Thesis--Friedrich-Wilhelms-Universität Berlin, 1845. / Vita. Includes bibliographical references.

Thèse--Lund.

"Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn." / Includes bibliographical references.

Thesis--Giessen. / Without thesis statement. Vita. Bibliography: leaf [40-41].

Thesis (M.S.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

It is the purpose of this paper to study the approximation to real functions by certain power series. Specifically, Taylor's series and generalizations of Taylor's series are considered. The importance of the behavior of the remainder, defined in chapter 1, demands a study of the difference between a function and the terms of an approximation sequence. Thus, this paper is devoted to the presentation of various forms of the remainder term when the approximation is by Taylor's expansion or some of its generalizations. / "May, 1955." / Typescript. / Advisor: B. F. Hadmot, Professor Directing Paper. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaves 72-73).

Thesis (M.A.)--University of Nevada, Reno, 2007. / "December 2007." Includes bibliographical references (leaves 26-28). Online version available on the World Wide Web.

Thesis (M.S.)--Ohio University, March, 2007. / Title from PDF t.p. Includes bibliographical references.

Orientador: Lucio Tunes dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T18:37:14Z (GMT). No. of bitstreams: 1 Davolio_Alessandra_M.pdf: 806001 bytes, checksum: 7d7f68058bc8b1bef1d6939e7aacb0d9 (MD5) Previous issue date: 2006 / Resumo: O estudo dos coeficientes de reflexão, de suas aproximações e consequentemente da análise de AVO (do inglês, Amplitude Variation with Offset) desenvolve um papel bastante importante na indústria do petróleo, por auxiliar na descrição litológica da região de interesse. Neste trabalho, inicialmente abordamos as principais idéias envolvidas na dedução das equações dos coeficientes de reflexão PP (ondas P incidente e P refletida) e PS (ondas P incidente e S refletida). Na sequência, são apresentadas diferentes aproximações para estas equações, seguidas de uma análise do comportamento das mesmas quando comparadas entre si e entre suas respectivas expressões exatas. Introduzimos uma nova aproximação para o coeficiente de reflexão PS similar à impedância de reflexão do coeficiente PP proposta recentemente. Finalizamos o trabalho discutindo o conceito de inversão de dados, avaliando a precisão dos indicadores apresentados, e fazendo um breve sumário da tradicional análise de AVO / Abstract: The study of the reflection coefficients, their approximations and the AVO (Amplitude Variation with Offset) analysis plays an important role in the oil industry as they can help to describe the interest region lithology. The first part of this work deals with the main ideas of the deduction of the reflection coefficients PP (P incident and P reflected waves) and PS (P incident and S reflected waves). Then, different approximations for these equations are presented, followed by a discussion of their behavior when compared among them and with their exact expressions. We introduce a new approximation for the reflection coefficient PS similar to the reflection impedance of PP coefficient proposed recently. To conclude, some indicators and their accuracy are discussed and a brief summary about the traditional AVO analysis is presented. / Mestrado / Mestre em Matemática Aplicada

This thesis looks at power series, particularly in the areas of: radius of convergence, properties of functions represented by power series, algebra of power series, and Taylor's Theorem and continuation by means of power series.