
Course unit
MATHEMATICAL ANALYSIS 1 (Iniziali cognome MZ)
SC05100190, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Practice 
3.0 
24 
51.0 
No turn 
Lecture 
5.0 
40 
85.0 
No turn 
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)
MONTEFALCONE
FRANCESCOPAOLO
(Supplente)
MONTI
ROBERTO
(Supplente)

8 Analisi Matematica 1 
01/10/2018 
30/11/2019 
VITTONE
DAVIDE
(Presidente)
TREU
GIULIA
(Membro Effettivo)
MARASTONI
CORRADO
(Supplente)
MONTEFALCONE
FRANCESCOPAOLO
(Supplente)
MONTI
ROBERTO
(Supplente)

7 Analisi Matematica 1 
01/10/2017 
30/11/2018 
VITTONE
DAVIDE
(Presidente)
MARASTONI
CORRADO
(Membro Effettivo)
MONTI
ROBERTO
(Supplente)

Prerequisites:

The contents of a precalculus course.
See for instance
Precalculus: the Mathematics of Numbers, Functions and Equations:
https://www.futurelearn.com/courses/precalculus
Advanced Precalculus: Geometry, Trigonometry and Exponentials
https://www.futurelearn.com/courses/advancedprecalculus 
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, nth 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) Mediumdifficulty 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 OF ONE VARIABLE AND LIMITS
Real functions, notion of limit and properties of limits.
SEQUENCES OF REAL NUMBERS
Sequences and countable sets. Limit of a sequence. Topology vs.
sequences. Monotone and recursive sequences.
CONTINUITY
Definition of continuity for real functions. Bolzano and Weierstrass
theorems. Uniform continuity.
DIFFERENTIATION
Differentiation. Monotonicity and classical theorems. L'Hôpital's
rule. Higher derivatives and convexity. Taylor formula. Function
study.
INTEGRATION
Riemann integral. Primitives and integration techniques. Area of planar regions.
BASIC ORDINARY DIFFERENTIAL EQUATIONS
Generalites. Cauchy problems and qualitative studies. First order
differential equations, separation of variables. Linear differential
equations: generalities, the second order case with constant
coefficients. 
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 elearning platform (Moodle) 
Additional notes about suggested reading:

The course content will be present entirely on the Moodle elearning 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: BollatiBoringhieri, 2002.

Giusti, Enrico, Esercizi e complementi di analisi matematicaEnrico Giusti. Torino: Bollati Boringhieri, 1991.

De Marco, Giuseppe, Analisi uno: primo corso di analisi matematicateoria ed esercizi. Padova: Decibel, Bologna, Zanichelli, 1996.

, 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
Sustainable Development Goals (SDGs)

