Learning outcomes of the course unit
To provide students with the basic notions of mathematics used for applications, at the same time getting them accustomed to using the specific language correctly .
Real number and algebraic and ordinal properties of real numbers. ELEMENTS OF ANALYTICAL GEOMETRY
Course contents summary
ELEMENTS OF NAIVE SET THEORY: Sets and their representations. Relationships of equality and inclusion. Operations of union, intersection, difference and cartesian product. Relationships over a set. functions, symbology and nomenclature.Natural, integersand rational numbers. Percent and problem solving. Irrational numbers and real numbers. Operations and ordering of numerical sets. Real line.Absolute value. The symbols + infinite and - infinite.Interval.Powers with natural and integer exponents. and their properties. Powers with rational exponent. Concept of equations and of set-solutions.Integer, rational equations and disequations. logarithms.
ANALYTICAL GEOMETRY: cartesian plane,distance between two points. Linear functions and straight lines in plane.
Parabola and circumference as locus of points: canonical equations and Cartesian representation.
REAL FUNCTIONS OF REAL VARIABLE: SYMBOLOGY AND NOMENCLATURE. GENERAL PROPERTIES: LIMITEDNESS, MONOTONICITY, SYMMETRIES, ABSOLUTE AND RELATIVE EXTREMES, Language of limits.ELEMENTARY FUNCTIONS AND THEIR GRAPHS: CONSTANTS, LINEARS, POWER, EXPONENTIAL AND LOGARITHMIC. LALGEBRA OF FUNCTIONS AND GRAPHS BY POINTS. GRAPHIC RESOLUTION OF DISEQUATIONS.
Angles and their measurement. Elements of trigonometry. sine, cosine of an angle. FUNCTIONS TRIGONOMETRIC.
Appunti del docente
Two written exercises during the course, or a written exam with the possibility of improving one’s grade with an oral exam in the case of a grade between 15 and 17 out of thirty.