CALCULUS - 1

This course belongs to the curricular activities of the the Bachelor in Computer Science.

The course aims at providing students with the basic instruments of Calculus to analyse and scatch the graph of real functions of one real variable.

The aim of this course is to develop skills one needs to solve Differential and Integral questions arising in technology, science, and computer science.

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 continuum and deductive reasoning;
-- acquire knowledge and understanding regarding basic concepts of Mathematical Analysis concerning one-variable functions.
-- acquire knowledge regarding infinitesimal and differential calculus.

2. (Applying knowledge and understanding)
-- compute the domain and codomain of a function;
-- compute the points of minimum and maximum, saddle points and the asymptotes of a function;
-- draw the graph of one-variable functions;
-- apply the fundamentals of infinitesimal and differential calculus.

3. (Making judgements)
-- correctly understand mathematical statements concerning one-variable functions.

Basic mathematical notions, as acquired in a high school or in the Basic Mathematics course. In particular: cartesian coordinates, trigonometric functions, logarithms and exponentials, solution of equations and inequalities.

1. Real numbers and elements of topology.
2. Sequences and limits of sequences.
3. Functions of a real variable and elementary functions.
4. Definition of limit, algebra of limits, and notable limits.
5. Continuity and differentiability of functions of a real variable.
6. Local properties and theorems of differential calculus.
7. Higher-order derivatives and finding minima, maxima, and inflection points.
8. Function analysis and graphing.
9. Taylor polynomials, infinites and infinitesimals.

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

Additional notes freely available online:
-- Luciano Battaia, Introduzione al Calcolo differenziale http://www.batmath.it/matematica/0-appunti_uni/testo_analisi.pdf
-- Per il calcolo integrale: Luciano Battaia, Appunti per un corso di matematica http://www.batmath.it/matematica/0-appunti_uni/corso-ve.pdf (chapter 7)

Other suggested textbooks:
-- Pagani Salsa. Analisi Matematica 1, Zanichelli
-- Salsa Squellati. Esercizi di Analisi Matematica 1. Zanichelli

The exam consists of a written test with open-ended problems aimed at assessing students’ ability to solve problems covered during the course. No midterm tests are scheduled.
The written test lasts 1 hour and 45 minutes.
During the written test, students may consult one A4 sheet containing a formula sheet and may use a non-programmable pocket calculator.
Some sample exams from previous years will be made available on the course Moodle platform for reference.
The grade for the test is given by the sum of the points assigned to each problem: each problem consists of several questions, whose score is proportional to their intrinsic difficulty.
The exam is passed with a minimum score of 18. Honors (lode) are awarded for scores strictly above 30.

Guidelines for the final grade in Calculus:
Both Module 1 and Module 2 exams are partial exams.
Only students who have passed the Module 1 exam may take Module 2.
It is possible to take both Module 1 and Module 2 on the same day, in this strict order.
The final grade for the Calculus exam will be the average of the grades of the two modules (rounded up).
Honors (lode) for the final grade are awarded only with the unanimous approval of both instructors.
The grade for Module 1 remains valid until Module 2 is passed; however, students are strongly advised to pass 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.