https://ri.ufs.br/jspui/handle/riufs/2568 Thu, 29 Oct 2026 00:06:21 GMT 2026-10-29T00:06:21Z https://ri.ufs.br/jspui/handle/riufs/26215 Title: Introdução às equações de diferenças e aplicações Authors: Santos Júnior, José Adenualdo dos Abstract: This work presents a comprehensive introduction to difference equations and stability theory, exploring everything from mathematical foundations to applications in contemporary scenarios. The research begins with the exposition of finite difference calculus, defining difference (∆) and shift (E) operators and the importance of discretizing continuous models for computational purposes. The study delves into the resolution of first-order and higher-order linear equations, using tools such as the Casoratian and the Schur-Cohn criterion to determine the stability of solutions. In the applied phase, the work demonstrates the utility of these equations in numerical methods (Newton-Raphson and Euler) and in socio-economic analyses relevant to the Brazilian reality, such as the mathematical proof of the inevitability of player ruin in betting platforms (“Fortune Tiger”) and the modeling of National Income (GDP) through Samuelson’s model. The results reinforce the capacity of difference equations to predict complex behaviors and diagnose trajectories of discrete dynamic systems.; Este trabajo presenta una introducción integral a las ecuaciones de diferencias y a la teoría de estabilidad, explorando desde los fundamentos matemáticos hasta sus aplicaciones en escenarios contemporáneos. La investigación comienza con la exposición del cálculo de diferencias finitas, definiendo los operadores de diferencia (∆) y de desplazamiento (E), así como la importancia de discretizar modelos continuos con fines computacionales. El estudio profundiza en la resolución de ecuaciones lineales de primer orden y de orden superior, utilizando herramientas como el Casoraciano y el criterio de Schur-Cohn para determinar la estabilidad de las soluciones. En la fase aplicada, el trabajo demuestra la utilidad de estas ecuaciones en métodos numéricos (Newton-Raphson y Euler) y en análisis socioeconómicos relevantes para la realidad brasileña, tales como la demostración matemática de la inevitabilidad de la ruina del jugador en plataformas de apuestas (“Fortune Tiger”) y la modelación del Ingreso Nacional (PIB) a través del modelo de Samuelson. Los resultados refuerzan la capacidad de las ecuaciones de diferencias para predecir comportamientos complejos y diagnosticar trayectorias de sistemas dinámicos discretos. Fri, 31 Jul 2026 00:00:00 GMT https://ri.ufs.br/jspui/handle/riufs/26215 2026-07-31T00:00:00Z https://ri.ufs.br/jspui/handle/riufs/25759 Title: Geometria esférica : uma abordagem axiomática dos conceitos fundamentais e da trigonometria Authors: Santana, David Rezende de Abstract: This work presents a systematic study of Spherical Geometry, covering its axiomatic construction, fundamental properties, and an introduction to spherical trigonometry. It begins with a historical contextualization, from ancient civilizations to its mathematical consolidation. It discusses the concept of a line on the sphere via geodesics, distinguishing between intrinsic and extrinsic approaches, and formally establishes concepts such as great circles, antipodality, spherical distance, and convexity. The main focus is on the theory of spherical triangles, including properties, congruence criteria (such as the AAA case), and the relationship between the sum of angles and curvature. It also addresses the area of spherical triangles, culminating in the Girard-Euler Theorem, and presentes proofs of the Spherical Pythagorean Theorem and the Spherical Law of Sines. Finally, it compares plane and spherical geometry, presents the extrinsic viewpoint, and original results on antipodal and parallel circles. The work aims to offer a formal and accessible exposition of Non-Euclidean Geometries, highlighting their historical, educational, and modern geometrical relevance. Fri, 10 Jul 2026 00:00:00 GMT https://ri.ufs.br/jspui/handle/riufs/25759 2026-07-10T00:00:00Z https://ri.ufs.br/jspui/handle/riufs/25757 Title: Uma introdução histórica à geometria hiperbólica e aplicações trigonométricas Authors: Santos, Gabriel dos Abstract: This work analyzes the historical and mathematical evolution of geometry, focu-sing on the rupture of the Euclidean dogma and the consolidation of hyperbolic geometry as a foundation for modern physics. The research aims to describe the transition from Euclid’s axiomatic system to non-Euclidean models, demonstrating how the negation of the fifth postulate grounds new understandings of space. The method utilizes a bibliographic and documental review of a deductive nature, based principaly in Barbosa’s works to reconstruct the logical rigor of geometric demonstrations(BARBOSA, 2007). The discussion covers the failed attempts by mathematicians such as Ptolemy, Proclus, and Saccheri to prove the parallel postu-late, culminating in the independent discovery by Gauss, Bolyai, and Lobachevsky. The text details elementary properties of neutral and hyperbolic geometry, suchas Saccheri and Lambert quadrilaterals, generalized triangles, and hyperbolic tri-gonometry. The results highlight that hyperbolic geometry provides the necessarymathematical framework for Einstein’s Theory of Relativity. Fri, 10 Jul 2026 00:00:00 GMT https://ri.ufs.br/jspui/handle/riufs/25757 2026-07-10T00:00:00Z https://ri.ufs.br/jspui/handle/riufs/25672 Title: O jogo cashflow, adaptado ao scratch, como ferramenta pedagógica para o ensino de educação financeira Authors: Santos, Beatriz Oliveira Abstract: This study investigates the potential of the game Cashflow, adapted for the Scratch platform, as a pedagogical tool for teaching Financial Education. Given the complexity of the current economic scenario and the guidelines of the National Common Curricular Base (BNCC), the research seeks to answer how the use of this digital tool contributes to the development of financial skills. Methodologically, the study adopts a mixed-methods approach and is grounded in Didactic Engineering, structured into the phases of preliminary analysis, a priori analysis, experimentation, and a posteriori analysis. In this context, the analysis of interactions was based on the Theory of Didactic Situations (TDS), following the phases of action, formulation, validation, and institutionalization. Furthermore, the experiments were conducted with undergraduate students in Mathematics and 3rd-year high school students. Thus, the results demonstrate that the game promotes collaborative teaching and the active construction of knowledge, allowing the simulation of real-life situations such as cash flow management, decision-making, and investment analysis. Moreover, the mobilization of BNCC skills related to percentage and interest calculations was observed. Mon, 13 Jul 2026 00:00:00 GMT https://ri.ufs.br/jspui/handle/riufs/25672 2026-07-13T00:00:00Z