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CODE 115468
ACADEMIC YEAR 2024/2025
CREDITS
SCIENTIFIC DISCIPLINARY SECTOR MAT/05
LANGUAGE English
TEACHING LOCATION
  • IMPERIA
SEMESTER 2° Semester
TEACHING MATERIALS AULAWEB

OVERVIEW

The course provides the basic tools of Mathematical Analysis concerning functions of one real variable.

AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The knowledge of mathematical basic tools useful in physical problems modeling.  The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting. At the end of the course the student will be able

1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. integral , Existence and Uniqueness theorems for differential problems );

2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis;

3. to set up problem solving with an intuitive approach;

4. to select the suitable mathematical tools in problem solving;

5. to solve problems with deductive reasoning.

 

PREREQUISITES

Differential calculus for  functions of one real variable, i.e. the content of  Mathematical Analysis Module 1 course.

TEACHING METHODS

The course consists of 60 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Some guided practices will be held to help the student to valuate one's preparation. Several intermediate tests are provided.

Students  have several exercises at their disposal on Aulaweb

SYLLABUS/CONTENT

Antiderivatives. Riemann integral : definition and basic properties. Mean value Theorem. The Fundamental Theorem and Formula of Integral Calculus. Areas of plane regions. Changes of variable: the method of substitution. Integration by parts. Integrals of rational and trigonometric functions. Integral functions. Improper Integral.

Ordinary differential equations : the method of separation of variables and Existence and Uniqueness Theorems for the Cauchy Problem.

Ordinary linear differential equations : structure of the general solution in the Homogeneous and not homogeneus case. Solving methods for n order linear equations with constant coefficients and first order linear equations with continuous coefficients. Systems of linear differential equations.

 

RECOMMENDED READING/BIBLIOGRAPHY

Theory
C. Canuto – A. Tabacco : Analisi Matematica 1. Pearson. 2021.

M.Bramanti - C.D.Pagani - S. Salsa : Analisi Matematica 1. Zanichelli, 2008.

T. Zolezzi : Dispense di analisi matematica I e II.
F. Parodi – T. Zolezzi : Appunti di analisi matematica. ECIG, 2002
R. Adams : Calcolo differenziale I. Funzioni di una variabile reale. Casa ed. Ambrosiana, 1992.
P. Marcellini – C. Sbordone : Analisi Matematica II. Liguori Editori

Exercises

M. Baronti – F. De Mari – R. van der Putten – I. Venturi : Calculus Problems. Springer 2016
M. Pavone: Temi svolti di analisi matematica I.
Marcellini-Sbordone : Esercitazioni di matematica, I volume

S. Salsa – A. Squellati : Esercizi di Matematica, volume 1.

 

TEACHERS AND EXAM BOARD

Exam Board

ROBERTUS VAN DER PUTTEN (President)

ALBERTO DAMIANO

ANGELO MORRO (President Substitute)

LESSONS

LESSONS START

The lessons start on Febraury 17, 2025

 https://easyacademy.unige.it/portalestudenti//index.php?_lang=en

 

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists in a written and oral examination. The written examination consists in two problems concerning the topics treated. The students have two / three hours at their disposal. After the written examination, the students who obtained a grade higher than 13/30 may take the oral examination. Two intermediate examinations will be held which may substitute the written examination.

Students with certification of Specific Learning Disabilities (SLD), disabilities, or other special educational needs must contact the instructor at the beginning of the course to agree on teaching and examination methods that, while respecting the course objectives, take into account individual learning styles and provide appropriate compensatory tools. It is reminded that the request for compensatory/dispensatory measures for exams must be sent to the course instructor, the School representative, and the “Settore serviziper l'inclusione degli studenti con disabilità e con DSA” office (dsa@unige.it) at least 10 working days before the test, as per the guidelines available at the link: https://unige.it/disabilita-dsa

 

ASSESSMENT METHODS

The aim of the examination is verifying the skills acquired by the student. The problems proposed in the examination call for the choice and the application of suitable mathematical tools, besides their  solution needs the skill of constructing a logical connection applying theoretical topics treated. The student must solve the exercises justifying the most important passages recalling  theorems and definitions and underlying the physical and geometric interpretation of the problem.

The final evaluation depends also on the quality of the written exposition and on the ability of reasoning.

 

Exam schedule

Data appello Orario Luogo Degree type Note
16/06/2025 09:00 IMPERIA Scritto + Orale
11/07/2025 09:00 IMPERIA Scritto + Orale
15/09/2025 09:00 IMPERIA Scritto + Orale

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Agenda 2030 - Sustainable Development Goals
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