esculapio (Bologna), 2011.
• S.Greco, P.Valabrega, Algebra lineare, Levrotto & Bella, 2009.
• S.Greco, P.Valabrega, Geometria analitica, Levrotto & Bella, 2009.
• Odetti-Raimondo – Elementi di algebra lineare e geometria analitica – ECIG, 2002.

Web site:

http://www.diptem.unige.it/catalisano/default.htm

## LESSONS

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

 The examination consists of a written part and an oral discussion. The written part is made up  of 10 questions that cover all the material of the course. The use of notes, books, or electronic devices  is forbidden.

### ASSESSMENT METHODS

The questions of the written part will verify both the operational skills through problem solving and the learning of the theory, such as definitions and theorems. During the oral test there will be a discussion about the written part and two to three additional questions.

### Exam schedule

Date Time Location Type Notes