Unit MATHEMATICAL ANALYSIS IST
 Course
 Physics
 Studyunit Code
 GP005443
 Location
 PERUGIA
 Curriculum
 In all curricula
 Teacher
 Paola Rubbioni
 Teachers

 Paola Rubbioni
 Hours
 70 ore  Paola Rubbioni
 CFU
 10
 Course Regulation
 Coorte 2022
 Offered
 2022/23
 Learning activities
 Base
 Area
 Discipline matematiche e informatiche
 Academic discipline
 MAT/05
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa monodisciplinare
 Language of instruction
 Italian
 Contents
 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
Suggested:
Title: Analisi matematica. Con aggiornamento online
Authors: Bertsch M.; Dal Passo, R.; Giacomelli, L.
Editor: McGrawHill 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.  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 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/disabilitaedsa  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.