- Docente: Daniele Ritelli
- Credits: 10
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Statistical Sciences (cod. 8873)
Learning outcomes
The aim of the course is to provide the capability of the
student to face both theoretical and practical problems in
Mathematical Analysis, referring to the analysis of the behavior of
a real function of a real variable, computation of definite
integrals, development of a function in power series.
Course contents
Crash course contents
http://www.ems.unibo.it/it/corsi/insegnamenti/insegnamento/2018/423368
are intended as known and will be freely used during the whole course
The set R of real numbers. The main subsets of R: Natural, Integers and Rational numbers. Completeness axiom. Archimedean property. Mathematical Induction. Factorial and binomial coefficients, Newton formula. Bernoulli inequality. Arithmetic Geometric inequality.
Real functions. Limits and elementary functions. Asymptotics and Landau symbols. Continuous functions. Bolzano theorem on intermediate value and Weierstrass theorem on maxima and minima.
Derivatives. Theorems of Rolle, Lagrange, Cauchy and De l'Hopital. Graph of a function, extrema. Convex and concave functions. Inflexion points. Asymptotes. Taylor polynomials and series.
Riemann integral. Fundamental theorems of Calculus. Integration methods. Improper integrals
Sequences and Series. Limit of a sequence. Monotonic sequences and the number e. Cesaro Stolz Theorems. Geometric series. Series with positive terms and convergence tests. Series with alternating terms.
Complex Numbers. Algebraic representation of a complex number. The complex plane. Trigonometric form. De Moivre formulas.
Ordinary Differential Equation. Introduction to elementary differential equation of first order: separable and linear.
Readings/Bibliography
Daniele Ritelli. Lezioni di Analisi Matematica. Esculapio
2015 ISBN: 9788874888870
Marco Bramanti. Esercitazioni di Analisi Matematica 1. Esculapio ISBN: 9788874884445
Robert Carlson. A Concrete Introduction to Real Analysis, second edition. 2018 CRC Press ISBN 9781498778138
Teaching methods
Lessons ex cathedra using also video beamer. Homework. Computer
algebra will also be employed to support thoretical
arguments.
Assessment methods
Written examination of 2 hours, where is
possible to use calculators and books. The exam is completed by an
oral examination if the written examination is satisfactory. The
aim of the exam is to detect the capability of the student to face
both theoretical and practical problems in Mathematical Analysis.
The written examination can be divided, for the first call, in to
two partial examinantion and is composed by multiple choice
questions and solution of
exercises.
Teaching tools
Video beamer and blackboard. Computer algebra to illustrate
important topics.
Links to further information
https://www.dropbox.com/s/h4occ96pmiae1ws/CV_dr.pdf?dl=0
Office hours
See the website of Daniele Ritelli