referências bibliográficasdenebola.if.usp.br/~jbarata/notas_de_aula/arquivos/nc-cap46.pdf ·...

Referências Bibliográficas

A lista bibliográfica abaixo contém livros-texto onde parte do material contido nestas notas também pode ser encontradoe outros textos cuja leitura é igualmente recomendada.

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JCABarata. Notas para um Curso de F́ısica-Matemática Versão de 4 de dezembro de 2020. Bibliografia 2479/2512

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Apareceu também em http://jcnoticias.jornaldaciencia.org.br/21-simetrias-e-seu-papel-na-fisica/

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Mais informações sobre G. Hermann e traduções de seus trabalhos mais relevantes encontram-se em: Elise Crull and Guido Bacciagaluppi(Editores), “Grete Hermann - Between Physics and Philosophy” (Studies in History and Philosophy of Science) 1st ed. 2016 Edition.ISBN-13: 978-9402409680 Springer; 1st ed. 2016 edition.

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Índice Remissivo

∗-álgebra, 1989∗-álgebra de Banach, 1990∗-álgebras de Banach, 2125∗-bi-ideal, 2021∗-isomorfismo, 2031∗-morfismo, 1989∗-morfismo fiel, 20321-formas, 15721 + 2 + 3 + 4 + 5 + · · · = −1/12, 370A-módulo à direita, 101A-módulo à esquerda, 101C(R), 34C1(R), 34C∞(R), 34Ck(R), 34C0(R), 34G-torsor, 115I-incompat́ıveis, 47T0, 1454T1, 1455T2, 1455T3, 1455T4, 1455T5, 14562, 33Ker , 1979Mat (C, m, n), 32, 437Mat (C, n), 32, 437Mat (R, m, n), 32Mat (R, n), 32Ran , 1979Sn, 34, 15880a, b, 438

T (a, b)(M), 1572X (M), 1572X ∗(M), 1573B(X), 33♣, 33δij , 34〈·, ·〉

C, 32

〈·, ·〉R, 32

�, 124µ-quase em toda parte, 1325σ-álgebra, 69, 1293σ-álgebra de Borel, 1301, 1346σ-álgebra de Lebesgue, 1344, 1345σ-álgebra gerada, 70σ-álgebra gerada por A, 1301σ-álgebra indiscreta, 1295σ-álgebra induzida, 1305σ-álgebra produto, 1306σ-álgebra trivial, 1295σ-aditividade, 1322σ-anel, 68σ-anel gerado, 69σ-álgebra gerada, 1301σ-álgebra induzida, 1305σ-álgebras, 1293

σ-aditividade, 1322σ-compacidade, 1471♠, 33τ -aberto Euclidiano, 1539τcp, 1295d-limite, 1208f−1, função inversa, 41f−1, pré-imagem de uma função, 41g-simétrico, 1614n-atlas, 1540n-cone, 1584n-forma, 208n-forma linear, 208n-forma multilinear, 208r-ciclo, 999B(H), 1976B(H1, H2), 1976B(L), 33

Álgebras, 101Álgebras associativas, 1988Álgebras associativas normadas, 1989Álgebras com involução, 1988Órbitas, 113álgebra, 67, 101álgebra alternativa, 103álgebra ∗, 1989álgebra Abeliana, 102álgebra Booleana, 85álgebra associativa, 102, 1988álgebra associativa normada, 1989álgebra comutativa, 102, 1988álgebra de Banach, 1990álgebra de Banach-∗, 1990álgebra de Grassmann, 108, 195álgebra de Heisenberg, 1009, 1012álgebra de Jordan, 107álgebra de Lie, 105álgebra de Lie do grupo de Galilei, 1106álgebra de Lie do grupo de Lorentz, 1100álgebra de Lie nilpotente, 1157álgebra de Lie semissimples, 1158álgebra de Lie simples, 1158álgebra de Lie solúvel, 1157álgebra de Poisson, 107álgebra de divisão, 110álgebra de operadores não-degenerada, 2028álgebra de von Neumann, 2027álgebra de von Neumann gerada por um conjunto de operadores,

