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Facoltā di Scienze Agrarie e Alimentari Universitā degli Studi di Milano
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Mathematics and statistics - term 1
Code: G271BA
Teacher:  Giulia Bernardi
Term:  1 e 2 
CFU subdivision: Lectures: 3,5
Practices in classroom: 2,5
Basic aims:  Knowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals).Knowledge of descriptive statistics. Knowledge of the position and variability indicators. Knowledge of methods of inferential statistics. Acquisition of the principles and techniques of regression and correlation between various parameters.
Acquired skills:  Possibility of exploiting the basic tools of Maths in any context. Describe the phenomena by the main statistical indicators; plan sample surveys; use the methodology of the analysis of variance at 1 and 2 factors; understand the results of statistical surveys.
Course contents:  rational, trigonometric, exponential and logarithmic
equations. Basics about functions. Analytic geometry of
the plane: curves of first and second degree. Finding
solutions of a linear system. Sequences and limits of
sequences. Limits of functions and continuous functions.
Derivatives, extremal points, convexity. Qualitative
properties of the graph of a function. Integrals and
Program:  Basics of set theory. Number sets (N, Z, Q, R), real
numbers, Dedekind Axiom. Rational equations. Maps
(domain, codomain, image, definition set, composition of
maps), injective maps, invertible maps, absolute value,
powers, exponentials, logarithms, trigonometric functions
and their inverses. Exponential, logarithmic and
trigonometric equations. Basics of analytic geometry:
distance between two points in the plane, equation of a
line, parallel and orthogonal lines; second degree curves
(circle, ellipsis, hyperbole, parabola). Resolution of linear
systems with Gauss method. Limits of sequences:
definitions, operations with limits, some special limits.
Limits of functions and continuity: definitions, examples,
right and left limit, types of discontinuity, zeroes,
intermediate values, Weierstrass Theorem. Derivatives:
definition and geometrical meaning, derivatives of
elementary functions; operations with derivatives;
derivatives of composite and inverse maps. De L'Hopital
Theorem. Analysis of the graph of a function: extremal
points, Rolle and Lagrange Theorem, increasing and
decreasing functions, convex functions, asymptotes.
Integrals: geometrical meaning and basic properties.
Linearity of integral. Average Theorem. Primitives and
Fundamental Theorem of Calculus. Integrals of rational
functions, some integration techniques.
Prerequisites:  None.
Preparatory instructions:  None.
Learning materials:  Paolo Marcellini- Carlo Sbordone Elementi di calcolo
Versione semplificata per i nuovi corsi di laurea Liguori
Editore, Napoli. Paolo Marcellini- Carlo Sbordone
Esercitazioni di Matematica 1° volume parte prima e 1°
volume parte seconda Liguori Editore, Napoli.
Other info:  The exam consists of a written test (compulsory!), in
which the
student is requested to solve (usually) three exercises
the programme of the course, but without purely
questions. If this test is passed, but with a not entirely
satisfactory result, an oral examination will be necessary
as well.
However, any student who wishes to improve the result of
written test can do the oral examination. There will be
also mid-
term written tests which give the opportunity of skipping
the written part of the exam or the whole exam
(according to the
Program of Mathematics and statistics - term 1 (pdf version)
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