First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
MATHEMATICAL ANALYSIS 1 (Iniziali cognome M-Z)
SC05100190, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2018/19
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Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS 1
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance
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 GIULIA TREU MAT/05

Course unit code Course unit name Teacher in charge Degree course code
SC05100190 MATHEMATICAL ANALYSIS 1 (Iniziali cognome M-Z) GIULIA TREU SC1158

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/05 Mathematical Analysis 8.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 5.0 40 85.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
9 Analisi Matematica 1 01/10/2018 30/11/2019 TREU GIULIA (Presidente)
VITTONE DAVIDE (Membro Effettivo)
8 Analisi Matematica 1 01/10/2018 30/11/2019 VITTONE DAVIDE (Presidente)
TREU GIULIA (Membro Effettivo)
7 Analisi Matematica 1 01/10/2017 30/11/2018 VITTONE DAVIDE (Presidente)
MARASTONI CORRADO (Membro Effettivo)

Prerequisites: The contents of a precalculus course.
See for instance
Precalculus: the Mathematics of Numbers, Functions and Equations:

Advanced Precalculus: Geometry, Trigonometry and Exponentials
Target skills and knowledge: Ability of developing basic arguments about the topological properties
of the real line and the completeness axiom.

Computations with complex numbers: trigonometric forms, n-th roots.

Limits and continuity: computation of limits and study of the
continuity of a function. Knowledge of the fundamental results' proofs
(Bolzano's and intermediate value theorems).

Differential calculus: study of the derivative of a function and
mastery of the basic results of differential calculus (monotonicity
vs. sign of the derivative, convexity study). Ability to perform a
function study. Applications to the calculus of limits (Taylor
formula, de l'Hôpital rule).

Integration: ability to integrate basic functions and to utilize the
formulas for integration by substitution and by parts. ability of
integrating rational functions. Knowledge of the meaning of the
integral of a function (Riemann sums, areas). Mastery of the
Fundamental Theorem of Calculus.

Differential equations. Mastery of the tecniques for solving
differential equations with separation of variables, 1st order linear
equations, 2nd order linear equations with constant coefficients.
Knowledge of the meaning of a Cauchy problem.
Examination methods: The exam takes place in written form in one of the dates indicated on Uniweb.
Alternatively, the student will be able to perform in their place, two intermediate tests.

Some questions will focus on theoretical topics, both in the form of short proofs and exercises: they require mastering the theory performed in class.
Assessment criteria: The written test evaluates 3 components:
1) Calculus: in this part the student must show the ability to perform simple exercises on the concepts seen in class.
2) Medium-difficulty exercises that require reasoning.
3) Theory: questions on topics of theory and definitions: it is required that the student knows the definitions and carry out the demonstrations of the results seen in class. a part of the score on this aspect is dedicated to the resolution of theoretical exercises.

We strongly iencourage students to try to pass the exam within the first session.

Students who obtain a grade equal to or greater than 30 are offered the possibility of integrate the exam that may consist of a theoretical exercise or an oral test in orfder to obtain the Lode.
Course unit contents: NUMBER SETS
Elements of number theory. Induction. Natural, integer, and rational
numbers. The real line, completeness, max, min, inf, sup. Complex
numbers and complex roots. Topology of the real line.

Real functions, notion of limit and properties of limits.

Sequences and countable sets. Limit of a sequence. Topology vs.
sequences. Monotone and recursive sequences.

Definition of continuity for real functions. Bolzano and Weierstrass
theorems. Uniform continuity.

Differentiation. Monotonicity and classical theorems. L'Hôpital's
rule. Higher derivatives and convexity. Taylor formula. Function

Riemann integral. Primitives and integration techniques. Area of planar regions.

Generalites. Cauchy problems and qualitative studies. First order
differential equations, separation of variables. Linear differential
equations: generalities, the second order case with constant
Planned learning activities and teaching methods: The course consists of a traditional front part enriched with an online part, including files, quizzes, videos and other multimedia material, on the official university e-learning platform (Moodle)
Additional notes about suggested reading: The course content will be present entirely on the Moodle e-learning platform on pdf and / or multimedia files.
On this platform the student will also find test quizzes and a guide on the study path of the topics, week by week.
The textbooks and exercises suggested by the teacher remain essential.

A text of the teacher's exercises in pdf format will be provided for free.
Textbooks (and optional supplementary readings)
  • Giusti, Enrico, Analisi matematica 1Enrico Giusti. Torino: Bollati-Boringhieri, 2002. Cerca nel catalogo
  • Giusti, Enrico, Esercizi e complementi di analisi matematicaEnrico Giusti. Torino: Bollati Boringhieri, 1991. Cerca nel catalogo
  • De Marco, Giuseppe, Analisi uno: primo corso di analisi matematicateoria ed esercizi. Padova: Decibel, Bologna, Zanichelli, 1996. Cerca nel catalogo
  • --, MyMathLab Analisi 1. --: Pearson, --. Palestra interattiva di esercizi ISBN 9788865185148

Innovative teaching methods: Teaching and learning strategies
  • Problem based learning
  • Questioning
  • Action learning
  • Flipped classroom
  • Active quizzes for Concept Verification Tests and class discussions
  • Video shooting made by the teacher/the students
  • Use of online videos
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Kaltura (desktop video shooting, file loading on MyMedia Unipd)
  • Video shooting in studio (Open set of the DLM Office, Lightboard, ...)
  • Camtasia (video editing)
  • Top Hat (active quiz, quiz)
  • Latex
  • Mathematica

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