Study-unit GEOMETRY
| Course name | Building engineering and architecture |
|---|---|
| Study-unit Code | GP004889 |
| Curriculum | Comune a tutti i curricula |
| Lecturer | Marco Buratti |
| Lecturers |
|
| Hours |
|
| CFU | 6 |
| Course Regulation | Coorte 2019 |
| Supplied | 2019/20 |
| Supplied other course regulation | |
| Learning activities | Base |
| Area | Discipline matematiche per l'architettura |
| Sector | MAT/03 |
| Type of study-unit | Obbligatorio (Required) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Linear algebra. Elementary analytic geometry. |
| Reference texts | A. Basile, Algebra lineare e geometria cartesiana. Margiacchi-Galeno Editrice, 2010. |
| Educational objectives | Acquisizione del pensiero geometrico anche attraverso gli strumenti dell'algebra lineare. |
| Prerequisites | Scomposizioni di polinomi. Risoluzione di equazioni algebriche di primo e secondo grado. Equazioni binomie e trinomie. Equazioni algebriche risolubili con l'uso della regola di Ruffini. Geometria analitica elementare nel piano. Trigonometria. |
| Teaching methods | Lezioni frontali accompagnate da esercizi. Sarà sempre richiesta la partecipazione attiva degli studenti. |
| Other information | Attendance is not mandatory but highly recommended! |
| Learning verification modality | Two hours of class-work with 8 exercises: 4 exercises about linear algebra; 2 exercises about elementary analytic geometry in the space; 2 exercises about the sphere and/or the circle in the space. Then fifteen/thirty minutes of oral examination. |
| Extended program | Linear Algebra. Vector spaces. Linear independence. Steinitz Lemma. Bases. Theorem on the equicardinality of the bases. Dimension. Every independent set is contained in a suitable base. Subspaces. Intersection and sum of subspaces. Grassmann Theorem. Linear applications. Kernel and Image. Fundamental Theorem on the isomorphism between vector spaces. The vector sapce of real matrices of type m x n. Product between matrices. Matrix associated with a linear application. Determinant. Inverse matrix. Rank of a matrix. Linear systems. Rouché-Capelli Theorem. Homogeneus linear systems. The space of all solution of a homogeneous linear system. Cramer Theorem. General algorithm for determining the set of all solutions of a linear system. Geometry in the plane and in the space. Cartesian coordinates. Oriented segments. Geometric vectors. Parallel and coplanar vectors. Components of a vector. Parametric equations of a line. Equation of a plane. Intersection and parallelism between planes. Cartesian equations of a line. Sheaf of planes. Intersection and parallelism between a line and a plane. Intersection and parallelism between lines. Coplanar lines. Inner product. Distance between two points. Angle between two lines. Distance between a point and a plane. Angle between two planes. Angle between a line and a plane. Distance between a point and a line. Distance between two lines. Sphere. Circle in the space. |