Unit MATHEMATICAL ANALYSIS

MATHEMATICAL ANALYSIS - MOD. I

Code	GP004146
CFU	6
Teacher	Irene Benedetti
Teachers	Irene Benedetti
Hours	47 ore - Irene Benedetti
Learning activities	Base
Area	Formazione matematico-fisica
Sector	MATH-03/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	Functions. Limits and continuity. Differential calculus.
Reference texts	Title: Mathematical analysis 1 Authors: Canuto, C.; Tabacco, A. Editor: Pearson Year: 2021 ISBN: 9788891931115 - print ISBN: 9788891931122 - online https://he.pearson.it/catalogo/632 Further teaching material available on the course page in UniStudium: - exam topics carried out - supplementary handouts
Educational objectives	The course aims to provide students with the bases of Mathematical Analysis both from a methodological and a calculation point of view. At the end of the Module I the student must: have acquired the notions of limit, continuity, derivative, integral; to be able to carry out the complete study of a function of one variable; know how to calculate simple integrals; know how to expose and discuss the definitions and theorems presented in class.
Prerequisites	In order to be able to apply the calculation techniques given in teaching, it is necessary to know the basic mathematics topics covered in high school. In particular, the ability to calculate first and second degree equations and inequalities, rational, irrational, transcendent, as well as the knowledge of basic analytical geometry (lines, parabolas, circles) is required.
Teaching methods	Face-to-face lessons on all the topics of the course. In addition to a detailed theoretical presentation, for each topic will also be carried out the related exercises that will be a model to those proposed in the examination.
Other information	For communications and didactic material, reference is made to the UniStudium platform.
Learning verification modality	The assessment for Module I is divided into two parts. The first part, lasting two hours, consists of exercises to be completed. It is designed to assess knowledge and skills related to calculation and provides a grade expressed out of thirty. During this test, the use of the following is permitted: the textbook; handwritten notes containing personal annotations placed in a document folder; scrap paper; pens, pencils, ruler, etc. The following items are not allowed: bags or backpacks; smartphones, notebooks, calculators, or other similar devices; books other than the textbook. A score greater than or equal to 15/30 grants eligibility to access the second test. The second test, lasting one hour, consists of a written exam with theoretical questions. It is aimed at assessing the acquisition of methodology, language, and the fundamental theoretical knowledge of the subject. Students with disabilities and/or specific learning disorders (SLD) may benefit from compensatory measures or accommodations. For general information on support services, please refer to the page: http://www.unipg.it/disabilita-e-dsa
Extended program	Functions: generality and elementary functions; composition of functions and inverse functions. Limits and continuity: definition; calculus; asymptotes; continuity; properties of the continuous functions. Differential calculus: definition of derivative of a function; calculation rules; main theorems for the derivatives calculation; successive derivatives; convexity; study of the graph of a function. Taylor expansion.
Obiettivi Agenda 2030 per lo sviluppo sostenibile	Quality education

MATHEMATICAL ANALYSIS - MOD. II

Code	GP004147
CFU	6
Teacher	Paola Rubbioni
Teachers	Paola Rubbioni
Hours	47 ore - Paola Rubbioni
Learning activities	Base
Area	Formazione matematico-fisica
Sector	MATH-03/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	ITALIAN
Contents	Integral calculus. Improper integrals. Series. Basics of multivariable calculus.
Reference texts	Title: Mathematical analysis 1 Authors: Canuto, C.; Tabacco, A. Editor: Pearson Year: 2021 ISBN: 9788891931115 - print ISBN: 9788891931122 - online https://he.pearson.it/catalogo/632 Further teaching material will be available on the course page in UniStudium
Educational objectives	The course aims to provide students with the fundamentals of mathematical analysis, both from a methodological perspective and in terms of computational techniques. By the end of the course, students are expected to have acquired the main techniques of elementary analysis, particularly with regard to integrals (including improper integrals), series, and functions of two variables (partial derivatives and double integrals). They should also be able to present and discuss the definitions and theorems covered in lectures.
Prerequisites	The course aims to provide students with the foundations of Mathematical Analysis both from a methodological and a computational point of view. At the end of the course, the student must: have acquired the main techniques of basic analysis (limits, derivatives, integrals, series); be able to solve problems and exercises, reproduce the main statements and the main demonstrations presented in class, solve questions deriving from knowledge of the aforementioned topics.
Teaching methods	Face-to-face lessons on all the topics of the course. In addition to a detailed theoretical presentation, for each topic will also be carried out the related exercises that will be a model to those proposed in the examination. To support teaching, software as Geogebra or OneNote will be used.
Other information	For communications and didactic material, reference is made to the UniStudium platform.
Learning verification modality	Assessment for Module II is divided into two parts. The first part, lasting 2 hours, consists of problem-solving exercises. It is designed to assess knowledge and skills related to calculations and is graded on a scale of 30 points. During the exam, students may use: the textbook; handwritten notes containing their personal annotations placed in a plastic document folder; draft paper; pens, pencils, rulers, etc. Students are not allowed to keep with them: bags or backpacks; smartphones, notebooks, calculators, or similar devices; books other than the prescribed textbook. The second part, lasting 1 hour, consists of a written test with theoretical questions. It is intended to assess the acquisition of methodological skills, appropriate terminology, and the fundamental theoretical knowledge of the subject. Students with special educational needs and/or specific learning disabilities may benefit from compensatory measures or accommodations. For general information on support services, see: http://www.unipg.it/disabilita-e-dsa
Extended program	Indefinite integrals: antiderivatives; methods of integration. Definite integrals: definition of the Riemann integral; Fundamental Theorem of Calculus. Improper integrals and series: improper integrals; numerical series; notable cases and convergence criteria. Introduction to functions of two variables: limits and continuity; partial derivatives; double integrals.
Obiettivi Agenda 2030 per lo sviluppo sostenibile	Quality education