# Mathematics

Degree course:
Corso di First cycle degree in ENVIRONMENTAL AND NATURAL SCIENCES
Academyc year when starting the degree:
2017/2018
Year:
1
Academyc year when helding the course:
2017/2018
Course type:
Basic compulsory subjects
Credits:
9
Period:
First Semester
Standard lectures hours:
72
Detail of lecture’s hours:
Lesson (72 hours)
Requirements:

None

Final Examination:
Scritto e Orale Congiunti

Examinations consists in a written and oral oral part.

Assessment:
Voto Finale

Acquisition of theoretical and operational capabilities in the field of differential and integral calculus
Acquisition of rudiments of Probability and Statistics

Real numbers:
Elementary properties of real numbers. Absolute value. Power and logarithm. Sup and Inf.

Functions and Limits:
Monotone functions. Limits and their property. Continuity and properties of continuous functions.
Basic functions - Trigonometric functions, exponential, hyperbolic and their inverses.

Calculus:
Derivatives of a real function and their properties. Theorems of Rolle, Lagrange and Cauchy. Computation of limits by the l’Hopital’s rule. Taylor polynomials.

Integral calculus:
Definite integrals. Integration of continuous functions. Integral functions. First and Second Fundamental Theorem of Calculus. Indefinite integrals. Integration by parts and by substitution.

Statics and probability:
Populations and samples. Different types of statistics: descriptive, inferential, parametrics and non-parametrics.
Probability and probability distributions. Measures of statistical dispersion: variance, standard deviation and intervals of variation.
Classes and types of statistical variables: mean, median, mode and multimodal distributions.
Graphical representations of data.
Statistic significance: basic notions about statistical tests and errors.

Indications will be given during the lectures.

Lectures include exercises

Studens can meet the instructor for assistance at the end of each classroom lecture or requesting a meeting by email or phone.