
Course unit
MATHEMATICAL ANALYSIS
SCP4063959, 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 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
8.0 
64 
136.0 
No turn 
Prerequisites:

Basic elements of Calculus (inequalities, cartesian coordinates, trigonometric, logarithmic, and exponential functions). 
Target skills and knowledge:

The goal of the course is to introduce the basic principles of mathematical analysis for functions of one real variable, with particular care for differential and integral calculus. 
Examination methods:

The exam consists of two parts: the first one tests practical problemsolving ability, the second one checks the knowledge of the theory behind the exercises.
These two parts can be passed in the same exam or in two consecutive exams within the same session. 
Assessment criteria:

Understanding of the theory and ability to solve exercises
In particular, the student is asked
1) to be able to use the mathematical language correctly
2) to be able to prove a certain number of theorems in a rigorous way
3) to develop a critical approach that allows him/her to identify errors in faulty mathematical reasoning. 
Course unit contents:

Number sets (natural, integer, rational, real and complex). Euclidean plane and space (vectors in the plane and in the space; equations of lines and planes). Real Sequences. Limits and Derivatives of functions of one real variable. Basic theorems of differential calculus. Taylor's formula. Relative and local maxima and minima. Graphs of realvalued functions. Definite and indefinite integrals. Integration methods. Improper integrals. Numerical series. First order differential equations: linear and separable equations. Some introductory notions of Calculus of several variables. 
Planned learning activities and teaching methods:

The teaching method is based on traditional classroom lessons. During the semester there are partial exams.
If the student has a sufficient score in all of them, then the final grade of the exam will be the average of the scores on the partial exams.
Each week a quiz is assigned which, if carried out correctly within the set time limits, entitles the holder to a bonus on the score of the examination of the first call or on that of the partial exams.
In addition, the teacher and another collaborator will offer two hours of support per week for the preparation of the course. In these two hours the students, who wish to participate, will be divided into groups, and will try to solve the exercises that the teacher has proposed in class or proposes at the moment. 
Additional notes about suggested reading:

Further bibliographical references will be given during the course. All the material presented in the class is available in the Newsgroup of the course MOODLE 
Textbooks (and optional supplementary readings) 

LUCA BERGAMASCHI, Fondamenti di Analisi Matematica 1. : Ed. Libreria Progetto, via Marzolo 2, 2017.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Working in group
 Problem solving
 Auto correcting quizzes or tests for periodic feedback or exams
 Active quizzes for Concept Verification Tests and class discussions
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 One Note (digital ink)
 Kaltura (desktop video shooting, file loading on MyMedia Unipd)
 Top Hat (active quiz, quiz)
 Latex
 Mathematica

