Elements of Mathematical Analysis 2 A - E
Academic Year 2025/2026 - Teacher: Ornella NASELLIExpected Learning Outcomes
The aim of the course is to improve the knowledge of Calculus learned in the course of EAM1. In particular the course objectives are:
Knowledge and understanding: students will learn integral calculus for one real variable functions, differential calculus for two real variables functions, numerical and functions series.
Applying knowledge and understanding: by means of examples related to applied sciences, students will focus on the central role of Mathematics within science and not only as an abstract topic. Furthermore, they will be able to calculate integrals, to identify and compare the most common series, to individuate the analytic properties of a two real variables function and to apply differential calculus to optimization problems.
Making judgements: students will be stimulated, individually or in groups, to work on specific topics they have not studied during the class, developing exercises related on the field knowledge with greater independence. Seminars and lectures are scheduled to give students the chance to illustrate guided exercise on specidic topics in order to share them with the other students and to find together the right solutions.
Communication skills: studying Mathematics and dedicating time to guided exercise and seminars, students will learn to communicate with clarity and rigour both, in the oral and written analysis. Moreover, students will learn that using a properly structured language means to find the key to a clear scientific and non-scientific communication.
Learning skills: students, in particular the more willing one, will be stimulated to examine in depth some topics, thanks to individual activities or working in group.
Course Structure
The principal concepts and learning outcomes will be structured by planning frontal lectures. Furthermore, to improve the making judgements and communication skills, students will dedicate time to guided exercises (e.g. multiple choice) and they can work in groups or individually .
The course is organized by lectures. There will be some team practices, during which students can work in groups or individually.
There will be some integrative activities with tutors. Students will also participate in seminar discussions, developing exercises related on the field knowledge.
Learning assessment may also be carried out on line, should the conditions require it.
Students enrolled on CInAP are invited to meet te teacher before the exam.
Required Prerequisites
Students should have passed the EAM1 exam in order to do the EAM2 exam.
Attendance of Lessons
Detailed Course Content
1. Real functions of more real variables.
2. Integration.
3. Ordinary differential equations.
4. Numerical series.
Textbook Information
1. Notes of the teacher available on Studium.
2. A list of exercises is avalaible on Studium.
3. Further exercises could be found on P. Marcellini e C. Sbordone, Esercitazioni di Matematica, vol. 1 parte prima e vol. 2 parte seconda, ed. Liguori.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Integration, about 15 hours | 1 |
| 2 | Differential equations, about 9 hours | 1 |
| 3 | Series about 14 hours | 1 |
| 4 | Real functions of two real variables: limits, continuity and differential calculus , about 16 hours | 1 |
Learning Assessment
Learning Assessment Procedures
The final exam consists in a written test and an oral exam.
P.C. should be carried out only in presence. The final exam could be carried out electronically, should conditions require it.
Final grades will be assigned taking into account the following criteria:
Rejected: Basic knowledges have not been acquired. The student is not able to solve simple exercises.
18-23: Basic knowledges have been acquired. The student solves simple exercises and has sufficient communications skills and making judgements.
24-27: All the knowledges have been acquired. The student solves all the proposed exercises making few errors and has good communications skills and making judgements.
28-30 cum laude: All the knowledges have been completely acquired. The student applies knowledge and has excellent communications skills, learning skills and making judgements.