Enrollment year
2019/2020
Academic discipline
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Curriculum
PERCORSO COMUNE
Period
1st semester (30/09/2019 - 20/01/2020)
Lesson hours
60 lesson hours
Activity type
WRITTEN AND ORAL TEST
Prerequisites
The contents of the "Precorso di Matematica":
1. elements of algebraic and polynomial calculus. Polynomials: sum product, divisibility, factorization. Algebraic equations of first and second degree- Ruffini's Theorem.
2. Foundations of plane analytic geometry. Coordinates in the plane. Analytic representation of lines, circles, parabolas, ellipsis, hyperboles.
3. Concept of function and its graph. Elementary examples, exponential and logarithmic functions.
4. Elements of trigonometry. Sin, cosin, tan functions. Goniometric equations.
5. inequalities between functions of one variable.
Learning outcomes
The aim of the course is to give to the students the basic notions and techniques of linear algebra and analytic geometry. The scope of the course is for the students to understand the concepts of vector space, vector subspace, basisi and dimension, matrices, determinants, rank, linear systems and their resolubility, linear maps, diagonalization, scalar product, quadratic forms and their signature. From the practical pont of view, the sudent has gain the skills that enables him to solve simple exercises on the above described concepts.
Course contents
0. (some prerequisites)
1. Applied vectors in the 3-dimensional euclidean space, and its geometry.
2. Vector spaces, subspaces, bases and dimension.
3. Matrices, invertibility, determinant and rank.
4. Linear systems and their resolubility.
5. Linear maps and matrices. Matrices of a change of basis.
6. Diagonalization. Eigenvectors and eigenspaces.
7. Metric structure in vector spaces. Real Spectral theorem.
8. Quadratic forms and their applications.
Teaching methods
Traditional lessons and exercise sessions at the blackboard. There will be further exercise sessions (tutorati).
Reccomended or required readings
Fulvio Bisi, Francesco Bonsante, Sonia Brivio: Lezioni di Algebra Lineare con Applicazioni alla Geometria Analitica.
Edizioni La Dotta - Casalecchio di Reno (BO)
Assessment methods
The exam is composed of a written part (which itself has a first more theoretical part and a second computational one) and an oral part which is mandatory if the student has a written grade between 15 and 17, and in other cases at the discretion of the teacher.
Further information
More informations at the webpage
www.stoppino.it
Sustainable development goals - Agenda 2030
Università di Pavia - Offerta formativa