EDP: Um Curso de Graduação 9788524404221

O objetivo deste livro é servir de texto para um primeiro curso de graduaçcão em Equações Diferenciais Parciais (EDP’s).

291 93 93MB

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Table of contents :
Capítulo 1. Definições Básicas

1. Introdução
2. Linearidade e Suporsição
3. Condições de Contorno e Iniciais
4. Exercícios

Capítulo 2. Equações de Primeira Ordem: O Caso Linear

1. Alguns Exemplos
2. O problema de Cauchy
3. Solução Geral
4. Exercícios

Capítulo 3. Equações de Primeira Ordem: Nem Tudo São Flores

1. De Volta ao Problema de Cauchy
2. Propagação de Singularidades
3. Ondas de Choque
4. Exercícios

Capítulo 4. Equações Semi-Lineares de Segunda Ordem

1. Classificação
2. Formas Canônicas e Curvas Características
3. Exercícios

Capítulo 5. Equação de Onda

1. Solução Geral
2. A Corda Finita
3. Funções Pares, Ímpares e Periódicas
4. A Corda Finita
5. Exercícios

Capítulo 6. Separação de Variáveis e Séries de Fourier

1. O Método de Separação de Variáveis
2. Os Coeficientes de Fourier
3. Interpretação Geométrica
4. Exercícios

Capítulo 7. Convergência das Séries de Fourier

1. Sequência e Série de Funções
2. Convergência Pontual
3. Convergência Uniforme
4. Convolução
5. Exercícios

Capítulo 8. A Equação de Laplace

1. O Problema de Dirichlet em um Retângulo
2. O Problema de Dirichlet no Disco Unitários
3. Exercícios

Capítulo 9. A Equação de Calor

1. De Volta ao Problema de Transmissão de Calor
2. O Problema da Barra Infinita
3. Exercícios

Capítulo 10. A Transformada de Fourier

1. A Transformada em L1
2. O Espaço de Schwartz
3. A Operaço de Convolução
4. Aplicações
5. Exercícios

Capítulo 11. As Identidades de Green

1. Preliminares
2. As Identidades de Green
3. Exercícios

Capítulo 12. Princípios do Máximo e Teoremas de Unicidade

1. Princípio do Máximo para Funções Harmônicas
2. Princípio do Máximo para a Equação de Calor
3. Integrais de Energia
4. Exercícios

Capítulo 13. Sugestões e Respostas

Bibliografia

Índice
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