The common thread is the concept of function and its role in mathematical modeling to solve problems, introducing the fundamentals of differential and integral calculus and their application to inferential calculus with the study of the statistical significance of the sample regression line.
1. Real numbers and their application to the representation of points on the Cartesian straight line, plane and space.
2. Circumferences, straight lines, semi planes, stripes, ellipses, hyperbolas, parabolas in the Cartesian plane.
3. Equations, inequalities and systems of equations and inequalities in the Cartesian plane.
4. The problem of non-alignment: the sample regression line.
5. The least squares method for calculating the coefficients of the sample regression line
6. The power and polynomial functions, and their representation in the Cartesian plane.
7. The limit operation: asymptotic behavior, infinite and infinitesimal orders.
8. Continuous functions and differentiable functions.
9. Critical points of a function: maxima, minima and inflections.
10. Rational functions: the theorem of De l'Hôpital.
11. The transcendental functions exponential, logarithm, sine, cosine: Taylor's Formula.
12. The sigmoid and Gaussian function.
13. Introduction to the Riemann integral and the Fundamental Theorem of Integral Calculus.
14. Improper Riemann integral.
15. Overview of the main continuous random variables and their properties: Gaussian, Student t, Fisher F.
16. Their application to the inferential study of the statistical significance of the sample regression line: introduction to hypothesis tests.