Unit MATHEMATICAL ANALYSIS IST
- Course
- Fisica
- Study-unit Code
- GP005443
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- Teachers
-
- Paola Rubbioni
- Hours
- 75 ore - Paola Rubbioni
- CFU
- 10
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Base
- Area
- Discipline matematiche e informatiche
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Elementary functions and their properties. Limits and continuity. Differential calculus. Integral calculus. Improper integrals and numerical series.
- 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 Suggested: Title: Analisi matematica 1 - Esercizi con richiami di teoria Author: Marcelli, C. Editor: Pearson Year: 2019 ISBN print: 9788891904898 ISBN online: 9788891904904 https://he.pearson.it/catalogo/1074 Further teaching material available on the course page in UniStudium.
- Educational objectives
- 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. - Prerequisites
- Knowledge of basic mathematics topics covered in high school is required. In particular, the ability to calculate first and second degree equations and inequalities, rational, irrational, transcendent, is required, as well as the knowledge of basic analytical geometry (lines, parabolas, circles).
From the beginning of the course, manual skill and quick calculation will be required. It is therefore necessary to refresh one's knowledge and revive one's skills before the start of classes. To this end, high school textbooks can be used, or specific books as well. A concise, but comprehensive, book is
Title: Matematica zero - per i precorsi e i test di ingresso a ingegneria e scienze con MyLab e eText
Authors: F. G. Alessio - C. Marcelli - P. Montecchiari - C. de Fabritiis
ISBN 9788891902139 - Teaching methods
- Lectures on all the topics of the course.
In addition to a detailed theoretical presentation, the relative exercises will also be carried out for each topic that will serve as a model for those proposed in the exams.
To support teaching, the Geogebra software and the OneNote and Drawboard applications will be used. - Other information
- During the first written test it is allowed to use: textbook; handwritten cards with their personal notes inserted in a price list; draft sheets; pens, pencils, ruler, ...
However, it is not possible to keep with you: bags or backpacks; smartphones or notebooks or calculators or other similar devices; books other than textbooks.
For communications and teaching material, reference is made to the UniStudium platform. - Learning verification modality
- The assessment is divided into two examinations. The first examination is aimed at assessing knowledge and skills related to calculations. It consists of written exercises to be completed in 2 hours and 30 minutes. The second examination, lasting approximately 1 hour and 15 minutes, is designed to assess the acquisition of the method, terminology, and fundamental theoretical knowledge of the subject. The student will first provide written answers to 3 questions and will then discuss them orally with the examination board. The topics include statements and proofs of theorems, definitions, examples, and counterexamples from the course syllabus. Students with disabilities and/or specific learning disorders (SLD) are entitled to compensatory measures and exemptions: they may choose either to take both written examinations with an additional third of the time, or to complete one third fewer exercises. For information on services supporting students with disabilities and/or SLD, please visit: http://www.unipg.it/disabilita-e-dsa
- Extended program
- Functions and Sequences: Upper and lower bounds; properties of functions; sequences and their behavior.
Limits and Continuity: Topology of R and the extended real line; definition and properties of limits; special limits; Landau notation; infinitesimals and infinities. Compactness and connectedness; Bolzano–Weierstrass and Heine–Borel theorems. Continuity and global properties of continuous functions, including the Intermediate Value Theorem, the Zero Theorem, and Weierstrass’ Theorem. Uniform continuity; Heine–Cantor Theorem.
Differential Calculus: Definition of the derivative; basic derivatives and rules of differentiation. Maxima and minima; fundamental results for differentiable functions (Fermat’s theorem, Rolle’s theorem, Mean Value Theorems of Lagrange and Cauchy, de l’Hôpital’s Rule). Higher-order derivatives; convexity; optimization. Taylor polynomials and Taylor’s theorem with remainder forms.
Integral Calculus: Riemann integration. Indefinite integrals (antiderivatives and methods of integration). Definite integrals: definition of the Riemann integral; Fundamental Theorem of Calculus.
Improper Integrals and Series: Improper integrals; numerical series; notable examples and convergence criteria. - Obiettivi Agenda 2030 per lo sviluppo sostenibile
- Quality education