65934 - Principles of Mathematics 2

Learning outcomes

At the end of the course, the student will know the basic tools of multivariate calculus; he knows how to calculate simple curvilinear integrals and double integrals; he is also able to solve certain types of Ordinary Differential Equations (ODE) and systems of ODE. He also has knowledge of the basics of probability and statistics in order to analyze data and he is able to study the behavior of samples of a random variable.

Course contents

PART ONE:
R^N: vectors, distance, topology, limit, continuity;
partial derivatives and differentiability; Jacobian and Hessian matrices;
free extremals; line integrals and the theorem of Poincaré;
double integrals and change of variable;
ODE: general theorems, linear ODE of the first order; separation of variables; ODE of second order with constant coefficients;
Some introductory material to the stability of systems.

PART TWO:
Descriptive Statistics. Organization and description of data.
Probability. Sample space and events. Axioms of probability theory.
Conditional probability. Independent events. Discrete and continuous random variables. Expected value and variance. Models of random variables. Central Limit Theorem.

S. Ross, Probabilità e statistica per l'ingegneria e le scienze, 2nd ed. (2008), Apogeo

Readings/Bibliography

PRIMA PARTE:
Dispense del Prof. Bonfiglioli presenti sul sito di Scienze Ambientali;
libro: "Analisi matematica. Vol. 2", di Pagani C, Salsa S.
Zanichelli, 1991

SECONDA PARTE:
S. Ross, Probabilità e statistica per l'ingegneria e le scienze, 2nd ed. (2008), Apogeo

Teaching methods

PART ONE:
Classroom lessons and classroom exercises.

PART TWO:
Classroom lectures and recitations.

Assessment methods

PART ONE:
written examination.

PART TWO:
written examination.

Teaching tools

Learning module: Analysis
Teaching material (photocopies, files, notes) distributed in class or on the website;
exercises assigned in class or from the website.

Learning module: Statistics:
Web site for the learning module "Probability and Statistics":

http://www.dm.unibo.it/~lenci/teaching/15/ps/

Office hours

See the website of Andrea Bonfiglioli

See the website of Marco Lenci