Unit MATHEMATICAL ANALYSIS
- Course
- Informatics
- Study-unit Code
- GP004139
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- CFU
- 12
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Type of study-unit
- 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 matematico-fisica |
| Sector | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Functions. Limits and continuity. Differential calculus. Indefinite integrals. Definite integrals. |
| 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. To support teaching, the Geogebra software and the OneNote application will be used. |
| Other information | For communications and didactic material, reference is made to the UniStudium platform. |
| Learning verification modality | The assessment of Module I is divided into two parts. The first part consists of a 30-minute test with 10 questions, each worth a maximum of 3 points. Its purpose is to assess the acquisition of the method, terminology, and fundamental theoretical knowledge of the subject. A score equal to or higher than 15/30 grants both eligibility to take the second test and a bonus grade calculated as (score of the first test / 3) – 3. The second test is aimed at assessing knowledge and skills related to calculations. It consists of exercises to be completed in 2 hours and 30 minutes and is graded on a scale of thirty points. During the second test, the following materials may be used: the textbook; handwritten notes collected in a folder; scrap paper; pens, pencils, ruler, etc. The following items are not allowed: bags or backpacks; smartphones, notebooks, calculators, or similar devices; books other than the textbook. The final grade for the module is given by the grade of the second test plus the bonus obtained in the first. Students with disabilities and/or specific learning disorders (SLD) are entitled to compensatory measures and exemptions: they may choose either to take both written tests with an additional third of the time, or to complete one third fewer exercises. For general information on services supporting students with disabilities and/or SLD, please visit: 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. 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 matematico-fisica |
| Sector | MAT/05 |
| Type of study-unit | 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 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 on his web page https://boccuto.sites.dmi.unipg.it/corso-informatica.htm |
| Educational objectives | THE TRANSMISSION OF THE KNOWLEDGE AND THE EDUCATION!!! 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. |
| 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 SO-CALLED "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. |