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Mathematics and Statistics - part 1
Code: G240UA
Teacher:  Dario Fontana
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
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
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.
Program of Mathematics and Statistics - part 1 (pdf version)
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