2027álgebra dos quatérnios, 201álgebra exterior, 195, 1694álgebra exterior de formas, 1693álgebra fator, 191álgebra gerada, 68, 192álgebra involutiva, 1989álgebra quaterniônica, 201álgebra quociente, 191álgebra tensorial, 193

2492

JCABarata. Notas para um Curso de F́ısica-Matemática. Versão de 4 de dezembro de 2020. Índice Remissivo 2493/2512

álgebra universal, 80álgebra C∗, 1990álgebra C∗ gerada por um conjunto de operadores limitados agindo

em um espaço de Hilbert, 2011álgebra A∗, 1989álgebra B∗, 1990álgebras CCR, 1817álgebras de Banach, 2125álgebras de Lie, 105álgebras de Lie associadas aos grupos simpléticos, 1116álgebras de Lie nilpotentes, 588álgebras de Poisson, 107álgebras exteriores, 109álgebras unitais, 1778árvore de Cayley, 382órbita, 113ı́ndice, 500ı́ndice de um operador nilpotente, 500ı́ndices, 702ı́ndices de deficiência de um operador, 2157ı́ndices de uma equação diferencial, 702ı́nfimo, 56ângulo azimutal, 2372ângulo de nutação, 1047ângulo de precessão, 1047ângulo de rotação (intŕınseca), 1047ângulo latitudinal, 2372ângulo polar, 2372ângulos de Euler, 1045, 1046, 1060ângulos de Tait-Bryan, 10486, 33, 33

◊, 33

∗-representação de uma álgebra C∗, 2033

A conjectura de Riemann, 375ação, 2373ação à direita, 124ação à direita de G sobre M , 112ação à esquerda, 123ação à esquerda de G sobre M , 111ação cont́ınua, 116ação de um grupo, 111ação do grupo de translações no espaço de distribuições, 1853ação efetiva, 114ação fiel, 114ação fortemente cont́ınua, 116ação livre, 114ação regular, 114ação simplesmente transitiva, 114ação transitiva, 114ação trivial, 114ação trivial para um elemento do grupo, 114ações sobre funções, 112Abelianização de um anel, 188Abelianização de uma álgebra, 192Abeliano, 88aberto estrelado, 1702abertos, 74aceleração azimutal, 2337aceleração centŕıfuga, 2337aceleração de Coriolis, 2337aceleração de Euler, 2337aceleração inercial translacional, 2337aceleração transversa, 2337aderência, 1306adição de funções harmônicas esféricas, 807aditividade contável, 1322aditividade da Entropia de von Neumann, 2050

adjunto, 1977, 1986adjunto de um operador (caso não-limitado), 2145age efetivamente, 114age fielmente, 114age livremente, 114age transitivamente, 114Algoritmo de Euclides, 91Alternativa de Fredholm, 2085amálgama de dois grupos por homomorfismos, 147, 149Análise Convexa, 260Análise Funcional, 1229Anéis, 101Anéis de divisão finitos, 111Anéis não associativos, 100anel, 65, 101anel com unidade, 110anel de divisão, 110anel de integridade, 110anel fator, 188anel gerado, 67, 188anel não associativos, 100anel quociente, 188anel sem divisores de zero, 110anti-homomorfismo, 117, 118anticomutador, 108Anticomutatividade, 105anticomutatividade, 105antimorfismo de espaços vetoriais, 118Antissimetria, 107aplicação g-transposta, 1613aplicação g-dual, 1613aplicação diferenciável entre variedades, 1547aplicação diferencial, 1565Aplicação diferencial exponencial, 584aplicação diferencial exponencial, 585aplicação exponencial geodésica, 1659aplicação inclusão, 1381, 1544aplicação quociente, 49aplicação quociente à direita, 123aplicação quociente à esquerda, 123aplicações, 40aplicações congruentes, 1215aplicações lineares, 118aproximação de Stirling, 335aproximação de Stirling para a Função Gama, 336aproximação de Stirling para a função gama, 336aproximantes da identidade, 2019aproximantes da identidade de uma álgebra C∗, 2019aproximantes da unidade, 2019aproximantes da unidade de uma álgebra C∗, 2019aproximantes da unidade em álgebras C∗, 2019aproximantes de Bernstein, 1740, 1792Ascoli-Arzelà, 1490associador, 103Associatividade, 88associatividade, 80associatividade do produto de matrizes, 438atlas, 1540atlas de coordenadas normais, 1660atlas equivalentes, 1546atlas infinitamente diferenciável, 1546atlas maximal, 1547atlas maximal gerado por um atlas, 1547autofunção, 787automorfismo, 118, 138, 400automorfismo interno, 118autovalor, 787, 1984autovalor do Problema de Sturm-Liouville, 949autovalores, 448autovalores simpléticos, 535, 1120


