Study-unit Code
In all curricula
Paola Rubbioni
  • Paola Rubbioni
  • 70 ore - Paola Rubbioni
Course Regulation
Coorte 2022
Learning activities
Discipline matematiche e informatiche
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Basic elements of Calculus on the real line and first notion of Topology.
Reference texts
Title: Primo corso di Analisi Matematica: con prerequisiti ed esercizi svolti
Authors: Graziano Crasta, Annalisa Malusa
Year: 2022
ISBN: 9798842409730


Title: Analisi matematica. Con aggiornamento online
Authors: Bertsch M.; Dal Passo, R.; Giacomelli, L.
Editor: McGraw-Hill Education
Edition: 2
Year: 2014
ISBN: 9788838668949

Title: Mathematical analysis 1
Authors: Canuto, C.; Tabacco, A.
Editor: Pearson
Year: 2021
ISBN: 9788891931115 - print
ISBN: 9788891931122 - online

Further teaching material available on the course page in UniStudium (pdf of the lessons, supplementary handoutsoblems).
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 and integrals); 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.
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 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 verification of the profit is divided into a calculus test and a theoretical test. In the first test the student must perform some exercises in two hours to verify the knowledge and skills related to the calculation. In the second test the acquisition of the method, of the language and of the fundamental theoretical knowledge of the subject is verified; this test, lasting one hour, consists of three questions relating to statements and proofs of theorems, definitions, examples and counterexamples on the topics of the program.
It is advisable to present yourself to the thoretical exam only if at least the 15/30 evaluation of the calculus test has been achieved. The final vote deviates from the calculus test vote for a maximum of seven points.

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. To allow the teacher to adequately prepare the tests, the student must communicate his/her choice at least one week before the date of the session in which he intends to participate.

For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa
Extended program
Properties of the real line: upper and lower bounds. Induction principle. Functions, domains, codomini and graphs.
Limits and continuity: limits in expanded IR, sequences, monotone functions, right and left limits; significant limits and their use; infinitesimal and infinite. Continuity and theorems on continuous functions (Theorem of zeros, Properties of intermediate values, Weierstrass' theorem). Uniform continuity.
Derivatives: geometric meaning, fundamental derivatives and calculation rules. Maximums, minima and fundamental theorems on differentiable functions (Fermat, Rolle, Lagrange, Cauchy, l'Hospital). Subsequent derivatives, convexity, optimization and Taylor's formulas.
Indefinite integrals: primitives; integration methods.
Definite integrals: concept and geometric interpretation of the definite integral; the fundamental theorem of integral calculus.
Numerical series.
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