Elementary geometry in the plane and in the space.
Course Content - Last names A-D
Linear algebra and solutions of linear systems. Linear geometry in euclidean 3d-space. Vectors in 3d-space and operations between them. Eigenvectors and eigenvalues. Diagonal form of endomorphisms.
Course Content - Last names O-Z
Vector spaces; linear systems of equations; affine geometry; inner products and Hermitian products; eigenvectors; conics.
- C. Petronio, "Geometria e Algebra Lineare," Esculapio.
- G. Anichini, G. Conti, "Geometria analitica e algebra lineare", Ed. Pearson.
- G. Anichini, G. Conti, R. Paoletti, "Algebra lineare e geometria analitica - Eserciziario", Ed. Pearson.
- M. Abate, C. De Fabritiis, "
Geometria analitica con elementi di algebra lineare", McGraw-Hill.
Learning Objectives
Basic notions about analytic geometry (geometric interpretation of equations) and linear algebre (linear sistems, linearity, eigenvectors).
Learning Objectives - Last names A-D
Basic notions about analytic geometry (geometric interpretation of equations) and linear algebre (linear sistems, linearity, eigenvectors).
Prerequisites
Elementary geometry in the plane and n the space. Algebraic calculus.
Prerequisites - Last names A-D
Elementary geometry in the plane and n the space. Algebraic calculus.
Teaching Methods
Class teaching (lessons and exercises) according to the given timetable.
Teaching Methods - Last names A-D
Class teaching (lessons and exercises) according to the given timetable.
Further information
See the personal web page.
Further information - Last names A-D
See the personal web page.
Type of Assessment
Written test and eventually oral examination.
Type of Assessment - Last names A-D
Written test. A couple of written tests during the course (to be confirmed).
Type of Assessment - Last names O-Z
Written exam. Intermediate exams.
Course program
Free and applied vectors. Sum, multiplication with numbers and related
properties. Linear dependence, parallelism and complanarity. Generated
subspaces and bases. Scalar, wedge and mixed products. Ortogonal
projections.
The vector spaces R^2, R^3, R^n.
Matrices: elementary operations and their properties. Vector space of
matrices.
Special matrices. Determinant and invertible matrices.
Linear systems: generality, structure of the space of solutions. Gauss
elimination method.
Analytic geometry on the plane and in the space: straight lines and planes;
parallelism and orthogonality conditions; relative positions. Distances.
Linear applications: definition, kernel and image; associated matrix.
Eigenvalues and eigenvectors. Diagonalization of linear applications.
Conics and quadrics.
Course program - Last names A-D
Free and applied vectors. Sum, multiplication with numbers and related
properties. Linear dependence, parallelism and complanarity. Generated
subspaces and bases. Scalar, wedge and mixed products. Ortogonal
projections.
The vector spaces R^2, R^3, R^n.
Matrices: elementary operations and their properties. Vector space of
matrices.
Special matrices. Determinant and invertible matrices.
Linear systems: generality, structure of the space of solutions. Gauss
elimination method.
Analytic geometry on the plane and in the space: straight lines and planes;
parallelism and orthogonality conditions; relative positions. Distances.
Linear applications: definition, kernel and image; associated matrix.
Eigenvalues and eigenvectors. Diagonalization of linear applications.