autovetor, 451, 1984Axioma da Escolha, 45axioma da escolha, 153axiomas, 45axiomas de fecho de Kuratowski, 1312axiomas de Kuratowski, 1312axiomas de separação, 1452axiomas de separabilidade, 1452

Baker, Campbell e Hausdorff, 587base algébrica, 150base canônica de coordenadas, 1557base de coordenadas, 1557base de Hamel, 150, 152, 153base de uma topologia, 1302base dual canônica, 155base integral, 649base ortonormal completa, 1925base sobrecompleta, 1933base supercompleta, 1933base topológica, 154, 1927base topológica completa, 154Bases algébricas em espaços vetoriais, 150bases de Hamel, 153bases ortonormais completas, 1928bases singulares à esquerda e à direita, 530Bases topológicas em espaços vetoriais, 154bi-ideal, 186bi-ideal algébrico, 190bi-ideal autoadjunto, 2021bicompacto, 1472bicomutante, 2026bidual (topológico), 1959bidual algébrico, 159bidual algébrico de um espaço vetorial, 158bimódulo, 101binômio de Newton, 771birapport, 393boa-postura, 873bola aberta, 228, 1220bola fechada, 228Bolzano-Weierstrass, 1476bom ordenamento, 55boost de Lorentz, 1091boosts de Galilei, 1105bordo de uma bola, 228Bourbaki, 79, 1472box product topology, 1515Breit-Wigner, 1859

Cálculo Funcional, 471cálculo funcional, 471ćırculos de Gershgorin, 456cabo transatlântico, 2226calibre de Coulomb, 2326calibre de Lorenz, 2287campo de Jacobi, 1665campo de Killing, 1669, 1672campo geodésico, 1675campo tensorial, 1572campo tensorial diferenciável, 1572campos vetoriais, 1572cancelável à direita, 94cancelável à esquerda, 94caráter de uma representação, 1188caracteŕıstica, 98, 886, 888, 910Caracteŕıstica de um corpo, 97caracteŕıstica zero, 98cardinalidade, 58carta, 1540

carta de coordenadas, 1540carta local, 1540carta local de coordenadas, 1540cartas compat́ıveis, 1546catedral de Braśılia, 494Cauchy-Schwarz, 215causalidade de Einstein, 2225centralizador, 131centro de massa, 2340centro do grupo, 131chessboard transformation, 446choque, 904ciclo, 999cilindro eĺıptico, 495cilindro hiperbólico, 495cilindro parabólico, 495cilindro ultra-hiperbólico, 495classe C1, 34classe Ck, 34classe de conjugação, 1189classe de equivalência, 48classe monótona, 70classe monótona crescente, 70classe monótona decrescente, 70Classes Ck, 34classes de difeomorfia, 1547classes de difeomorfia suave, 1548classes de elementos conjugados, 1189Classificação de EDPs de segunda ordem, 877codimensão, 1570codomı́nio, 40coeficientes de Fourier, 1755coeficientes de uma conexão, 1618coeficientes do tensor de curvatura, 1645Cofatores, 446colagem de conjuntos por uma função, 50colapso da função de onda, 2454colchetes de Poisson, 107, 2397combinação linear, 150combinação linear afim, 261combinação linear convexa, 260, 261, 1912compacidade, 1471compacidade contável, 1471compacidade local, 1472compactificação de um ponto, 385compatibilidade, 2438complemento ortogonal, 1914completamento, 1216completamento canônico, 1216completamento canônico dos racionais, 1252completeza, 1209, 1211completeza de um espaço métrico, 1211complexo de cocadeias, 1699complexo de de Rham, 1699componente conexa, 1451componente de um vetor na direção de outro vetor, 229componente de uma partição, 43componentes de uma forma diferencial, 1693componentes contravariantes, 180, 1611componentes contravariantes do tensor métrico, 179, 1610componentes covariantes, 180, 1611componentes covariantes do tensor métrico, 179, 1610componentes de um tensor, 170, 1561, 1572componentes do tensor de curvatura, 1645comprimento de uma curva, 1657comutador, 105comutante, 2026Comutatividade, 108comutatividade, 80comutatividade graduada, 195, 1694


