
Course unit
MATHEMATICAL ANALYSIS 1 (Ult. numero di matricola dispari)
IN10100190, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/05 
Mathematical Analysis 
12.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
12.0 
96 
204.0 
No turn 
Prerequisites:

Algebra of polynomials and of quotients of polynomials. Systems of equations and inequalities. Lines, circles, ellipses, parabolas and hyperbolae in the Euclidean plane. Basics on trigonometric functions (sinus, cosinus, tangent, cotangent), equations and inequalities involving these functions.
ONLINE PRECALCULUS COURSE *GRATIS*
https://www.futurelearn.com/courses/precalculus 
Target skills and knowledge:

The aim of this course consists of
 learning concepts at the very basis of Mathematical Analysis, that will be needed for example for modelling purposes;
 mastering cosciently the elementary techniques for solving basic exercises on the different topics that will be presented. 
Examination methods:

The exam will mostly consist in two parts, usually one just after the other:
1. Answering about three questions on the theory covered during the course.
2. Solving about three or four problems.
During the semester there will be weekly assignments, which could contribute to the final evaluation. These assignments will be fundamental for preparing the final written exam. 
Assessment criteria:

Richness, correctness, clearness and consistency of answers and explanations.
The final evaluation will be determined by an average of the evaluation of
1. the knowledge of the theory, as demostrated by the student in the first part of the exam, and
2. the competences in problem solving, as demostrated in the second part of the exam.
All parts of the final assessment should be sufficient in order to pass the exam. The commitment shown during the term might also contribute to the final evaluation.
In case of doubts, an additional mandatory colloqium will be required by the professor. 
Course unit contents:

Number sets: Natural Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers.
Basics in Combinatorial Calculus and Set Theory.
Maximum, minimum, infimum and supremum of number sets.
Sequences of number, orders of inifinities and of infinitesimals.
Functions of one real variable: elementary functions, limits, continuity, monotonicity, invertibility. Differential calculus in one real variable, convexity and concavity. Taylor expansions with applications to limits and to compute derivatives. Study of functions.
Number series.
Riemann integrals in one real variable: indefinitive, proper and generalized integrals.
Introduction to calculus in several variables, mostly two. 
Planned learning activities and teaching methods:

Lectures, exercise classes, individual and/or group study and practice with weekly assignmenets, tutorial activities, online quiz and online numerical open questions. 
Additional notes about suggested reading:

Rough notes and exerciese from lectures are available in Moodle almost daily or weekly during the course.
Standard books on calculus could be used.
A library is also available close to classrooms.
Online precalculus course *gratis*:
https://www.futurelearn.com/courses/precalculus 
Textbooks (and optional supplementary readings) 


