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 Prerequisites
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.
Teaching Methods
Traditional lessons and exercise sessions at the blackboard. There will be further exercise sessions (tutorati).
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.
Texts
Fulvio Bisi, Francesco Bonsante, Sonia Brivio: Lezioni di Algebra Lineare con Applicazioni alla Geometria Analitica.
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.