comutativo, 88concatenação de palavras, 148concavidade da Entropia de von Neumann, 2048condição de Dini, 1784Condição de Dirichlet, 926condição de Hölder, 1736condição de Lipschitz, 1380condição de Lorenz, 2287Condição de Neumann, 926condição de suporte, 1879condição forte de energia, 1678, 1682condição forte de exergia, 619Condição mista, 926condições de contorno, 871, 937Condições de Dirichlet, 923, 924, 929, 932condições de Dirichlet, 872condições de fronteira, 871Condições de Neumann, 923, 925, 929, 933condições de Neumann, 872condições iniciais, 871, 872Condições mistas, 929, 933condições mistas, 872condições subsidiárias, 873condutibilidade térmica, 2192, 2193cone, 494, 1584cone n-dimensional, 1584cone de luz futuro, 2225cone de luz passado, 2224conexão afim, 1617conexão compat́ıvel com um tensor métrico, 1628conexão de Einstein-Cartan, 1634conexão de Levi-Civita, 1634conexão de Riemann-Cartan, 1634conexão de Weyl, 1634conexão dual, 1625conexão livre de torção, 1626conexão métrica, 1628conexão Riemanniana, 1628conexão simétrica, 1626conexões de Weyl, 1634congruência, 1574congruência de curvas, 1675congruência geodésica, 1675conjectura de Riemann, 357, 375conjugação, 1189conjugado quaterniônico, 204conjunto contável, 58conjunto τ -compacto, 1473conjunto τ -denso, 1314conjunto τd-compacto, 1480conjunto d-aberto, 1220conjunto d-limitado, 1480conjunto aberto, 1220conjunto absorvente, 227conjunto afim, 261conjunto bem-ordenado, 55conjunto bicompacto, 1472conjunto com medida σ-finita, 1338conjunto compacto, 1473conjunto complementar, 38conjunto conexo, 1449conjunto convexo, 261, 1912conjunto convexo gerado, 263conjunto das partes de X, 39conjunto de Cantor, 1451conjunto de Cantor ternário, 1352conjunto de Vitali, 1321conjunto denso, 1314, 1447conjunto denso em parte alguma, 1353, 1447conjunto denso em si mesmo, 1447

conjunto derivado, 1311conjunto desconexo, 1448conjunto diagonal, 1459conjunto dirigido, 54, 1371, 2180conjunto enumerável, 58conjunto equicont́ınuo de funções, 2078conjunto fechado, 74, 1294conjunto fechado em um espaço métrico, 1221conjunto gerador, 103conjunto invariante pela ação de um grupo, 113conjunto limitado, 1480conjunto limitado inferiormente, 56conjunto limitado superiormente, 56conjunto minimizante, 544conjunto não-mensurável, 1321conjunto ortonormal, 1918conjunto ortonormal completo, 1925conjunto ortonormal de vetores, 230conjunto parcialmente ordenado, 52conjunto perfeito, 1447conjunto pré-compacto, 1480conjunto pré-ordenado, 51conjunto quase-ordenado, 51conjunto relativamente compacto, 1474, 1480conjunto resolvente, 448, 2000, 2053, 2054conjunto sequencialmente compacto, 1480conjunto total, 1930conjunto totalmente desconexo, 1451conjunto totalmente limitado, 1480conjuntos τ -abertos, 74conjuntos abertos, 1294conjuntos Borelianos, 1301, 1403Conjuntos contáveis, 58conjuntos de Borel, 1301conjuntos de Cantor, 60, 1352conjuntos densos, 1314, 1447Conjuntos enumeráveis, 58conjuntos fractais, 1330conjuntos mensuráveis, 1294conjuntos mensuráveis por Lebesgue, 1345conjuntos precisamente separados por uma função, 1454conjuntos separados, 1454conjuntos separados por uma função, 1454conjuntos topologicamente separados, 1454constante cosmológica, 1655constante de difusão térmica, 2193constante de Einstein, 1654constante de Euler-Mascheroni, 321, 348, 749constante de gravitação universal, 1654constante de Lipschitz, 621, 1262, 1380constante de Lyapunov, 1123constante de movimento, 2398constante de Planck, 869constante de separação, 880constante Omega, 1267constantes de estrutura, 103, 1071constantes de estrutura de su(3), 1071construção GNS, 2037contável, 58continuidade em um ponto, 1383continuidade por partes, 1380continuidade uniforme, 1484contração, 1262contração de ı́ndices, 1563, 1564contradomı́nio, 40Contraexemplo de Tikhonov, 2215convenção de Einstein, 170, 177, 871, 1554convergência de produtórias infinitas, 303convergência de sequências de conjuntos, 63convergência forte de operadores limitados, 1512


