Financial mathematics: from algebraic study to applications in ordinary differential equations
We present Financial Mathematics as a study of money application over time, considering the interest phenomena. With this goal, we develop all the necessary theoretic tools, as, for example, a sketch of the theory of functions, uniform series, progressions, ordinary differential equations and elementary financial mathematics.
After this theoretical framework was developed, we give two applications. In the first, we exhibit results that may be useful for a deeper analysis of the elements that compose the financial variables. In the second, by a series of activities proposed to the teacher that are applicable to high school, aiming to study the variables of financial mathematics, we use analytical and computational methodologies that seek to encourage and improve the comprehension by a critical investigation and parameter simulations.