Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Uma ferramenta didática para ajudar na fixação dos conceitos introdutórios de análise combinatória

Humans, as well as some animals are born gifted with the ability to perceive quantities. The needs that came from the evolution of societies and technological resources make the the optimization of such counting methods necessary. Although necessary and useful, there are a lot of diculties in the teaching of such methods.In order to broaden the range of available tools to teach Combinatorial Analysis, a owchart is presented in this work with the goal of helping the students to x the initial concepts of such subject via pratical exercises

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Função Afifim: Teoria e aplicações

In this work we present a proposal to contribute to the teaching and learning of affine function in the first year of high school having as prerequisite mathematical knowledge of basic education. The proposal focuses on some properties, special cases and applications of affine functions in order to show the importance of the demonstrations while awaken student interest by showing how this function is important to solve everyday problems

Um estudo dos sistemas de amortizações SAC e francês no ensino médio apoiado na construção de planilhas Eletrônicas

The aim of this work is to provide a text to support interested in the main systems of amortization of the current market: Constant Amortization System (SAC) and French System, also known as Table Price. We will use spreadsheets to facilitate calculations involving handling exponential and decimal. Based on [12], we show that the parcels of the SAC become smaller than the French system after a certain period. Further then that, we did a comparison to show that the total amount paid by SAC is less than the French System

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Área e volume da esfera

In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Desenvolvendo e gerenciando compostagem de resíduos sólidos urbanos: para geração de renda e repasse de tecnologia à acrevi

Nowadays, as well as in the past decades, the dumping of biodegradable organic waste in landfill is common practice in Brazil, as well as in most parts of the world. Nevertheless due to its rapid decomposition and release of odors, this practice hamper’s the operation and implementation of a recycling system. These facts encouraged our research to find an efficient system for the management of organic waste, not only for the use of official workers responsible for managing these wastes, but also for non-governmental institutions. The Recycling for Life Community Association – ACREVI (Associação Comunitária Reciclando para a Vida), together with the municipal authorities of Mossoró-RN, Brazil, have assumed the social role of collecting and recycling solid waste produced by most of the local population. However, it was observed that the organic waste it collected was not receiving any treatment. This present work aims to make compost with mixed waste (green waste and organic household), and then do chemical analysis of the material in view to use the waste as organic fertilizer. The objective being: to share the knowledge acquired by putting it into a very simple language accessible to people with little education. The experiment was conducted at ACREVI, Mossoró (RN), and the compost was obtained following the method "windrow", forming three cells (I, II, III) with conical shape, dimensions of 1.6 meters and 2.0 meters in diameter for cells I and II, and 1.0 meters high and 2.0 meters in diameter for cell III. The process was accompanied by analysis: CHN elemental, a variation of cell temperature, humidity, pH, TKN, bulk density, nutrients and heavy metals. Stabilized organic compounds reached the C/N ratio of 10.4/1 cell I and 10.4/1 in the cell II in the cell, showing how good soil conditions, with potential to improve the physical properties of any soil and pH acid soils, has presented the cell III at the end of the process the C/N 26/1, is a high ratio may be associated with the stack size III, thus changing the optimal conditions for the occurrence of the process. The levels of heavy metals in the analyzed compounds were lower than those established by the SDA normative instruction, Nº 27, of 5 June, 2006. The use of pruning trees and grass are used in small-scale composting, while generating a quality compost in the final process, it also created an important condition for a correct sizing of the composting piles. Under the studied conditions it is not advisable to use cells with a height of 1.00 m in height and 2.00 m in diameter, as these do not prevent the rapid dissipation of heat and thus can not be a good product at the end of composting. The composting process in the shed of the association and the preparation of the primer enabled the development of an alternative technology to generate income for members of ACREVI.

Síntese, sinterização e caracterização de ferrita de níquel

In this work we obtain nickel ferrite by the combustion synthesis method whcih involves synthesising in an oven at temperatures of 750oC, 950oC and 125oC. The precursors oxidizing used were nickel nitrate, ferric as an oxidizing and reducing urea (fuel). After obtaining the mixture, the product was deagglomerated and past through a 270 mesh sieve. To assess the structure, morphology, particle size, magnetic and electrical properties of nanoparticles obtained the samples were sintered and characterized by x-ray distraction (XRD), x-ray fluorescence spectroscopy (FRX); scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), vibrating sample magnetometer (MAV ) and electrical permittivity. The results indicated the majority of phase inverse spinel ferrite and Hematite secondary phase nickel and nickel oxide. Through the intensity of the distraction, the average size of the crystallization peaks were half-height width which was calculated using the Scherrer equation. From observing the peaks of all the reflections, it appears that samples are crystal clear with the formation of nanoparticles. Morphologically, the nanoferritas sintered nickel pellet formation was observed with three systems of particle size below 100mn, which favored the formation of soft pellets. The average size of the grains in their micrometric scale. FRX and EDS showed qualitatively the presence of iron elements nickel and oxygen, where through quantitative data we can observe the presence of the secondary phase. The magnetic properties and the saturation magnetization and the coercive field are in accordance with the nickel, ferrite where the curve of hysteresis has aspects of a soft material. Dielectric constant values are below 10 and low tangent loss

Métricas de sistemas de middleware orientado a aspectos e Aplicação em um sistema de monitoramento de Poços de Petróleo

Nowadays, there are many aspect-oriented middleware implementations that take advantage of the modularity provided by the aspect oriented paradigm. Although the works always present an assessment of the middleware according to some quality attribute, there is not a specific set of metrics to assess them in a comprehensive way, following various quality attributes. This work aims to propose a suite of metrics for the assessment of aspect-oriented middleware systems at different development stages: design, refactoring, implementation and runtime. The work presents the metrics and how they are applied at each development stage. The suite is composed of metrics associated to static properties (modularity, maintainability, reusability, exibility, complexity, stability, and size) and dynamic properties (performance and memory consumption). Such metrics are based on existing assessment approaches of object-oriented and aspect-oriented systems. The proposed metrics are used in the context of OiL (Orb in Lua), a middleware based on CORBA and implemented in Lua, and AO-OiL, the refactoring of OIL that follows a reference architecture for aspect-oriented middleware systems. The case study performed in OiL and AO-OiL is a system for monitoring of oil wells. This work also presents the CoMeTA-Lua tool to automate the collection of coupling and size metrics in Lua source code

Aplicação do método B ao projeto formal de software embarcado

This work shows a project method proposed to design and build software components from the software functional m del up to assembly code level in a rigorous fashion. This method is based on the B method, which was developed with support and interest of British Petroleum (BP). One goal of this methodology is to contribute to solve an important problem, known as The Verifying Compiler. Besides, this work describes a formal model of Z80 microcontroller and a real system of petroleum area. To achieve this goal, the formal model of Z80 was developed and documented, as it is one key component for the verification upto the assembly level. In order to improve the mentioned methodology, it was applied on a petroleum production test system, which is presented in this work. Part of this technique is performed manually. However, almost of these activities can be automated by a specific compiler. To build such compiler, the formal modelling of microcontroller and modelling of production test system should provide relevant knowledge and experiences to the design of a new compiler. In ummary, this work should improve the viability of one of the most stringent criteria for formal verification: speeding up the verification process, reducing design time and increasing the quality and reliability of the product of the final software. All these qualities are very important for systems that involve serious risks or in need of a high confidence, which is very common in the petroleum industry