convergência fraca, 2071convergência fraca de operadores limitados, 1511Convergência pontual, 1727Convergência uniforme, 1727convex closure, 263convex envelope, 263convex hull, 263coordenada azimutal, 254coordenada longitudinal, 254coordenada radial, 254coordenadas ćıclicas, 2364coordenadas Gaussianas normais, 1679coordenadas generalizadas, 2371coordenadas normais, 1660core de um operador, 2154corpo, 94corpo negro, 378corpos não comutativos, 111correções perturbativas, 658correlação, 2437coset, 126coset à direita, 123coset à esquerda, 123Cosets, 123Cosets à direita, 123Cosets à esquerda, 123covariância, 2437, 2443covetores, 176covetoriais, 1572CPT, 1097Critério de Lebesgue para integrabilidade de Riemann, 1395cross-ratio, 393cruzamento de curvas caracteŕısticas, 896Cubo de Hilbert, 1519curva caracteŕıstica, 892Curva de Koch, 1363curva envoltória, 637curva geodésica em relação a uma conexão afim, 1656curva integral, 1574curva integral completa, 1574curva tipo espaço, 1657curva tipo tempo, 1657curvas caracteŕısticas base, 892curvas caracteŕısticas planares, 892curvas de Bézier, 1740curvatura de Gauss, 1647curvatura de Ricci, 1652curvatura escalar, 1652curvatura Gaussiana, 1647curvatura seccional, 1650

dados composicionais, 121dados de Cauchy, 885, 2238decomposição KAN , 525decomposição p-ádica, 1255decomposição convexa, 261Decomposição de Iwasawa, 525decomposição de Iwasawa, 525Decomposição de Jordan, 498Decomposição de Schmidt, 518decomposição de Schmidt para matrizes, 520decomposição em fatores primos, 354Decomposição em valores singulares, 515decomposição espectral, 470, 2108Decomposição KAN, 525decomposição polar de A, 2068Decomposição polar de matrizes, 513degenerescência finita, 1985delta de Krönecker, 34, 176denso em parte alguma, 1447, 1525

denso em si mesmo, 1447derivação, 184derivação covariante, 1621derivada covariante, 1619derivada de Fréchet, 1399derivada de Lie, 1575–1577derivada de Lie de um campo escalar, 1575derivada de Lie de uma função, 1575derivada de Schwarz, 420derivada de uma distribuição, 1863derivada exterior de formas, 1696derivada normal, 926desigualdade de Cauchy, 1238Desigualdade de Cauchy-Schwarz, 214, 218desigualdade de Cauchy-Schwarz, 215, 1603, 2443desigualdade de Grönwall, 1291Desigualdade de Hölder., 1234Desigualdade de Hadamard, 549desigualdade de Hadamard, 277, 549desigualdade de Hermite-Hadamard, 277desigualdade de Jensen, 267, 275, 281desigualdade de Minkowski, 216, 222, 287, 288Desigualdade de Minkowski., 1234desigualdade de Young, 282, 284desigualdade triangular, 220, 221, 223, 224, 1204desigualdades de Bessel, 1924desigualdades de correlação, 2465desvio padrão, 1810, 2437determinante, 213, 442Determinante de exponenciais de matrizes, 567Determinante de matrizes, 213determinante de Slater, 1942determinante Wronskiano, 629, 944determinantes de Fredholm, 982, 984diâmetro, 1348, 1480diagonalização, 467diagonalizabilidade de matrizes autoadjuntas, 485diagrama comutativo, 1700, 1708difeomorfismo, 1546, 1547difeomorfismo infinitamente diferenciável, 1547difeomorfismo local, 1548difeomorfismo suave, 1547difeotipo, 1548diferença simétrica, 39diferenças finitas, 1930dilatação, 383dimensão, 151dimensão algébrica, 151dimensão algébrica finita, 151dimensão Hausdorff, 1351dimensão topológica, 154discos de Gershgorin, 456distância entre conjuntos, 1452distribuição, 1797, 1847distribuição de Cauchy, 1859distribuição de Cauchy-Lorentz, 1859distribuição de Dirac, 1851distribuição de Heaviside, 1850distribuição de Lorentz, 1859distribuição de probabilidades, 2436distribuição delta de Dirac, 1413, 1851distribuição delta de Dirac diagonal, 1883distribuição delta diagonal, 1883distribuição Gaussiana, 1810distribuição normal, 1810distribuição sinal, 1851distribuição temperada, 1848distribuição valor principal de Cauchy, 1855distribuições parte finita de Hadamard, 1857distribuições regulares, 1849


distribuições regulares temperadas, 1849distribuições temperadas regulares, 1849distributividade, 80divergente, 1637, 1638divergente de um campo segundo uma conexão afim, 1638Divisão Euclidiana, 91divisor de zero, 110domı́nio da forma, 2162domı́nio da relação, 40domı́nio de dependência, 2224domı́nio de influência, 2225domı́nio de integridade, 110dominância diagonal, 456dominação diagonal, 1271Doppelverhältnis, 393Du Bois-Reymond, 1762dual, 1847dual (topológico) duplo, 1959dual algébrico, 154, 158dual algébrico de um espaço vetorial, 154dual topológico, 156, 1916, 1959dual topológico de um espaço vetorial, 156dualidade de Hodge, 183, 1706duplo comutante, 2026

EDO, 603EDP, 866efeito Bohm-Aharonov, 1701, 2178Efeito Dzhanibekov, 2357efeito Eötvös, 2340eixo de rotação, 2332eixos principais de inércia, 2350elemento inverso, 1997elemento maximal, 55elemento minimal, 55Elemento neutro, 88elemento nulo, 95elemento nulo de um reticulado, 84elemento unitário, 2007elipsoide, 494emparelhamento, 1847, 1848endomorfismo, 118, 119energia mecânica, 2347ensemble canônico, 2439ensemble micro-canônico, 2439Entropia de von Neumann, 2047enumerável, 58envoltória convexa, 263epigráfico, 265epigráfico estrito, 265epigrafo, 265epimorfismo, 117, 1063equação a coeficientes constantes, 605equação a derivadas parciais, 866equação anaĺıtica no infinito, 688equação caracteŕıstica, 886, 888, 910Equação da Óptica Geométrica, 870equação da corda pendurada com densidade variável, 2199equação da corda pendurada homogênea, 2200Equação de Airy, 609equação de Airy, 727, 971equação de Bernoulli, 625Equação de Bessel, 609equação de Bessel, 746equação de Bessel esférica, 757equação de Bessel generalizada, 756equação de Bessel modificada, 758Equação de Burgers, 870Equação de Burgers invisćıvel (i.e., sem viscosidade), 870equação de Clairaut, 636

