Calculus and Statistics

Real numbers, coordinates on the line and in the plane. Form of a real number.
- Remarkable products. Equations and inequalities.
- Notion of function and its graph. Domain and codomain. Properties of functions: injective; surjective; bijective. Inverse function and compound function.
- Graphs of elementary functions, in particular: lines, powers, absolute value, parabolas, exponentials, logarithms and goniometric functions.
- Translations and symmetries starting from the graph of elementary functions.
- Notion of Limit. Limits of elementary functions. Infinity scale.
- Continuous functions.
- Theorems on continuous functions. Weirstrasse theorem; Theorem of zeroes and Darboux's theorem.
-Points of discontinuity. Asymptotes.
- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.
- Rules of derivation; sum, product, quotient and composition of functions.
- Higher order derivatives.
Theorems on differentiable functions: Rolle, Lagrange and Fermat theorem.
- Application of derivatives to the study of the graph of a function.
-Definition of indefinite integral. Methods of integration.
-Theory of the definite integral. The integral function.
The fundamental theorem of integral calculus.
The mean value theorem.
- Discrete random variables.
- Mean value, variance, standard deviation, standard deviation.
- Double entry tables. Conditional distributions.
- Theoretical frequencies of independence. Contingencies. The normalized chi-square index.
- Linear regression (least squares method).
-Linear correlation.