# MATEMATICA STATISTICA

9 CFU - 1° Semester

FABIO RACITI

## Learning Objectives

• Mathematics

basics on mathematical logic and real numbers basics on linear systems of equations basics on lines and curves on the plane basics on limit of a function basics on differential calculus applied to the study of the graph of a function

• STATISTICA

Basics of statistics

## Detailed Course Content

• Mathematics

1. I Real Numbers and functions *. Elementary set theory. Axioms of real numbers. Integer and rational numbers. It does not exist any rational number \$c\$ such that \$c^2 =2\$. Density of rational numbers in \$\R\$. Theorem on the n-root of a positive number. Algebraic equation \$x^n = a\$. Functions and diagrams. Absolut value. Powers, exponentials and logarithms, and related inequalities. Absolute maximum and minimum of a function.

2. LINEAR ALGEBRA *. Matrices and determinants. Matrix operations. Determinants. Linear systems. Cramer and Rouche-Capelli. Theorems, Homogeneous systems.

3.ANALYTIC GEOMETRY *. Points and lines in the plane. Distance point-line.. Parallelism and orthogonality between lines. Elements of Trigonometry.

4. Limits of Sequences and Functions *. Limit of a sequence and of a function. Recursive sequences. Right and left limits. Teorem of uniqueness of limit. Algebraic operations with limits. Indeterminate forms. Important limits. Limites of compositions. Continuous functions. Continuity of elementary functions. Neper's number and related limits.

5. Differential calculus *. Concept of derivative. Points of non-differentiability. Relationship between differentiability and continuity. Algebraic operations with derivatives Derivatives of elementary functions. Derivative of a composition. De L'Hopital rule. Relative maximum and minimum.Increasing and decreasing functions on intervals. Derivatives and monotone functions. Search for maximum and minimum of a function. Concavity and convexity of a function. Asymptots. Study of the graph of a function.

• STATISTICA

Linear regression, Aritmetic mean. Variance and standard deviation.Least square method. Correlation.

## Textbook Information

• Mathematics

1) Alessio, Fabritiis, Marcelli, Montechiari, Matematica zero, Pearson, 2016

2) Marcellini-Sbordone, Elementi di Calcolo, Liguori Editore, 2002

3) Sheldon M Ross, Probabilità e statistica per l'Ingegneria e le Scienze, Apogeo, 2003

• STATISTICA

1) Alessio, Fabritiis, Marcelli, Montechiari, Matematica zero, Pearson, 2016

2) Marcellini-Sbordone, Elementi di Calcolo, Liguori Editore, 2002

3) Sheldon M Ross, Probabilità e statistica per l'Ingegneria e le Scienze, Apogeo, 2003

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