# Mathematics

Degree course:
Corso di First cycle degree in ENVIRONMENTAL AND NATURAL SCIENCES
Academyc year when starting the degree:
2016/2017
Year:
1
Academyc year when helding the course:
2016/2017
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 Separati
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.