Elements of Mathematical Analysis 1 A - E

1. Knowledge and understanding: The student will be able to understand and assimilate the definitions and main results of the basic mathematical analysis for functions of several real variables, necessary for the treatment and modeling of problems deriving from applied sciences.

2. Applying Knowledge and understanding: The student will be able to acquire an appropriate level of autonomy in theoretical knowledge and in the use of basic analytical tools. 3. Making judgments: Ability to reflect and calculate. Ability to apply the notions learned to solving problems and exercises. 4. Communication skills: Ability to communicate the notions acquired through an adequate scientific language. 5. Learning skills: Ability to deepen and develop acquired knowledge. Ability to critically use tables and analytical and computer tools of symbolic computation. PLEASE NOTE: Information for students with disabilities and / or SLI To guarantee equal opportunities and in compliance with the laws in force, the interested students can ask for a personal interview so to program any compensatory and / or dispensative measures, according to the didactic objectives and specific needs. It is also possible to contact the referent of CInAP (Centro per l’integrazione Attiva e Partecipata - Servizi per le Disabilità e/o i DSA) of the Department.

1. Number sets and general notions about functions.

2. Limits of sequences and functions.

3. Continuous functions and their properties.

4. Differential calculus.

5. Applications of differential calculus.

A detailed outline of the course will be given at the end of it.

Any argument contained in the latter can be asked during the final exam.

2. Lessons dictated in class by the teacher 

Learning will be constantly monitored through student interview in class. 

The final exam consists of a written test to be taken in one of the scheduled exam sessions. It lasts 90 minutes and is made up of a theoretical part (T) and a practical part (E).

Part T consists of two questions, part E consists of two technical exercises. 

Evaluation: in part T a maximum of ten points can be achieved, in part E a maximum of twenty points. The evaluation takes into account both correctness and clarity of presentation. To pass the written test it is necessary to obtain at least six points in part T and at least twelve points in part E. 

The result of the test will be communicated within a few days of the test itself on the Studium portal. 

However, the presence of the student will be necessary for the verbalization, who will be able to accept the grade obtained or choose to withdraw. 

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; solves the exercises completely and without errors.

To participate in the exam you must have booked on the SmartEdu portal.

The final assessment of learning can also be carried out electronically, should conditions require it. In this case, it will consist of an oral interview, lasting a maximum of 20 minutes, including both theory questions and the carrying out of some exercises.

For the theoretical part:

statement of a theorem in correct language

proof of a theorem or a proposition

definition of a mathematical entity

production of an example verifying given properties

production of a counterexample to a given implication

determination of a true statement between some dates

For the practical part: 

determination of the extrema of a numerical set

study of a function

calculation of the tangent line to a given function at a point on its graph

determination of a limit, possibly dependent on a parameter

verification of a given asymptotic comparison

calculation of the limit of a sequence defined by recurrence

resolution of an equation in the field of complex numbers

verification of a given inequality with a graphical method

determination of the absolute extrema of a function

derivative of the inverse function at a given point