Mathematical analysis
The sets and their operations, various notations. Numerical sets: from N to R, need for expansion.
Definition of function and relative classification; even and odd functions: examples, recognition and graphic consequences.
Summation symbol and its use to indicate polynomials of degree n.
Set of rational numbers, set of reals and field structure.
Absolute value of a number and triangular inequality.
Interval definition: closed, open; definition of around.

Classification of functions. Domain and sign of rational and irrational, transcendent algebraic functions.
Definition of finite limit for x that tends to a finite value: limit verification.
Infinite limit for x which tends to a finite value: check; vertical asymptote.
Finite and infinite limits for x which tends to infinity: horizontal asymptote; oblique asymptote of rational rational algebraic functions.

Continuous function at a point and in an interval. Classification of discontinuities: the integer part function, the functions whose graph admits vertical asymptotes; discontinuity can be eliminated: functions defined by branches.
Elementary functions as continuous functions. Uniqueness of the limit theorem. Limits of continuous functions
Theorem of confrontation or "of the carabinieri". Theorems on continuous functions: Weierstrass, intermediate values, existence of zeros.
Definition of Nepero's number. Remarkable limits of transcendent functions and their consequences: relative examples.

Definition of derivative and its geometric meaning. Application to physics and other applied sciences.
Non-derivable functions in one point, classification of non-derivability points: angular points, cusps and flexions with vertical tangent; examples of all kinds.
Derivatives of elementary functions with proof.
Derivative of a sum and a product with demonstration and application examples.
Relationships between derivability and continuity.
Definition of ascending and descending function.
Derivative of the reciprocal function of a derivable function (with proof) and of a quotient: examples of application.
Compound functions: definitions, examples, derivative of a compound function. Complete study of a function.
Definition of relative max and min and Fermat's theorem. Search for relative max and min
(with the method of studying the sign of the first derivative) and absolutes.
Rolle, Cauchy and Lagrange theorems: examples and geometric meanings.
De l'Hopital theorem. Comparison of infinitesimals and comparison of infinites.
Calculation of subsequent derivatives. Convexity and concavity of a curve, determination of bending at oblique tangent: determination of inflectional tangents.
Development of a Taylor / Mc Laurin series function: application to some remarkable
Statistic analysis
Descriptive statistics: tables and graphs, histograms and pie charts. Position indices: mean, fashion and median percentiles and quartiles, weighted average.
Dispersion indices: variance and standard deviation.
Evaluation of measurement uncertainties: absolute, relative and percentage errors.
Bimodal statistical tables: joint distributions; addiction and independence.
Least squares method, Covariance, Linear correlation coefficient.
Combinatorial calculation. Simple and repetitive arrangements; simple and repetitive permutations; simple and repetitive combinations; binomial coefficient in its different forms, power of a binomial with Newton's formula.
Classical definition of probability: relative examples. Total and compound probability theorems.
The concept of random variable and discrete and continuous distributions.
Discrete distribution: binomial distribution, definition and related examples.
Normal distribution: density function, Gauss curve. Introduction of the distribution function and use of tables for calculating the probability of random events with normal distribution: relative examples

PER ACQUISIRE PRE-REQUISITI NON GIA' IN POSSESSO
P.Boieri, G.Chiti, Precorso di matematica , Zanichelli
  
TESTI BASE
 Silvia Annarone
Matematica sul campo
Metodi ed esempi per le scienze della vita
Pearson
Marco Bramanti, Carlo Domenico Pagani, Sandro Salsa,
Analisi matematica 1 con elementi di geometria e algebra lineare,
2014, Zanichelli
P.Marcellini, C.Sbordone, Esercitazioni di matematica – Vol.I tt.1,2,3,4, 2009, Liguori