# GEOMETRY

6 credits during the 1st year of 10375 CHEMICAL AND PROCESSES ENGINEERING (L-9) GENOVA

**Electrical Engineering 8716 (coorte 2018/2019)**- POWER GENERATION 60221
- MATHEMATICAL PHYSICS 1 60352
- APPLIED PHYSICS 60359
- MATHEMATICAL ANALYSIS II 60241
- MECHANICS OF MACHINES 86899
- ELECTRIC AND MAGNETIC FIELDS 60335
- CIRCUIT THEORY 60336
- STRUCTURAL MECHANICS 66283
- ELECTRONICS FOR ELECTRICAL ENGINEERING 84372

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.

RECOMMENDED READING/BIBLIOGRAPHY

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

**Ricevimento:** Besides the hours of exercises in the afternoon, every student can fix an appointment.

Exam Board

ETTORE GIOVANNI CARLETTI (President)

ANNA ONETO (President)

MARIA VIRGINIA CATALISANO

## LESSONS

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.

LESSONS START

17 september 2018

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## 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.