Problemas e modelos que contribuíram com o desenvolvimento do cálculo diferencial e integral: dos gregos à Newton

This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article

Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient

Análise da magnetohidrodinâmica com transferência de calor em canais de placas paralelas via transformação integral

The main goal of the present work is related to the dynamics of the steady state, incompressible, laminar flow with heat transfer, of an electrically conducting and Newtonian fluid inside a flat parallel-plate channel under the action of an external and uniform magnetic field. For solution of the governing equations, written in the parabolic boundary layer and stream-function formulation, it was employed the hybrid, numericalanalytical, approach known as Generalized Integral Transform Technique (GITT). The flow is sustained by a pressure gradient and the magnetic field is applied in the direction normal to the flow and is assumed that normal magnetic field is kept uniform, remaining larger than any other fields generated in other directions. In order to evaluate the influence of the applied magnetic field on both entrance regions, thermal and hydrodynamic, for this forced convection problem, as well as for validating purposes of the adopted solution methodology, two kinds of channel entry conditions for the velocity field were used: an uniform and an non-MHD parabolic profile. On the other hand, for the thermal problem only an uniform temperature profile at the channel inlet was employed as boundary condition. Along the channel wall, plates are maintained at constant temperature, either equal to or different from each other. Results for the velocity and temperature fields as well as for the main related potentials are produced and compared, for validation purposes, to results reported on literature as function of the main dimensionless governing parameters as Reynolds and Hartman numbers, for typical situations. Finally, in order to illustrate the consistency of the integral transform method, convergence analyses are also effectuated and presented

Análise técnica e econômica do processo de obtenção de espaguetes com adição de farinha de trigo integral e farinha de linhaça

This work studies the fabrication of spaghetti through the process at high temperatures through the use of flour added to flour and flaxseed meal, with the aim of evaluating the final product quality and estimate the cost of production. The values of moisture, ash, protein, wet gluten, gluten index, falling number and grain of flour and mixtures to test to be the possible use in mass manufacturing and technological criteria for compliance with current legislation. Spaghetti noodles type were manufactured by adding 10% and 20% flour and 10% and 20% flaxseed meal with performance of physical-chemical, sensory and rheological properties of the products. Further analysis was performed on the product acceptance and estimation of production cost in order to create subsidies to enable the introduction of products with greater acceptance and economic viability in the market by the food industry. On the rheology of the product test was cooking the pasta, specifying the volume increase, cooking time and percentage of solid waste. In the sensory evaluation was carried out the triangular test of product differentiation with 50 trained judges and acceptance testing by a hedonic scale with evaluation of the aspects color, taste, smell and texture. In defining the sensory profile of the product was performed with ADQ 9 judges recruited and trained at the factory, using unstructured scale of 9 cm, assessing the attributes of flavor of wheat, flax flavor, consistency, texture of raw pasta, raw pasta color and color of cooked pasta. The greater acceptance of product quality was good and the pasta with 20% flour, 10% followed by the full product, 10% and 20% flaxseed characterized the average quality of the criterion of loss analysis of solids, together with mass full commercial testing. In assessing the estimated cost of production, the two products more technologically feasible and acceptable (20% whole and 10% flaxseed) were evaluated in high temperature processes. With total cost of R $ 4,872.5 / 1,000 kg and R $ 5,354.9 / 1,000 kg respectively, the difference was related to the addition of lower inputs and higher added value in the market, flour and flaxseed meal. The comparative analysis of cases was confirmed the reduction in production time (10h), more uniform product to the drying process at high temperature compared to conventional

Estratégias de cuidado integral à saúde: os CAPS no processo de implementação do apoio matricial em Natal/RN

This study aims to analyzing the implementation of the Matrix Support proposal with professionals of Substitutive Services in Mental Health in the city of Natal/RN. The Matrix Support (MS) is an institutional arrangement which has been recently adopted by the Health Ministry, as an administrative strategy, for the construction of a wide care net in Mental Health, deviating the logic of indiscriminate follow-through changed by one of co-responsibility. In addition to this, its goal is to promote a major resolution as regards health assistance. Integral attention, as it is intended by the unique health system, may be reached by means of knowledge and practices interchange, establishing an interdisciplinary work logic, through an interconnected net of health services. For the accomplishment of this study, individual interviews of semi-structured character were used as instrument, with the coordinators and technical staff of the CAPs. The data collection was done in the following services: CAPS II ( East and West) and CAPS ad ( North and East), in the city of Natal/RN. The results point out that the CAPs to initiate of the discussion the process in the implementation of the MS aiming, to promote the reorganization and redefinition of the flow in the net, thus not acting in a fragmented way. Nevertheless, there is no effective articulation concerning the basic attention services, there is a major focus of the attention in mental health on the specialized services, little insertion in the territory and in the everyday life of the community