Unit MATHEMATICAL ANALYSIS IST
- Course
- Physics
- Study-unit Code
- GP005443
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- Teachers
-
- Paola Rubbioni
- Hours
- 75 ore - Paola Rubbioni
- CFU
- 10
- Course Regulation
- Coorte 2024
- Offered
- 2024/25
- 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
Title: Primo corso di Analisi Matematica: con prerequisiti ed esercizi svolti
Authors: Graziano Crasta, Annalisa Malusa
Year: 2022
ISBN: 9798842409730
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, 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 achievement test is divided into two written tests.
The first test is aimed at verifying the knowledge and skills related to calculation and consists of exercises to be completed in writing in 2 hours and 30 minutes.
The second test, lasting approximately 45 minutes in total, aims to verify the acquisition of the method, language and fundamental theoretical knowledge of the subject; the student must first answer 2 questions in writing and then orally 1 question, in both cases on statements and demonstrations of theorems, definitions, examples and counterexamples on the topics of the program.
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.
For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa - Extended program
- Upper and lower bound. Functions and their properties: domain, image, graph, invertibility, monotonicity, composition.
Limits and continuity: limits in expanded IR, limits of sequences, theorems on the limits; notable limits; infinitesimal and infinite. Continuity and global properties of continuous functions (Zeros theorem, Intermediate value theorem, Weierstrass theorem). Uniform continuity. Differential calculus: the derivative; fundamental derivatives and calculation rules. Maximums, minimums and fundamental theorems on differentiable functions (Fermat, Rolle, Lagrange, Cauchy, De l'Hopital). Subsequent derivatives, convexity and optimization.
Indefinite integrals: primitives; integration methods.
Definite integrals: Riemann integral; the Fundamental Theorem of integral calculus. Improper integrals and numerical series. - Obiettivi Agenda 2030 per lo sviluppo sostenibile
- Quality education