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. Improper integrals

-- 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)

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.

During the course, students are invited to perform three tests with multiple-choice answers, which allow to give up to 2 bonus points to the grade of the exam.

To obtain a grade higher than 27 it is mandatory to take an oral exam, where the student's preparation on the theory will be evaluated. The oral exam is optional for the other students. Students with grades 15, 16 or 17 can take the oral exam to try to obtain a sufficient grade.

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

Italian

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