Unit MATHEMATICS I AND GEOMETRY
- Course
- Engineering management
- Study-unit Code
- A002892
- Curriculum
- In all curricula
- CFU
- 12
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
GEOMETRY
| Code | A002894 |
|---|---|
| CFU | 6 |
| Teacher | Giuliana Fatabbi |
| Teachers |
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| Hours |
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| Learning activities | Base |
| Area | Matematica, informatica e statistica |
| Academic discipline | MAT/02 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | Linear algebra and an introduction to analytic geometry. |
| Reference texts | Notes in English will be uploaded in the Unistudium platform |
| Educational objectives | The course fits into the study program by pursuing some of the general learning objectives. Specifically, it contributes to developing an understanding of fundamental scientific and engineering principles and their application in key technologies used in business settings. In line with the educational objectives outlined in the SUA-CdS program sheet, the course aims to provide students with the foundational principles of vector calculus in the plane and in space, as well as its applications to analytic geometry, with the goal of developing skills to: Model decision-making problems typical of businesses across various sectors; Plan tactical and strategic actions using algebraic-geometric tools; Employ efficient techniques and algorithms for problem-solving. A further objective is to prepare students to apply the course techniques to other engineering disciplines. Expected learning outcomes: Knowledge of the fundamental elements of linear algebra and their application in solving simple geometric problems; Ability to state and prove basic theorems; Critical understanding, not limited to merely recalling definitions and results, but capable of distinguishing between different situations and making informed choices, justifying the methods used; Accuracy in calculations and the ability to present theory clearly and coherently. |
| Prerequisites | Students are expected to have a strong foundation in the mathematical topics covered in upper secondary school, particularly: Polynomial algebra (operations, factorization, equations, and inequalities); Basic elements of analytic geometry (lines, conic sections, Cartesian coordinates). |
| Teaching methods | The course will be delivered through lectures, adopting the following approach: Theoretical presentation of topics, supported by practical examples; Guided problem-solving sessions to reinforce skills; Student interaction to address questions and encourage active participation. |
| Other information | Usage of Unistudium platform |
| Learning verification modality | The exam includes: A written test (to be taken in one of the available exam sessions); A short oral examination (approx. 15 minutes), which may cover: Theorem statements; Brief proofs. Support for students with disabilities/DSA and working students: For support services, visit: http://www.unipg.it/disabilita-e-dsa. The instructor is available to assess, on a case-by-case basis: Compensatory measures and tailored paths for students with disabilities and/or DSA; Customized learning arrangements for working students or non-attendees. |
| Extended program | 1. Vector Spaces Definition, examples (Rn, Cn), operations, linear dependence, bases, subspaces. 2. Linear Maps & Matrices Kernel, image, matrix algebra, associated matrices, change of basis. 3. Determinant Definition, properties, computation (Gauss, Laplace), rank. 4. Linear Systems Solving (Gauss, Rouché-Capelli), affine subspaces, lines and planes. 5. Eigenvalues Eigenvectors, characteristic polynomial, diagonalization. 6. Euclidean Spaces Inner product, orthonormal bases, Gram-Schmidt, orthogonal matrices. 7. Analytic Geometry Lines (plane/space), planes, mutual positions, distances. |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile |
MATHEMATICS I
| Code | A002893 |
|---|---|
| CFU | 6 |
| Teacher | Laura Angeloni |
| Teachers |
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| Hours |
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| Learning activities | Base |
| Area | Matematica, informatica e statistica |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | ENGLISH |
| Contents | The purpose of the course is to present the fundamental issues of basic calculus. |
| Reference texts | The teacher will advise some text at the beginning of the course. Among them: 1. "Calculus for Scientists and Engineers", Martin Brokate, Pammy Manchanda, Abul Hasan Siddiqi, Springer, 2019. 2. "Mathematical Analysis 1", Claudio Canuto, Anita Tabacco, Pearson, 2021. 3. "Calculus for Business, Economics, Life Sciences, and Social Sciences", Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker, Pearson ed. 2019. 3. "Calculus: Early Transcendentals", James Stewart, Daniel Clegg, Saleem Watson, Cengage Learning, 2020. Moreover, in the UniStudium webpage of the course, slides on the main topics of the course and on exercises will be available. |
| Educational objectives | The purpose of the course is to furnish the main concepts of mathematical analysis and to support the competence in calculus skills, fundamental tools that contribute to the future management engineer. The main knowledge (descriptor Dublin 1) will be acquired: • knowledge of the concept of function and of calculating the limits of functions together with the basic concepts of topology; • knowledge of the differentiability of functions of one variable and all those concepts that enable the student to carry out the study of function; • knowledge of the notion of integral, main results and integral calculus. The main skills acquired (ability to apply their knowledge, descriptor Dublin 2, and to take with independent judgment the appropriate approach, Dublin descriptor 3) will be: • ability to solve equations, inequalities, limits, derivatives, integrals; • ability to develop an argument that leads the student to identify the methods of solving the problem; • ability to identify a common logical-deductive methodology in various topics to enable it to identify the approach to be followed. |
| Prerequisites | General notions about sets theory, equations and inequalities of first and second degree, elementary functions. |
| Teaching methods | The course is organized as follows: 1) Lectures on all topics of the course. 2) Classroom exercises. |
| Other information | Attendance is recommended for all lessons. |
| Learning verification modality | The verification of the educational objectives of the course (test) includes a written and an oral test. The written test will be held on the dates set out on the calendar of the CdS. The written test, of about 2,5 hours, consists in solving some problems regarding the main topics of the course and some multiple choice theoretical questions. The test has the aim to verify: i) the ability to understand the problems proposed during the course, ii) the ability to correctly apply the theoretical knowledge (descriptor Dublin 2), iii) the ability to formulate the appropriate approach for the solution of the problems (descriptor Dublin 3), iv) the ability to suitably and efficaciously communicate in written form (descriptor Dublin 4). The oral examination consists of a discussion no longer than 15 minutes aimed to verify: i) the level of knowledge about the theoretical contents of the course (descriptor Dublin 1), ii) the level of expertise in exposing their own logical-mathematical abilities (descriptor Dublin 2), iii) the independence of judgment (descriptor Dublin 3) to propose the most suitable approach to argue about the posed questions. The oral examination also aims to verify the student's ability to answer with proper language to the questions proposed by the Commission, to support a dialectical relationship during the discussion and to show logical deductive skills and synthetic exposition (descriptor Dublin 4). The final evaluation will be made by the Commission taking into account also of the evaluation of the written test. For information on support services for special needs students, please visit the page https://www.unipg.it/en/international-students/general-information/facilities-for-special-needs-students . In any case, the teacher is available to personally evaluate, in specific cases, any compensatory measures and / or personalized paths in the case of students with special needs. |
| Extended program | Set theory, number sets, equations, inequalities. Functions: main definitions, injectivity, surjectivity, one-to-one functions, inverse functions, composition, graphs and main functions (power functions, exponential, logarithmic, trigonometric functions). Concept of limit: calculation and properties. Infinite and infinitesimal. Continuity and main results about continuous functions. Derivatives: geometric meaning, calculation and main results. Fundamental theorems on differentiable functions. Convexity. Study of the graph of a function of one real variable. Riemann integration: definition, geometric meaning, calculation rules and main results. |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile |