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 some simple cases of ordinary differential equations
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 power and polynomial functions, and their representation in the Cartesian plane.
5. The limit operation: asymptotic behavior, infinite and infinitesimal orders.
6. Nonlinear equations: the continuous functions, the Bolzano theorem and the bisection method; the differentiable functions and the Newton method.
7. Critical points of a function: maxima, minima and inflections.
8. Rational functions: the theorem of De l'Hôpital.
9. The transcendental functions exponential, logarithm, sine, cosine: Taylor's Formula.
10. The sigmoid and Gaussian function.
11. Introduction to the Riemann integral and the Fundamental Theorem of Integral Calculus.
12. Improper Riemann integral.
13. Ordinary differential equations of the first order with separable variables and the linear case.
14. Ordinary differential equations of the second order with constant coefficients.
15. The Cauchy problem.