Unit GEOMETRY
- Course
- Building engineering and architecture
- Study-unit Code
- GP004889
- Curriculum
- In all curricula
- Teacher
- Marco Timpanella
- Teachers
-
- Marco Timpanella
- Hours
- 54 ore - Marco Timpanella
- CFU
- 6
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Base
- Area
- Discipline informatiche, di elaborazione delle informazioni e matematiche
- Academic discipline
- 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
- E. Schlesinger, Algebra lineare e geometria. Zanichelli editore. K. Nicholson, Algebra lineare, McGraw Hill Additional supplementary material available on Unistudium.
- Educational objectives
- At the end of the course, students should be able to solve linear systems and simple linear algebra problems (determine the basis and dimension of a subspace, determine the rank of a matrix that may depend on a parameter, determine the kernel and image of a linear application, determine the eigenvalues and eigenvectors of an endomorphism). They should also be able to apply linear algebra to geometric problems in space. Additionally, they should be able to express the main theoretical concepts of the course in a mathematically correct and unambiguous language, demonstrating familiarity with the basic notations of modern mathematics.
- Prerequisites
- Basic notions of mathematics and logic.
- Teaching methods
- The course is organized in classroom lectures covering all topics in the syllabus. The lectures are supplemented with notes, exercises, and examples.
- Other information
- Attendance is not mandatory but highly recommended.
- Learning verification modality
- The exam consists of a final written test and an oral examination. The written test is divided into two parts, to be completed within a total of 180 minutes. The first part of the exam is theoretical, and passing this section is required in order to proceed to the second part of the written test. The first part does not contribute to the final grade. The second part of the written test consists of exercises on the following topics: linear systems, matrices, linear applications, affine and euclidean geometry. The grade for the written test will be expressed on a scale of 30. Students who obtain a score of at least 15/30 will be admitted to the oral exam. The oral examination aims to assess the student’s level of knowledge and understanding of the theoretical and methodological content covered in the course. It also serves to evaluate the student's ability to communicate effectively, using appropriate language and demonstrating an independent and organized presentation of the same theoretical topics. For information on support services for students with disabilities and/or specific learning disorders (SLD), please 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.
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- 4