Mathematical analysis (2016/2017)

Course code
4S00006
Name of lecturers
Simone Ugolini, Alberto Benvegnu'
Coordinator
Simone Ugolini
Number of ECTS credits allocated
6
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
Italian
Location
VERONA
Period
I sem. dal Oct 3, 2016 al Jan 31, 2017.

Lesson timetable

I sem.
Day Time Type Place Note
Monday 8:30 AM - 10:30 AM lesson Lecture Hall Gino Tessari  
Tuesday 8:30 AM - 10:30 AM lesson Lecture Hall Gino Tessari from Oct 3, 2016  to Jan 23, 2017
Thursday 8:30 AM - 10:30 AM lesson Lecture Hall Gino Tessari  

Learning outcomes

The course aims to introduce differential and integral calculus in one real variable.

Syllabus

1) Some notions of set theory.
2) The complete ordered field of the real numbers. Subsets of R. Complex numbers.
3) Euclidean distance and induced topology on the real line. Absolute value of a real number. Cartesian plane.
4) Real functions of one real variable.
5) Polynomials and polynomial functions. Power, exponential and logarithmic functions. Trigonometric functions.
6) Sequences.
7) Limit of a function of one real variable.
8) Continuity of a function of one real variable at one point. Fundamental theorems on continuos functions.
9) Derivative of a function. Derivation rules. Fundamental theorems on differentiable functions.
10) Monotonicity of a function. Local and global minima and maxima of a function.
11) Convex functions.
12) Taylor polynomials.
13) Riemann integral. Integration rules. Improper integrals.

Reference books
Author Title Publisher Year ISBN Note
M.Bramanti,C.D.Pagani,S.Salsa Analisi Matematica 1 Zanichelli 2009 978-88-08-06485-1

Assessment methods and criteria

The exam is written. It consists of open-ended questions. Any topic covered during the lectures will be part of the exam program. Detailed information about the program of the course can be retrieved from the slides of the lectures, which can be found in the e-learning webpages. An intermediate test will take place during the first semester.

STUDENT MODULE EVALUATION - 2016/2017