
Course unit
MATHEMATICAL ANALYSIS 1 (Ult. numero di matricola pari)
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:

Real and rational numbers: elementary properties.
Algebra of polynomials. Absolute values of real numbers.
Basics on powers and logarithms.
Rational and irrational equations and inequalities.
Systems of equations and inequalities.
Lines, circles, ellipses, parabolas and hyperbolae in the Euclidean plane.
Basics on trigonometric functions (sinus, cosinus, tangent, cotangent),
ONLINE PRECALCULUS COURSE
https://www.futurelearn.com/courses/precalculus 
Target skills and knowledge:

The aim of this course consists in learning basic notions of Mathematical Analysis.
At the end of the course, a student should be able to consciously apply the classical methods of Mathematical Analysis both to compute limits of sequences and functions
and to solve derivability and integrability questions. 
Examination methods:

The exam will mostly consist in two parts, usually one just after the other:
1. Answering about three questions on the theoretical part of the course (usually, a definition, a statement of a theorem, a proof).
2. Solving about three or four problems.
During the semester there will be weekly assignments, which could help in the preparation of the final final written exam. 
Assessment criteria:

The final evaluation will take into account both the theoretical notions acquired during the course, and the competences in problem solving proved in the second part of the exam.
We strongly recommend an active participation in the lessons and in the office hours. 
Course unit contents:

Set theory. Number sets: Natural Numbers, Integers, Real Numbers.
Basics in Combinatorial Calculus. Maximum, minimum, infimum and supremum of number sets. Functions of one real variable: elementary functions, limits, continuity, monotonicity, invertibility.
Sequences of number, bounded sequences, monotone sequences. Limit of a sequence.
Differential calculus in one real variable, convexity and concavity. Taylor expansions with applications to limits and to compute derivatives. Local study of functions.
How to draw the graph of a function.
Number series. Convergence criteria.
Riemann integrals in one real variable: definite and indefinite integration.
Generalized integrals.
Introduction to calculus in several variables, various notions of differentiability. 
Planned learning activities and teaching methods:

Lectures, exercise classes, individual and/or group study and practice with weekly assignmenets, tutorial activities.
We also refer to the website http://static.gest.unipd.it/mateinrete/, where past exam texts may be found. 
Additional notes about suggested reading:

Rough notes and exercises from lectures are available in Moodle almost daily or weekly during the course.
Any standard book on calculus could be used.
A library is also available close to classrooms. 
Textbooks (and optional supplementary readings) 

Bramanti, Marco; Salsa, Sandro, Analisi matematica 1. Bologna: Zanichelli, . NON E' OBBLIGATORIO ACQUISTARE QUESTO LIBRO (vedi "Eventuali indicazioni sui materiali di studio").

Bramanti, Marco, Esercitazioni di analisi matematica 1. Bologna: Esculapio, . NON E' OBBLIGATORIO ACQUISTARE QUESTO LIBRO (vedi "Eventuali indicazioni sui materiali di studio").

Innovative teaching methods: Teaching and learning strategies
 Problem solving
 Flipped classroom
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex

