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Mathematical Analysis II

Academic Year 2023/2024 - Teacher: Salvatore Angelo MARANO

Expected Learning Outcomes

Students must be able to: 

1) identify and understand qualitative or quantitative properties of real functions of several real variables, as well as to apply them to both theoretical and practical problems;

2) knowing how to solve an equation or a system of differential equations of moderate difficulty. 

They must also acquire the necessary skills to deal with the study of other courses that use mathematical analysis.

General educational objectives of teaching in terms of expected learning outcomes. 

1. Knowledge and understanding: the objective of the course is to acquire the theoretical foundations and some applications concerning the differential and integral calculus for functions of several real variables. 

2. Ability to apply knowledge and understanding: students will acquire the necessary skills to study simple models. 

3. Making judgements: through concrete examples and exercises, students will be able to independently develop their own solutions to some simple problems. 

4. Communication skills: students will acquire further communication skills and expressive appropriateness in the use of theoretical language in the general field of Mathematical analysis.

5. Learning skills: the course aims, as an objective, to provide students with the necessary theoretical and practical methodologies to be able to independently face and solve problems that may arise during modelling.

Course Structure

Blackboard lessons. 
If the teaching is given in mixed or distance learning mode, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus. 
Information for students with disabilities and/or DSA To guarantee equal opportunities and in compliance with the laws in force, interested students can request a personal interview in order to plan any compensatory and/or dispensatory measures, based on the educational objectives and specific needs. It is also possible to contact the CInAP (Centre for Active and Participatory Integration - Services for Disabilities and/or DSA) referent professor of our Department, prof. Filippo Stanco.

Required Prerequisites

The main contents of Mathematical analysis I and some topics of Linear Algebra and Geometry.

Attendance of Lessons

Strongly recommended.

Detailed Course Content

Differential and integral calculus for real functions of several real variables. Ordinary differential quations and systems.

Textbook Information

N. FUSCO – P. MARCELLINI – C. SBORDONE, Lezioni di analisi matematica due, Zanichelli Editore, Bologna, 2020.

C.D. PAGANI – S. SALSA, Analisi matematica 2, Zanichelli Editore, Bologna, 2016.

M. BRAMANTI, Esercitazioni di Analisi Matematica 2, Esculapio Editore, Bologna, 2012.

P. MARCELLINI – C. SBORDONE, Esercitazioni di Analisi Matematica Due, Zanichelli Editore, Bologna, 2017.

Course Planning

 SubjectsText References
1Differential Calculus1-2-3-4
2Integral Calculus1-2-3-4
3Ordinary differential equations and systems2-4

Learning Assessment

Learning Assessment Procedures

The overall assessment of skills is carried out in the traditional way. Once a written test has been passed, which aims to ascertain the student's ability to carry out exercises of low difficulty, access to the oral test, which consists of an interview on the topics treated during the lessons.

Both for the ongoing tests and for the final exam, clarity of presentation, completeness of knowledge and the ability to connect different topics will be taken into account. The student must demonstrate that he has acquired sufficient knowledge of the main topics covered during the course and that he is able to carry out at least the simplest of assigned exercises. There is no average between the written and oral grades. The following criteria will normally be followed to assign the grade: 
not approved: the student has not acquired the basic concepts and is not able to carry out the exercises. 
18-23: the student demonstrates minimal mastery of the basic concepts, his skills in exposition and connection of contents are modest, he is able to solve simple exercises. 24-27: the student demonstrates good mastery of the course contents, his presentation and content connection skills are good, he solves the exercises with few errors. 
28-30 cum laude: the student has acquired all the contents of the course and is able to explain them fully and connect them with a critical spirit; she solves the exercises completely and without errors.

Examples of frequently asked questions and / or exercises

See Studium.