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).
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Portuguese Pages 347 [354] Year 2016
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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
Citation preview
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