Salta al contenuto principale della pagina

## GEOMETRY

CODE 56716 2022/2023 6 cfu during the 1st year of 10375 INGEGNERIA CHIMICA E DI PROCESSO (L-9) - GENOVA 6 cfu during the 1st year of 8716 INGEGNERIA ELETTRICA (L-9) - GENOVA 6 cfu during the 1st year of 8715 INGEGNERIA CIVILE E AMBIENTALE (L-7) - GENOVA MAT/03 Italian GENOVA 1° Semester Prerequisites (for future units) This unit is a prerequisite for: Civil and Environmental Engineering 8715 (coorte 2022/2023) MATHEMATICAL ANALYSIS II 60243 STRUCTURAL MECHANICS II 66285 GEOMATHICS 84520 MATHEMATICAL PHYSICS 60354 Electrical Engineering 8716 (coorte 2022/2023) APPLIED PHYSICS 60359 ELECTRONICS FOR ELECTRICAL ENGINEERING 84372 SOLID AND MACHINE MECHANICS 80338 ELECTRIC AND MAGNETIC FIELDS 60335 CIRCUIT THEORY 60336 STRUCTURAL MECHANICS 66283 MECHANICS OF MACHINES 86899 FOUNDATIONS OF ELECTRICAL ENGINEERING 60334 POWER GENERATION 60221 MATHEMATICAL ANALYSIS II 60243 MATHEMATICAL PHYSICS 1 60352 AULAWEB

## OVERVIEW

The course aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry

## AIMS AND CONTENT

### LEARNING OUTCOMES

The student must learn the concept of number of solutions of a mathematical problem, must know how to work with complex numbers vectors and matrices, including their diagonalization, must be able to solve equations and linear systems, must know how to make a change of coordinates in the plane and in space, as well as knowing how to solve simple problems concerning lines, planes, spheres, circles and conic sections

### AIMS AND LEARNING OUTCOMES

Complex numbers and representation in the Gauss plane: powers and solution of particular equations.

Real / complex coefficient polynomials: factor breakdown, fundamental theorem of Algebra and Ruffini's theorem.

Geometric vectors: equivalence, module, versorem operations and properties. Scalar and vottorial product and property. Mixed product of carriers.

Linear systems: elementary operations on equations and Gauss theorem-algorithm

Matrices: various definitions, operations and properties. Reverse matrix. Definition of characteristic and Rouchè Capelli Theorem with method for determining the solutions of a linear system. Determinant definitions e

Finitely generated vector spaces: basic definitions of size and relative theorems, subspaces.

Definition of linear application.

Changes of coordinates in the plane and in space, formulas of rotations and translations. Orthogonal matrices.

Matrix diagonalization: definition of eigenvalue, eigenvector and relative theorems. Spectral theorem for symmetric matrices.

Lines in the plane and lines and planes in space: parametric and Cartesian equations. Various formulas of analytic geometry.

Spheres and circumferences in space.

Quadratic forms and Conic sectionss: associated matrices and defining character.

Conic sections classification:   parabolic, elliptic and hyperbolic type (canonical equations and theorems on canonical form reduction.

### PREREQUISITES

Algebra: factor decomposition: binomial and trinomial square, equation and inequalities of first, second degree and fractional.

Trigonometry: definitions of the sine, cosine, tangent, their graphical representations and main formulas.

Euclidean geometry: similitudes and equality of triangles, theorems of Pythagoras and Euclid, circles.

### TEACHING METHODS

The course (four-months) consists of 3 hours of theory + 2 hours of exercises a week for 12 weeks.

There are also two optional afternoon hours of guided exercises in the presence of tutors and lecturers.

Notes and exercises can be found on the website AulaWeb of the web classroom

Suggested book:

Odetti-Raimondo Elementi di Algebra lineare e geometria analitica   (ECIG)

## TEACHERS AND EXAM BOARD

### Exam Board

MARIA EVELINA ROSSI (President)

EMANUELA DE NEGRI

ARVID PEREGO (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/8716/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

The exam consists of a written test and an oral test.

### ASSESSMENT METHODS

Knowledge of the statements and demonstrations of the most important theorems is required, as well as the ability to use these tools in a critical way, also for the resolution of new problems for the student.

### Exam schedule

Date Time Location Type Notes
18/01/2023 09:00 GENOVA Scritto
17/02/2023 09:00 GENOVA Orale
07/06/2023 09:00 GENOVA Scritto
17/07/2023 09:00 GENOVA Scritto
04/09/2023 09:00 GENOVA Scritto