equação de continuidade, 2287equação de D’Alembert, 636Equação de difusão, 868Equação de difusão de calor, 868equação de difusão de calor, 2193equação de difusão de calor homogênea, 2193equação de difusão e causalidade de Einstein, 2215equação de difusão não-homogênea, 1893, 1894, 2278equação de difusão relativ́ıstica, 2215, 2269Equação de Dirac, 871Equação de Duffing, 608Equação de Euler, 608, 871equação de Euler, 686, 744, 2346, 2352equação de Euler da Mecânica dos Fluidos, 870Equação de Gauss, 609equação de Gauss, 713equação de Gauß, 761Equação de Gross-Pitaevsky, 869equação de Heisenberg, 2441Equação de Helmholtz, 868Equação de Hermite, 609equação de Hermite, 725Equação de Heun, 610, 713Equação de Hill, 609equação de Jacobi, 1665equação de Killing, 1669, 1670Equação de Klein-Gordon, 869equação de Klein-Gordon, 2269Equação de Korteweg-de Vries, 870equação de Korteweg-de Vries, 2229equação de Korteweg-de Vries modificada, 2231Equação de Kummer, 610equação de Kummer, 764equação de Lagrange, 636Equação de Laguerre, 609equação de Laguerre, 759Equação de Laguerre associada, 609equação de Laguerre associada, 769equação de Laguerre generalizada, 823Equação de Langevin, 608Equação de Laplace, 868Equação de Legendre, 609equação de Legendre, 722equação de Legendre associada, 609, 767Equação de Mathieu, 609Equação de Navier-Stokes, 871equação de ondas amortecidas, 2269Equação de ondas homogênea, 868Equação de ondas homogênea com amortecimento, 868Equação de ondas homogênea com amortecimento interno, 868equação de ondas livres, 933equação de ondas simples, 2198equação de Papperitz, 707Equação de Poisson, 868equação de Poisson, 1892, 1893, 2277equação de ponto fixo, 1261equação de Riccati generalizada, 626equação de Riemann, 707equação de Riemann-Papperitz, 707Equação de Schrödinger, 869Equação de Schrödinger independente do tempo, 869Equação de Schrödinger não-linear, 869Equação de Sine-Gordon, 869equação de Sine-Gordon, 2231equação de Sturm-Liouville, 423Equação de Tchebychev, 609equação de Tchebychev, 729Equação de Tricomi, 869equação de Tricomi, 878equação de van der Pol, 604


equação diferencial exata, 634equação diferencial homogênea, 605equação diferencial impĺıcita, 603equação diferencial não-homogênea, 605equação diferencial ordinária, 603equação diferencial ordinária de ordem n, 603equação diferencial parcial, 603Equação do calor, 868Equação do oscilador anarmônico amortecido, 608Equação do oscilador harmônico forçado amortecido, 608equação do potencial de poço-duplo, 2234Equação do telégrafo, 869equação do telégrafo, 2226, 2269equação exata, 632equação Fuchsiana, 693Equação Hipergeométrica, 609equação hipergeométrica, 713, 761Equação Hipergeométrica Confluente, 610equação hipergeométrica confluente, 764equação indicial, 738Equação Integral de Fredholm, 958equação integral de Fredholm, 1273equação integral de Fredholm de primeiro tipo, 980equação integral de Fredholm de segundo tipo, 981equação integral de Fredholm linear de primeiro tipo, 2087equação integral de Fredholm linear de segundo tipo, 2087Equação Integral de Fredholm linear homogênea de segundo tipo,

958equação integral de Volterra, 1274equação integral de Volterra de primeiro tipo, 981equação integral de Volterra de segundo tipo, 981Equação KdV, 870equação KdV, 2229Equação linear de segunda ordem e homogênea, 608Equação linear de segunda ordem não-homogênea, 608equação MKdV, 2231equação quase-linear, 875equação secular, 2380equação semi-linear, 875equação separável, 627equações com retardo, 607equações de Einstein, 1654equações de Euler da Mecânica de Corpos Ŕıgidos, 2346equações de Euler-Lagrange, 2375equações de Hamilton, 2394equações de Jefimenko, 2289equações de Killing, 1672Equações de Maxwell, 870Equações de Maxwell em meios materiais, 871Equações de Maxwell fora de meios materiais, 870equações de onda não-homogêneas, 871equações de Riccati, 627equações de Riccati generalizadas, 626equações diferenciais homogêneas, 874equações diferenciais não-homogêneas, 874equações eĺıpticas, 877, 878, 889, 890equações Fuchsianas, 693equações hiperbólicas, 878, 890equações integrais de Fredholm, 981equações integrais de Volterra, 981equações mistas, 878equações parabólicas, 877, 878, 890equações ultra-hiperbólicas, 878, 890equicontinuidade, 1491equilimitação, 1491equilimitação global, 1491equilimitação pontual, 1490, 1491equivalência de normas, 222escalar de curvatura, 1652escalares, 95, 98

