Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-10-21T17:49:12Z No. of bitstreams: 2 Dissertação - Evandro Barbosa Nunes - 2014.pdf: 3739731 bytes, checksum: cbe9d0902f876b1f65e9268e0f6256c3 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-10-21T18:16:43Z (GMT) No. of bitstreams: 2 Dissertação - Evandro Barbosa Nunes - 2014.pdf: 3739731 bytes, checksum: cbe9d0902f876b1f65e9268e0f6256c3 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-21T18:16:43Z (GMT). No. of bitstreams: 2 Dissertação - Evandro Barbosa Nunes - 2014.pdf: 3739731 bytes, checksum: cbe9d0902f876b1f65e9268e0f6256c3 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-07-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Optimization problems seek to maximize or minimize a certain function, they play an important role in the real world. Many practical applications of sciences like engineering and economics can be formulated through optimization problems, for example, minimizing the amount of energy used in a factory or maximizing the investment of a person. In this work we will deal with issues of functions of one, two or three variables in the search for the point whose value is maximum or minimum, will be treated contents that can be worked in high school, as the Inequality of Means, Quadratic Function and also themes that can be explored in graduate course, in the case of Derivative and Method of Lagrange, all threads have interesting examples of applications of the concepts studied. / Problemas de otimização procuram maximizar ou minimizar uma determinada função, eles desempenham um papel importante no mundo real. Muitas aplicações práticas de ciências como engenharia e economia, podem ser formuladas através de problemas de otimização, como, por exemplo, a minimização da quantidade de energia usada em uma fábrica ou a maximização dos investimentos de uma pessoa. Nesse trabalho trataremos com questões de funções de uma, duas ou três variáveis na busca pelo ponto cujo o valor e máximo ou mínimo, ser a tratado conte udos que podem ser trabalhados no ensino médio, como a Desigualdade das Médias, Função Quadrática e também, temas que podem ser explorados em cursos de graduações, no caso das Derivadas e o Método de Lagrange, todos os tópicos possuem exemplos interessantes sobre aplicações dos conceitos estudados.

Philosophiae Doctor - PhD / In recent years, there has been a great interest towards the higher order numerical methods for singularly perturbed problems. As compared to their lower order counterparts, they provide better accuracy with fewer mesh points. Construction and/or implementation of direct higher order methods is usually very complicated. Thus a natural choice is to use some convergence acceleration techniques, e.g., Richardson extrapolation, defect correction, etc. In this thesis, we will consider various classes of problems described by singularly perturbed ordinary and partial differential equations. For these problems, we design some novel numerical methods and attempt to increase their accuracy as well as the order of convergence. We also do the same for existing numerical methods in some instances. We find that, even though the Richardson extrapolation technique always improves the accuracy, it does not perform equally well when applied to different methods for certain classes of problems. Moreover, while in some cases it improves the order of convergence, in other cases it does not. These issues are discussed in this thesis for linear and nonlinear singularly perturbed ODEs as well as PDEs. Extrapolation techniques are analyzed thoroughly in all the cases, whereas the limitations of the defect correction approach for certain problems is indicated at the end of the thesis. / South Africa

This thesis includes solving the basic examples of differential calculus (especially two and three variables). The work covers examples of the solutions of the domain, the first and second partial derivatives, determining the functions of local extremes (both explicitly and implicitly given) and find the equation of the tangent plane to a point in the graphs of functions. The examples are sorted by difficulty.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-04-25T19:31:06Z No. of bitstreams: 1 TeseSMP.pdf: 1382232 bytes, checksum: 8758d122cc415ab540988c4f92e38cc8 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-02T13:03:01Z (GMT) No. of bitstreams: 1 TeseSMP.pdf: 1382232 bytes, checksum: 8758d122cc415ab540988c4f92e38cc8 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-02T13:03:17Z (GMT) No. of bitstreams: 1 TeseSMP.pdf: 1382232 bytes, checksum: 8758d122cc415ab540988c4f92e38cc8 (MD5) / Made available in DSpace on 2017-05-02T13:06:24Z (GMT). No. of bitstreams: 1 TeseSMP.pdf: 1382232 bytes, checksum: 8758d122cc415ab540988c4f92e38cc8 (MD5) Previous issue date: 2015-11-26 / Não recebi financiamento / The main aim of this work is to develop alternative queuing models to M/ G/l, in which arrivals follow a Poisson process, the total number of customers on the system and the total number of service channels are unknown. Our interest is just to observe the service channel that will offer the maximum or minimum service time. Wherefore, the service distributions are obtained from the composition of the Conwav-Maxwell-Poisson distribution truncated at zero, used to model the number of service channels, with the general distribution to the maximum and minimum service time. Thus, we obtain new distributions for service time, which are called Maximum-Conwav-Maxwell-Poisson-general, denoted by MAXCOMPG distribution, and Minimum-Conwav-Maxwell-Poisson-general, denoted by MINCOMPG distribution, consequently, we obtain the queue models M/MAXCOMPG/1 and M/MINCOMPG/ 1, respectively. As general distributions, we use the distributions exponential, Weibull and Birnbaum Saunders, To illustrate the proposed queue models, a simulation study is done and also real data are used. / Este trabalho tem como objetivo apresentar modelos de filas alternativos ao M/G/l, nos quais as chegadas seguem um processo de Poisson, o número total de usuários no sistema e o número total de canais de atendimento são desconhecidos. Neste caso, observamos apenas o canal de serviço que irá oferecer o máximo ou o mínimo tempo de serviço. Para isto, as distribuições de serviço são obtidas a partir da composição da distribuição Conwav-Maxwell-Poisson truncada no ponto zero, usada para modelar o número de canais de atendimento, com uma distribuição geral para o máximo e o mínimo tempos de serviço. Desta forma, surgem novas distribuições de serviço que são denominadas de Máximo-Conwav-Maxwell-Poisson-geral, denotada por distribuição MAXCOMPG, e Mínimo-Conwav-Maxwell-Poisson-geral, denotada por distribuição MINCOMPG, e, assim, obtemos os modelos de fila M MAXCOMPG 1 e M MINCOMPG 1. Como distribuições gerais usamos as distribuições exponencial, Weibull e Birnbaum Saunders, Para ilustrar os modelos de fila propostos um amplo estudo de simulação é feito e dados reais também são utilizados.