# MATHEMATICS AND STATISTICS

**Academic Year 2018/2019**- 1° Year

**Teaching Staff:**

**Mario Pennisi**

**Credit Value:**6

**Taught classes:**21 hours

**Exercise:**42 hours

**Term / Semester:**1°

## Learning Objectives

To acquire adequate knowledge of the main basics and key mathematical tools necessary for understanding of simple mathematical models and the processing and interpretation of experimental data.

## Course Structure

The lessons will be frontal and participated. Exercises are planned.

## Detailed Course Content

Set and subset. Operations between sets. Cartesian product. Relation between sets. Function. One-to-one function . Inverse function. Composition of functions.

The numerical sets: N, Z, Q, R. logarithms. Equations and inequalities.

Matrix. Determinant. system of linear equations. The "pivot method".

The Cartesian plane. Distance between two points. midpoint of a segment. Symmetrical of a point with respect to a point. Area of a triangle. analytical representation of a straight line. Angular coefficient. Parallel lines. Unit circle. Radians. Trigonometric functions and identities. geometric meaning of the angular coefficien of a line. Perpendicular lines. Symmetrical of a point from a straight. Distance of a point to a line. Circles. Parabolas. Ellipses. Hyperbolas.

Extremes of a numerical set. Intervals. Around. of accumulzione points, isolated, indoor, outdoor, border. real function of real variable. Graph of a function. Extremes of a function. increasing and decreasing function function. Graph of an inverse function. exponential and logarithmic function. Inverse functions of the trigonometric functions. qualitative study of functions.

Limit of a function. Number e. Limit theorems. lateral limits. continuous function and discontinuous function. Theorems on continuous functions.

Derivative of a function. Differentiability and continuity. Rules of derivation. Derivatives of elementary functions. Theorem of derivation of composite functions. Geometric meaning of the derivative. Maximum and minimum relative. The theorems of Rolle, Lagrange and Cauchy. Convexity, concavity, inflections. Asymptotes. Study of simple functions. Gaussian function.

Primitive of a function. Indefinite Integral. Methods of integration. definite integral. integral function. fundamental theorem of calculus. improper integral. Calculation of areas.

differential equations.

Population, sample, statistical unit, characters. Dimensional distribution of frequencies. Histogram. Median. Box plots. Arithmetic average. Standard deviation. joint distribution of two quantitative traits. linear regression.

Event. Probability of an event. normal probability distribution.

## Textbook Information

[1] M. Gionfriddo, Istituzioni di matematiche, Culc, Catania.

[2] A. Guerraggio, Matematica per le scienze, Pearson.

[3] V. Villani – G. Gentili, Matematica 5/ed Comprendere e interpretare fenomeni delle scienze della vita, Mc Graw-Hill.