Curso de matematica para economistas, Capitulos I e II: funções, algebra linear e aplicações

Os autores objetivam, com este trabalho preliminar, bem como com aqueles que lhe darão continuidade, na sequência de composição de um livro de matemática para economistas, registrar as suas experiências ao longo dos últimos anos ministrando cadeiras de matemática nos cursos de pós-graduação em economia da Fundação Getúlio Vargas, da UFF (Universidade Federal Fluminense) e da PUC-RJ. Reveste-se de constante repetição em tais cursos a discussão sobre que pontos abordar, bem como com qual grau de profundidade, e em que ordem. É neste sentido que os autores esperam, com a sequência didática que aqui se inicia, trazer alguma contribuição para o assunto.

Curso de matematica para economistas - Capitulo IV : otimização estatica

Os autores objetivam, com este trabalho preliminar, bem como com aqueles que lhe darão continuidade, na sequência de composição de um livro de matemática para economistas, registrar as suas experiências ao longo dos últimos anos ministrando cadeiras de matemática nos cursos de pós-graduação em economia da Fundação Getúlio Vargas, da UFF (Universidade Federal Fluminense) e da PUC-RJ. Reveste-se de constante repetição em tais cursos a discussão sobre que pontos abordar, bem como com qual grau de profundidade, e em que ordem. É neste sentido que os autores esperam, com a sequência didática que aqui se inicia, trazer alguma contribuição para o assunto. A parte teórica relativa à demonstração do Teorema de Kuhn Tucker aqui apresentada transcreve, com a aquiescência do autor, textos selecionados de "Análise Convexa do Rn." de Mario Henrique Simonsen.

Função quadrática

In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning

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

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 class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Predictive formulas for food base excess and urine pH estimations of cats

Food base excess (BE, mEq/kg) can be calculated from the diet macroelements, together with either the sulfur amino acids methionine and cysteine (BEaa) or total sulfur (BEs) concentrations. The present study compared the use of sulfur or methionine and cysteine for calculating the food BE (experiment 1) and investigated the influence of food BE on blood gas analysis and the urine pH of cats, and proposes a prediction equation to estimate the urine pH of cats fed kibble diets based on the calculated food BE (experiments 2 and 3). In experiment 1, nine healthy, adult cats were used in a change-over design and fed with nine commercial dry cat foods. The cats were housed in metabolism cages over seven days for adaptation and three days for total urine collection. All of the urine produced over 24h was pooled by cat and diet. The cats' acid-base status was assessed through blood gas analysis after 10 days of diet consumption. A mean difference of -115mEq/kg between BEs and BEaa was observed, which could be explained by a greater concentration of sulfur in the whole diet than in methionine and cysteine. Urine pH presented a stronger correlation with food BEs (R2=0.95; P<0.001) than with food BEaa (R2=0.86; P<0.001). Experiment 2 included 30 kibble diets, and each diet was tested in six cats. The food BEs varied between -180 and +307mEq/kg, and the urine pH of the cats varied between 5.60 and 7.74. A significant correlation was found between the measured urine pH and the food BEs (urinary pH=6.269+[0.0036×BEs]+[0.000003×BEs2]; R2=0.91; P<0.001). In experiment 3, eight kibble diets were tested (food BEs between -187mEq/kg and +381mEq/kg) to validate the equation proposed in experiment 2 and to compare the obtained results with previously published formulae. The results of the proposed formula presented a high concordance correlation coefficient (0.942) and high accuracy (0.979) with the measured values, and the estimates of urine pH did not differ from the values obtained in cats (P>0.05). The cats' venous blood pH, bicarbonate, and blood BE were correlated with food BEs (P<0.001); the consumption of diets with low food BEs induced a reduction in these parameters. In conclusion, food macroelement composition has a strong influence on cats' acid-base equilibrium and food BEs calculation is a useful tool to formulate and balance kibble diets for felines. © 2013 Elsevier B.V.

Agregação e viés em medidas de diversidade: uma abordagem computacional intensiva

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Disciplina história da matemática e a formação do professor de matematica: dados e circunstâncias de sua implantação na Universidade Estadual Paulista, campi de Rio Claro, São José do Rio Preto e Presidente Prudente

Pós-graduação em Educação Matemática - IGCE

Analiticidade e efeito gráfico da dilatação em funções octoniônicos quaseconformes do tipo F(Z)=Zn

Pós-graduação em Matemática - IBILCE

Matematica e lingua materna: um estudo sobre utilização conjunta com atividades para o ensino fundamental

This work is a study and a repost on a possible way that can be worked together Mathematics and Native Language, presenting activities for the middle school, trying to make teaching more interesting, dynamic and playful. The work presents proposal for activities based on stories from the book “O Homem que calculava” by Malba Tahan, with questionnaires to be answered by the students and guidance for teachers on how to apply these activities in the classroom. Applications of these activities were carried out and this work also includes analysis and records of them

A importância do planejamento financeiro: uma abordagem de matematica financeira para o ensino médio com o uso do excell

The financial health of a family is one of the main generators of quality of life, and this is only possible through financial planning, which is nothing more than save and analyze before contracting debts. To do this, students must have notion of financial mathematics, especially of that used by the banks on overdraft interest, in investments and in the short-term and longterm loans, that is, compound interest, equivalent rates, depreciation and others. Starting from the knowledge of arithmetic and geometric progressions and, based on real situations which allow the application of the content learned, one intends to develop activities applied to high education. To start from real situations is one of the main lines of thought of the Problem Solving Methodology, in which the student is the active agent in the construction of his or her knowledge. As the National Curricular Parameters point out, the practice in the use of computers is essential for gaining a job. Therefore, this project proposes an activity where knowledge of Financial Mathematics can to be practiced, associated with the use of Microsoft Excel® spreadsheet

Orthogonality relations and supercharacter formulas of U(m vertical bar n) representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.

Predicted preoperative maximal static respiratory pressures in adult cardiac surgeries: evaluation of two formulas

Objectives: Cardiac surgery (CC) determines systemic and pulmonary changes that require special care. What motivated several studies conducted in healthy subjects to assess muscle strength were the awareness of the importance of respiratory muscle dysfunction in the development of respiratory failure. These studies used maximal inspiratory pressure (MIP) and maximal expiratory pressure (MEP) values. This study examined the concordance between the values predicted by the equations proposed by Black & Hyatt and Neder, and the measured values in cardiac surgery (CS) patients. Methods: Data were collected from preoperative evaluation forms. The Lin coefficient and Bland-Altman plots were used for statistical concordance analysis. The multiple linear regression and analysis of variance (ANOVA) were used to produce new formulas. Results: There were weak correlations of 0.22 and 0.19 in the MIP analysis and of 0.10 and 0.32 in the MEP analysis, for the formulas of Black & Hyatt and Neder, respectively. The ANOVA for both MIP and MEP were significant (P <0.0001), and the following formulas were developed: MIP = 88.82 - (0.51 x age) + (19.86 x gender), and MEP = 91.36 -(030 x age) + (29.92 x gender). Conclusions: The Black and Hyatt and Neder formulas predict highly discrepant values of MIP and MEP and should not be used to identify muscle weakness in CS patients.