Unit MATHEMATICAL ANALYSIS
 Course
 Informatics
 Studyunit Code
 GP004139
 Curriculum
 In all curricula
 Teacher
 Paola Rubbioni
 CFU
 14
 Course Regulation
 Coorte 2021
 Offered
 2021/22
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa integrata
MATHEMATICAL ANALYSIS  MOD. I
Code  GP004146 

CFU  7 
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  Sets, upper and lower extremes, numerical sequences, elementary functions. Limits, continuity and derivation for real functions of one variable. Riemann Integral. 
Reference texts  Marco Bramanti Carlo Domenico Pagani Sandro Salsa Analisi matematica 1 Zanichelli, 2008. Volume unico Pagine: 392 ISBN: 9788808064851 .Ebook  versione Booktab ISBN: 9788808642752 .Ebook licenza 9 mesi  versione Booktab ISBN: 9788808842541 Marco Bramanti "Esercitazioni di Analisi matematica 1" Esculapio editore, 2018 
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, derivative, integral; to be able to carry out the complete study of a function of one variable; know how to calculate simple Riemann integrals; know how to expose and discuss the definitions and theorems presented in class. 
Prerequisites  First and second degree equations and inequalities, rational, irrational, transcendent. Elements of analytical geometry. 
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. 
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 any additional material, reference is made to the Unistudium platform. 
Learning verification modality  The final exam is inclusive of both modules. For each module there are: a written test in which the student must perform some exercises in two hours to verify the knowledge and skills related to the calculation; an oral test of about fifteen minutes 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. For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilitaedsa 
Extended program  Basic concepts on sets; upper extreme. Functions of one variable: generality and elementary functions; composition of functions and inverse functions. Limits and continuity: numerical sequences; limits of functions, continuity, asymptotes; calculation of limits; global properties of continuous functions. Differential calculus for functions of one variable: derivative of a function; rules for calculating derivatives; the theorem of the mean value and its consequences; second derivative; study of the graph of a function. Riemann Integral: integral of a function; properties of the integral; the fundamental theorem of integral calculus; calculation of indefinite and defined integrals. 
MATHEMATICAL ANALYSIS  MOD. II
Code  GP004147 

CFU  7 
Teacher  Antonio Boccuto 
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 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  Theoretical lectures on a projector or on a computer with examples and exercises, solved in detail. 
Other information  Attending the lectures is very important, fundamental and warmly suggested. 
Learning verification modality  Thanks to the COVID, there will be only the oral examination, in ehich there will be also some exercises to solve 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. If we return to THE SITUATION BEFORE COVID, then the rules will be as follows. Written (the time is 2 hours) and oral examination. G E N E R A L R U L E S The oral examination is given within two sessions after the written part. In some cases there is the possibility of establishing a calendar, but in any case the exams have to be NECESSARILY BOOKED. The registration to both the written and the oral part MUST BE DONE BY EMAIL, to which the teacher will answer, some day before the exam. The address is antonio.boccuto@unipg.it It is not possible to receive nonbooked or nonconfirmed students. The written part consists of two exercises with theoretical sketches. The oral examination is on the WHOLE PROGRAM, included exercises. The material consists of the "set union" of the didactic material and the lectures of the teacher. 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. 