First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
MATHEMATICAL ANALYSIS 1 (Numerosita' canale 1)
IN10100190, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
IN0507, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track Common track
Number of ECTS credits allocated 12.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS 1
Department of reference Department of Information Engineering
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge FRANCO RAMPAZZO MAT/05

Course unit code Course unit name Teacher in charge Degree course code
IN10100190 MATHEMATICAL ANALYSIS 1 (Numerosita' canale 1) FRANCO RAMPAZZO IN0513

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 12.0 96 204.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 course timetable

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).
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. Cerca nel catalogo
  • Marson, Baiti, Ancona, Rubino, Analisi Matematica 1. Teoria e Applicazioni. Roma: Carocci, 2010. Cerca nel catalogo