Study-unit GEOMETRY
| Course name | Building engineering and architecture |
|---|---|
| Study-unit Code | GP004889 |
| Curriculum | Comune a tutti i curricula |
| Lecturer | Daniele Bartoli |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2023/24 |
| 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 | Notes. |
| Educational objectives | Acquisition of the geometrical thought through algebraic tools. |
| Prerequisites | Polynomial factorizations. Solutions of the algebraic equations of the first and second degree. Binomial and trinomial equations. Equations solvable by applying Ruffini's rule. Elementary analytic geometry in the plane. Trigonometry. |
| Teaching methods | Frontal lectures. |
| Other information | Attendance is not mandatory but highly recommended. |
| Learning verification modality | The test consists of three parts -TEST concerning definitions and statements - WRITTEN TEST concerning the resolution of exercises - ORAL EXAM on theoretical notions The three tests must be done in the same appeal. Passing the TEST is necessary for the continuation of the exams. For information on support services for students with disabilities and / or SLD visit http://www.unipg.it/disabilita-e-dsa |
| 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. |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile | 4 |