Sets - Operations on sets - Ordered pairs and Cartesian product -
Numerical sets: Natural numbers, Integers, Rational numbers, Real
numbers - Relations and Functions – Injective, Surjective and Bijective
Functions – Composition of functions and Invertible functions -
Real functions - Operations on functions – Graphs of functions –
Mathematical models - Algebraic functions and trascendental - Limits: an
intuitive introduction, a rigorous approach – Computational techniques -
Indeterminate forms – Continuity - Tangent lines – The derivative –
Techniques of differentiation – Derivatives of functions - Related rates –
Intervals of increase and decrease – Concavity – Relative extrema – First
and second derivative tests –Maximum and minimum problems –
Lagrange’s theorem – L’Hopital’s rule - Sketching graphs of functions -
Introduction to integral calculus – Antiderivatives – The indefinite integral
– Integration by parts - Integration by substitution – Areas as limits – The
definite integral – The first fundamental theorem of calculus – The mean
value theorem for integrals – The second fundamental theorem of
calculus -
Application of integral calculus - A statistical investigation – Samples and
population - Constructing tables and graphs – Tables and diagrams –
Measures of the centre of a set of observations: the arithmetic mean, the
mean of grouped data, the geometric mean, the median, the mode - The
measurement of variability: range, variance and standard deviation,
variance and standard deviation of a grouped frequency distribution,
quartile deviation – Correlation – Simple linear regression.
Classical definition of probability; Combinatorics;
The binomial distribution; Other definition of probability (frequentist and subjective probability); conditional probability.