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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Calculus > Números Complexos e Funções Analíticas: Limites, Derivação e Integração de Funções de Variável Complexa
Números Complexos e Funções Analíticas: Limites, Derivação e Integração de Funções de Variável Complexa

Números Complexos e Funções Analíticas: Limites, Derivação e Integração de Funções de Variável Complexa


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About the Book

O conteúdo deste livro foi escrito de forma a adequar-se à uma primeira familiarização de estudantes de matemática e das engenharias com a teoria das funções complexas, e para ser um livro texto em um curso introdutório semestral da referida disciplina. A teoria apresentada possui uma estrutura lógica elegante que, além de ser proeminente em matemática pura, representa um instrumento indispensável para matemáticos aplicados, engenheiros e físicos. Um curso de cálculo, cobrindo derivadas e integrais, é um pré-requisito para um bom andamento do curso. Este livro está dividido em três partes. A primeira trata da teoria dos números com plexos. Nela damos ênfase aos aspectos algébricos e geométricos dos números complexos, a sua escrita na forma polar, a utilização da fórmula de De Moivre para o cálculo de raízes complexas, e a relação de Euler. Na segunda parte são apresentadas as funções de variáveis complexas, incluindo tópicos como limites, continuidade e derivadas dessas funções. Outrossim, é dado destaque especial às equações de Cauchy-Riemann e às funções elementares: exponencial, trigonométricas, hiperbólicas e logarítmica. A terceira parte expõe, primeiramente, a teoria básica da integral de funções complexas, destacando-se a renomada fórmula integral de Cauchy e o teorema de Cauchy-Goursat e suas implicações, e um estudo das primitivas de uma função complexa. Em seguida, finalmente, faz-se uma exposição de aplicações importantes da teoria. O livro é ainda dotado de vasta gama de exemplos de aplicações e de seções com exercícios resolvidos, os quais fornecem uma coletânea de modelos para a resolução dos problemas propostos em cada unidade, para os quais apresentamos as soluções completas no final de cada unidade. Finalmente, após cada uma das seções de respostas, apresentamos adendos que trazem curiosidades sobre números complexos, conjecturas envolvendo números primos e números perfeitos, e o teorema de Fermat.


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Product Details
  • ISBN-13: 9798311141062
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Height: 279 mm
  • No of Pages: 270
  • Returnable: N
  • Sub Title: Limites, Derivação e Integração de Funções de Variável Complexa
  • Width: 216 mm
  • ISBN-10: 8311141061
  • Publisher Date: 19 Feb 2025
  • Binding: Paperback
  • Language: Portuguese
  • Returnable: N
  • Spine Width: 14 mm
  • Weight: 662 gr


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