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Mathematics and Statistics - part 1
Code: G240UA
Teacher:  Mario Guido Lieta
Year: 
Term: 
CFU: 
CFU subdivision: Lectures: 5
Practices in classroom: 1
Basic aims:  Knowledge of the basics of Mathematics, in particular, of elementary Calculus (real functions in one variable,
limits, derivatives, integrals).
Acquired skills:  Ability of exploiting the basic tools of Mathematics in any context.
Course contents:  Algebraic equations of first and second degree. Rational, trigonometric, exponential and logarithmic
equations. Analytic geometry of the plane: curves of first and second degree. Basics about functions. Limits of functions and continuous functions. Derivatives, extremal points, convexity. Qualitative properties of the graph of a function. Integrals and primitives.
Program:  1. Basic concepts:

- Number sets (N, Z, Q, R), ordering of the real line and the symbol of infinite.
- Absolute value, powers and roots.
- The Cartesian plane: coordinates, straight lines, parabolas, circles, equilateral hyperbolas.
- Properties of elementary functions: powers with real exponent, exponentials, logarithms and trigonometric functions.
- Equations and inequalities: algebraic of first and second degree, rational, with roots, exponential and logarithmic.

2. Real functions of one real variable:

- Maps. Domain, codomain, graph of a function.
- Limits. Indeterminate forms and limits of special interest.
- Continuity and properties of continuous functions.
- Derivatives: definition and geometrical meaning, tangent lines. Computation of derivatives. Monotony and search for extremal points of a function.
- Second derivative, concavity and inflection points.
- Horizontal, vertical and oblique asymptotes.
- Qualitative study of the graph of a function.

3. Integrals:

- Indefinite integrals: definition, antiderivatives of elementary functions, methods of computation of the antiderivative of a function.
- Definite integrals: geometrical meaning and basic properties, the fundamental theorem of calculus, improper integrals.
- Computation of the area of a plane region.
Prerequisites:  Knowledge of elementary algebra.
Preparatory instructions:  None
Learning materials:  Courses Minimat e Matematica Assistita, available on line at
http://minimat.ariel.ctu.unimi.it/v1 and
http://matematicaassistita.ariel.ctu.unimi.it/v1.
Other info:  The exam consists of a written test divided into two parts, each
lasting 2 hours, and a subsequent oral exam.
For students enrolled in the first year during the A.Y. 2017/2018
there is no interim test. Instead, ONLY for the students who
participated in the MyMathLab project during the pre-courses,
performing at least 13 of the 16 activities proposed on the e-
learning platform in the required time, there is a final in-class
test in November.
Students who pass this final test will be exempted from Part 1 of
the Maths Written Examination until July 2018 inclusive. More
information about the MyMathLab project can be found on the
website regarding Maths pre-courses for Edolo
(http://pmorandopme.ariel.ctu.unimi.it).
Since it is an integrated course, the exam mark (from 18 to 30
cum laude) will then be combined with a weighted average of
the mark obtained in the Statistics examination, thus giving the
final mark in Maths and Statistics, which corresponds overall to
10 credits.
DOWNLOAD
Program of Mathematics and Statistics - part 1 (pdf version)
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