Unit MATHEMATICS I AND GEOMETRY

GEOMETRY

Code	A002894
CFU	6
Teachers	Massimo Giulietti (Codocenza)
Hours	54 ore (Codocenza) - Massimo Giulietti
Learning activities	Base
Area	Matematica, informatica e statistica
Sector	MATH-02/B
Type of study-unit	Obbligatorio (Required)

MATHEMATICS I

Code	A002893
CFU	6
Teachers	Laura Angeloni (Codocenza)
Hours	54 ore (Codocenza) - Laura Angeloni
Learning activities	Base
Area	Matematica, informatica e statistica
Sector	MATH-03/A
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