Unit MATHEMATICS I AND GEOMETRY
 Course
 Engineering management
 Studyunit Code
 A002892
 Curriculum
 In all curricula
 CFU
 12
 Course Regulation
 Coorte 2023
 Offered
 2023/24
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa integrata
GEOMETRY
Code  A002894 

CFU  6 
Teacher  Giuliana Fatabbi 
Teachers 

Hours 

Learning activities  Base 
Area  Matematica, informatica e statistica 
Academic discipline  MAT/02 
Type of studyunit  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  Teaching is part of the course of study pursuing some of the general learning objectives. In particular, the teaching contributes to the development of the understanding of fundamental scientific and engineering principles and their declination in the main technologies adopted in the company. Consistently with the educational objectives of the course of study foreseen in the SUACdS sheet, the course aims to provide the student with the fundamental principles of vector calculus in the plane and in space and its applications to analytical geometry in order to develop the ability to model decision problems typical of companies in different sectors, plan tactical and strategic actions also using geometric algebraic tools and resorting to efficient solution techniques and / or algorithms; Another objective is to prepare the student for the application of the techniques of the course to other engineering disciplines. We expect the knowledge of the fundamental elements of linear algebra and their application to the solution of simple geometric problems, to be able to state and prove some basic theorems. An understanding not limited to the statement of definitions and results and to the resolution of standard exercises is expected, but critical and able to distinguish the different situations and to make informed choices, justifying the procedures followed. Furthermore, an adequate correctness in the calculations and a wellargued exposition of the theory is expected. 
Prerequisites  The student is required to have a good knowledge of the mathematics topics covered in secondary school, in particular the algebra of polynomials and main elements of analytical geometry. 
Teaching methods  Face to face lessons. 
Other information  Usage of Unistudium platform 
Learning verification modality  The exam includes a written test on one of the sessions and a short oral test lasting about 15 minutes. In the first part of the written test there will be 2 or 3 exercises while in a second part examples, enunciated examples and short demonstrations may be requested. For information on support services for students with disabilities and / or SLD, visit the page http://www.unipg.it/disabilitaedsa. The teacher is in each case available to personally evaluate, in specific cases, any compensatory measures and / or personalized paths in the case of students with disabilities and / or SLD. The teacher is also available to evaluate any personalized courses for working or nonattending students. 
Extended program  VECTOR SPACES. Examples and definition. The spaces R ^ n and C ^ n. Vectors and operations between vectors. Linear dependence, generators and bases. Coordinates. Dimension. Vector subspaces. Sum, intersection, Grassmann's formula, direct sum. LINEAR APPLICATIONS AND MATRIX . Definitions and examples. Kernel and image. Matrix algebra. Linear application associated with a matrix. Matrix associated with a linear application. Change of base. DETERMINING. Determinant of 2x2 and 3x3 matrices and geometric meaning. General definition and characterizing properties. Gauss method, Laplace expansions. Binet's theorem and inverse matrix. Rank. LINEAR SYSTEMS AND AFFINE SUBSPACES. Gauss method. Homogeneous systems. RouchéCapelli theorem. Cramer's rule. Parametric and Cartesian equations of an affine subspace. Lines and planes in space. EIGENVALUES AND EIGENVECTORS. Invariant subspaces, eigenvalues, eigenvectors and eigenspaces. Characteristic polynomial. Existence of bases of eigenvectors and diagonalizability. REAL AND COMPLEX EUCLIDICAL SPACES. Scalar and Hermitian product, norm and orthogonality, orthonormal bases. GramSchmidt orthonormalization procedure. Canonical scalar and Hermitian product in R ^ n and C ^ n. Orthogonal and unitary matrices. Diagonalization of symmetric and Hermitian matrices. ELEMENTS OF GEOMETRY IN THE PLANE AND IN SPACE Lines in the plane. Lines and planes in space: parametric and Cartesian equations. Mutual positions. Distances. Angles. 
Obiettivi Agenda 2030 per lo sviluppo sostenibile 
MATHEMATICS I
Code  A002893 

CFU  6 
Teacher  Laura Angeloni 
Teachers 

Hours 

Learning activities  Base 
Area  Matematica, informatica e statistica 
Academic discipline  MAT/05 
Type of studyunit  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 logicaldeductive 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 logicalmathematical 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/internationalstudents/generalinformation/facilitiesforspecialneedsstudents . 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, onetoone 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. 