Unit MATHEMATICAL ANALYSIS
 Course
 Informatics
 Studyunit Code
 GP004139
 Curriculum
 In all curricula
 Teacher
 Paola Rubbioni
 CFU
 12
 Course Regulation
 Coorte 2023
 Offered
 2023/24
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa integrata
MATHEMATICAL ANALYSIS  MOD. I
Code  GP004146 

CFU  6 
Teacher  Paola Rubbioni 
Teachers 

Hours 

Learning activities  Base 
Area  Formazione matematicofisica 
Academic discipline  MAT/05 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  Italian 
Contents  Functions. Limits and continuity. Differential calculus. Indefinite integrals. Definite integrals. 
Reference texts  Title: Elementi di ANALISI MATEMATICA E GEOMETRIA con prerequisiti ed esercizi svolti Authors: Crasta, G.; Malusa, A. Editor: Edizioni LaDotta Edition: 2 Year: 2017 ISBN: 9788898648252 Further teaching material available on the course page in UniStudium:  pdf of the lessons  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  Facetoface 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, the Geogebra software and the OneNote and Drawboard applications will be used. 
Other information  During the written test the use of: textbook is allowed; handwritten cards with their own personal notes inserted in a portalistini; sheets for draft; pens, pencils, ruler, ... It is not possible to keep with you: bags or backpacks; smartphones or notebooks or calculators or other similar devices; books other than text. For communications and didactic material, reference is made to the UniStudium platform. 
Learning verification modality  The final exam is inclusive of both modules. For the modulus I there are: a first written test in which the student must perform some exercises in two hours to verify the knowledge and skills related to the calculation; a second written test of one hour of verification of the acquisition of the method, of the language and of the fundamental theoretical knowledge of the subject. The final grade is the average of the marks obtained in the two modules. Students with disabilities and / or SLDs can take advantage of compensations and dispensatory measures: the student can choose whether to take the two written tets using one third more time or one third less exercises. For general information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilitaedsa 
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. Indefinite integrals: primitives; integration methods. Definite integrals: concept and geometric interpretation of the definite integral; the fundamental theorem of integral calculus. 
Obiettivi Agenda 2030 per lo sviluppo sostenibile  Quality education 
MATHEMATICAL ANALYSIS  MOD. II
Code  GP004147 

CFU  6 
Teacher  Paola Rubbioni 
Teachers 

Hours 

Learning activities  Base 
Area  Formazione matematicofisica 
Academic discipline  MAT/05 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  ITALIAN It is possible to do the exam also in English. 
Contents  Series. Different types of techniques for solving them. Double integrals and generalized integrals. Applications to Probability and Statistics. Maxima and minima of functions of several variables, and eigenvalues. Taylor series and applications. 
Reference texts  Didactic material given by the teacher 
Educational objectives  THE TRANSMISSION OF THE KNOWLEDGE!!! The aim of the course is to give different techniques and methods of calculus for series, improper integrals, double integrals, local maxima and minima of functions of several variables, the Taylor series, with several applications, among which to Probability and Statistics and to the calculus of irrational numbers with a given fixed precision. 
Prerequisites  The WHOLE Course of Mathematical Analysis I Modulus, of course. 
Teaching methods  Lectures with examples and exercises, solved in detail. 
Other information  Attending the lectures is very important, fundamental and warmly suggested. 
Learning verification modality  Oral examination, in which there will be also some exercises to solve and to explain immediately. Please book the examination BY EMAIL 7/10 days before, writing a message to the addressantonio.boccuto@unipg.it The exam has to be done INSIDE THE SOCALLED "WINDOW" PERIODS, WHICH ARE COMMUNICATED BY THE TEACHER. P.S.: During the oral examination it should be possible to ask to do writtenly some subjects. A RESPONSIBLE DAILY STUDY IS FUNDAMENTAL. 
Extended program  Series. Different types of techniques for solving them. Double integrals and generalized integrals. Applications to Probability and Statistics. Maxima and minima of functions of several variables, and eigenvalues. Taylor series and applications. 
Obiettivi Agenda 2030 per lo sviluppo sostenibile  What circumstances make it advisable. 