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 Mathematical Analysis, concerning one-variable functions.

The aim of this course is to develop skills one needs to solve Differential and Integral questions 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 some basic concepts in 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;
-- draw the graph of one-variable functions;
-- compute the area under a graph;

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

-- 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 notes will be available in the moodle page.

The examination is aimed to test the ability of each student in solving exercises of Mathematical Analysis for functions of one variable.
The evaluation is performed by open answer problems.
The grade is given by the sum of the scores assigned to the single problems. The exam will be passed if and only if the minimum grade is 18. The maximum grade of the written test is 30. An oral exam is (absolutely) optional: 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. In any case, students must pass the exams of both modules in the same academic year. Otherwise, any passing grade achieved in Module 1 will be cancelled.

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

written and oral