CALCULUS - 1

This course belongs to the basic activities of the the Bachelor in Computer Science.
The course aims at providing students with the basic instruments of Calculus to analyse and sketch 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 problems arising in technology, science, economics and business.

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 calculus, integrals and derivatives.

2. (applying knowledge and understanding)
-- describe and use simple Mathematical Models;
-- compute the domain and codomain of a function;
-- compute the points of minimum and maximum, saddle points and the asymptotes of a function;
-- sketch the graph of one-variable functions;
-- compute the area under a graph;
-- apply the fundamentals of infinitesimal, integral and differential calculus.

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

Each student must know the fundamental concepts of Basic Mathematical Logic, Algebra and Trigonometry.

1. Functions, domain and codomain
2. Sequences and series
3. Real Functions
4. Limits, and fundamental theorems
5.Continuity and differentiability
6. Classical theorems of differential calculus
7. Higher order derivatives.
8. Graph of a function.
9. Taylor series.
10. Indefinite integrals
11. Definite integrals
12. Volume of solids of revolution

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

Examination Module 2: it consists of a written test (duration: two hours) with open-ended problems aimed at verification of all the course contents in order to evaluate the ability of students in solving exercises of Mathematical Analysis for functions of one variable.

No mid-term exams are planned. During the written test, the students are allowed to consult theory notes. The grade is given by the sum of the scores assigned to the single problems: every problem consists of some questions whose score is proportional to the intrinsic difficulty. The exam will be passed if and only if the minimum grade is 18. The maximum grade of the written test is 30. In the moodle page of the course, some written tests of the previous years will be posted. An oral exam is (absolutely) optional: the student must show that she/he knows the basic concepts introduced during the lessons and is able to explain them in a formal way. In this case, the overall result may include failure and the final grade can at most be three points higher than the one of the written test. The maximum grade, 30 summa cum laude, is assigned exclusively to the students who have passed the written test with at least 28 points and have demonstrated mastery of the theoretical aspects in the oral exam.

Indications for the final grade of Calculus.
Only the students that already passed the exam of Module 1 can take the exam of Module 2. It is possible to take both the modules 1 and 2 in the same day, in this rigorous succession. The final grade of Calculus is the average of the grades of 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 advised to pass both modules in the same academic year.

written and oral

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.