
Course unit
MATHEMATICAL ANALYSIS 1 (Numerosita' canale 1)
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:

Number sets. Prime numbers. Linear and quadratic equations/inequalities and simple systems. Polynomials and their factorization. Exponentials and logarithms. Trigonometric concepts and functions. Euclidean geometry (axioms, criteria for triangles) and analytic geometry (lines, circles, ellypses, parabolas and hyperbolas, tangency conditions). 
Target skills and knowledge:

Learning mathematical language and basic techniques of one variable mathematical analysis, including limits of functions and sequences, convergence of series, differentiation and (Riemann and generalized) integration. 
Examination methods:

Written and oral exam. 
Assessment criteria:

Correct and well justified calculations. Mastering definitions (including formal definitions of limit) and some basic proofs. 
Course unit contents:

Sets and functions.
Natural numbers and induction.
Real numbers, infimum and supremum.
Elementary functions and inequalities.
Complex numbers.
Basic topology: neighborhood, open and closed sets.
Limits and basic properties (with rigorous statements and proofs).
Sequences.
Landau's o, O, and ~. Classical limits.
Number series and their convergence.
Continuous functions and their basic properties.
Derivative and their basic properties (with rigorous statements and proofs).
Higher order derivatives and convexity test. Graphing a function.
Riemann integral and computations of real integrals.
Generalized integrals and their convergence. 
Planned learning activities and teaching methods:

Lectures and homeworks. Possibly, some demonstrations using appropriate formal calculus software. Students are encouraged to attend office hours (two hours per week held by the instructor). 
Additional notes about suggested reading:

The course web site contains further exercises and exam tests.
Several other textbooks with similar contents are available. Every lesson, usually teached using a tablet, will be uploaded on the course web site. 
Textbooks (and optional supplementary readings) 

Bramanti, Pagani, Salsa, Analisi Matematica1. Bologna: Esculapio, 2011.

Marson, Baiti, Ancona, Rubino, Analisi Matematica 1. Teoria e Applicazioni. Roma: Carocci, 2010.


