CALCULUS-2

This course belongs to the basic activities of the Bachelor in Computer Science.
The course aims to illustrate the primary tools of integral calculus for functions of one and two variables

The objective of the course is to develop the skills necessary to address integral calculus problems arising in technological, scientific, and computer science contexts.

Regular and active participation in the teaching activities offered by the Course, together with independent learning activities, will enable students to:
1. (knowledge and understanding)
-- acquire knowledge and understanding regarding basic mathematical elements of the continuum and deductive reasoning.
-- acquire knowledge and understanding regarding some basic concepts of Calculus.

2. (applying knowledge and understanding)
-- evaluate the convergence of basic numerical series;
-- solve simple ODEs;
-- draw traces and level curves of two-variable functions;
-- compute the integral of one or two-variable functions;
-- apply the fundamental elements of infinitesimal, integral and differential calculus.

3. (making judgements)
-- correctly understand Math statements concerning bivariable functions.

The students are supposed to know the main concepts of the courses Calculus Module 1 and Linear Algebra.

Students must pass the Module 1 exam before they are eligible to sit the Module 2 exam.

Numerical series.
Indefinite integrals and integration methods.
Definite integrals and the Fundamental Theorem of Calculus
Improper Integrals
Basic, first order ordinary differential equations..
Basic notions for two-variables functions: domain, traces and level curves,
Partial derivatives and gradient.
Two-dimensional integrals and reduction methods; rule of change of variables.

It is recommended to study on the material provided in the moodle page of the course

The following books can be helpful:

M. Bertsch, R. Dal Passo, L. Giacomelli. Analisi Matematica. McGraw-Hill, Milano 2007
Bramanti Pagani Salsa. Analisi Matematica 2, Zanichelli
Salsa Squellati. Esercizi di Analisi Matematica 2. Zanichelli

Module 2 Exam: The exam consists of a written test with a maximum duration of one hour and 45 minutes. It includes open-ended problems designed to assess the student's mastery of the analytical tools and problem-solving techniques presented during lectures. No mid-term exams are planned. During the exam, students may consult a single A4 sheet containing theoretical notes and formulas. The use of a non-programmable calculator is also permitted. Sample past exam papers will be published on the course Moodle platform for practice purposes. The total score is the sum of the points assigned to individual problems. Each problem consists of several questions, with points allocated proportional to their intrinsic difficulty. A minimum score of 18 is required to pass. A grade of "30 summa cum Laude" is awarded for scores strictly exceeding 30.

Indications for the final grade of Calculus.
Please note that both Module 1 and Module 2 exams are partial exams. Only students who have already passed the Module 1 exam can take the Module 2 exam. It is possible to take both modules on the same day, but strictly in the following order: Module 1 and then Module 2. The final grade of Calculus is the average of the grades from the two modules, with approximation by excess. The maximum grade of Calculus, 30 summa cum laude, is assigned with the full agreement of both the teachers only. The grade of the first module is valid until the second module is passed: however, students are strongly encouraged to complete both modules within the same academic year.

written

The lecturer has a duty to ensure that the rules regarding the authenticity and originality of exam tests and papers are respected. Therefore, if there is suspicion of irregular conduct, an additional assessment may be conducted, which could differ from the original exam description.

Assessment grid:

A. range 18-22
- sufficient knowledge and understanding of the program;

B. range 23-26
- fair knowledge and understanding of the program;
- fair rigor in conducting the exercises;

C. range 27-30
- good knowledge and understanding of the program,
- good rigor in conducting the exercises;

D. honors will be awarded in the presence of excellent knowledge and understanding of the program.

Classroom lessons and exercises. The moodle platform is exploited, in order to deliver supplementary material.