GEOMETRY AND ALGEBRA
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
BIOENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (27/09/2021 - 21/01/2022)
ECTS
6
Lesson hours
60 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
STOPPINO LIDIA (titolare) - 6 ECTS
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. Vector spaces, subspaces, bases and dimension.
2. Matrices, invertibility, determinant and rank.
3. Linear systems and their resolubility.
45. Linear maps and matrices. Matrices of a change of basis.
5. Diagonalization. Eigenvectors and eigenspaces.
6. Metric structure in vector spaces. Real Spectral theorem.
7. Quadratic forms and their applications.
Teaching methods
Traditional lessons and exercise sessions at the blackboard. There will be further exercise sessions (tutorati).