esfera de Bloch, 2050Esfera de Riemann, 383, 385esfera padrão, 1589, 1590esfera unitária, 34, 804, 1588esferas exóticas, 1590espaço σ-compacto, 1471espaço ambiente, 1572espaço completamente normal, 1456espaço completamente normal Hausdorff, 1456espaço contavelmente compacto, 1471espaço cotangente, 1558espaço das formas, 1693espaço de órbitas, 115espaço de Banach, 1228espaço de Cantor, 62espaço de componentes canonicamente conjugadas, 1024espaço de configurações, 2371, 2393espaço de curvatura constante, 1652espaço de fase, 1558espaço de fases, 2393espaço de Fock, 192, 1942espaço de Fock antissimétrico, 192, 1943espaço de Fock simétrico, 192, 1943espaço de Fréchet, 1455espaço de Hausdorff, 1455espaço de Hilbert, 1229, 1234, 1909espaço de Kolmogorov, 1454espaço de Lindelöf, 1471espaço de Schwartz, 1798, 1800, 2212, 2213espaço Hausdorff, 1370espaço homogêneo, 115, 123, 124espaço homogêneo principal, 115espaço Lindelöf, 1471espaço localmente compacto, 1472, 1502espaço localmente Euclidiano de dimensão n, 1500, 1540espaço métrico, 1204Espaço Mensurável, 1292espaço mensurável, 1293espaço metrizável, 1521espaço normal, 1455espaço normal Hausdorff, 1455espaço paracompacto, 1472espaço perfeitamente normal, 1456espaço projetivo, 1593espaço projetivo bidimensional, 1592espaço projetivo real, 1041espaço quasecompacto, 1472espaço quociente, 162espaço real projetivo, 50espaço regular, 1455espaço regular Hausdorff, 1455espaço simétrico, 1455espaço supermétrico, 1206espaço tangente, 1552, 1554espaço tipo T0, 1454espaço tipo T1, 1455espaço tipo T2, 1455espaço tipo T3, 1455espaço tipo T4, 1455espaço tipo T5, 1456Espaço Topológico, 1292espaço topológico, 74, 1293espaço topológico σ-compacto, 1471espaço topológico compacto, 1471espaço topológico contavelmente compacto, 1471espaço topológico localmente compacto, 1472espaço topológico normal, 1453espaço topológico paracompacto, 1472espaço topológico perfeitamente normal, 1453espaço topológico quociente, 1514, 1545


espaço topológico regular, 1453espaço topológico segundo-contável, 1314, 1460, 1508espaço topológico separável, 1314espaço topológico soma, 1514espaço ultramétrico, 1206espaço uniformemente convexo, 1241espaço-tempo, 1080espaços compactos, 1471espaços de Banach, 1234espaços de deficiência, 2157espaços de Fock, 1942espaços fibrados, 1596espaços homeomorfos, 1381espaços métricos completos, 1209, 1211espaços métricos isométricos, 1215espaços reflexivos, 1959espaços ultramétricos, 1254espaços vetoriais isomorfos, 151espectro, 448, 2000, 2054espectro cont́ınuo, 2054espectro de autovalores, 2054espectro de um operador, 2000espectro discreto, 2054espectro pontual, 2054espectro residual, 2054esquema de Riemann, 708estado, 2036, 2436estado de Gibbs, 2439estado de mistura, 2040estado de uma álgebra C∗, 2036estado f́ısico, 2436estado puro, 2040, 2438estados coerentes, 1930, 1933, 2449estimativa de Cauchy, 401Estrela de Koch, 1330, 1361estrelas binárias, 824estrutura, 79estrutura algébrica, 79estrutura complexa, 235estrutura infinitamente diferenciável, 1547estrutura infinitamente diferenciável gerada por um atlas, 1547estrutura relacional, 79Euler-Lagrange, 2375Euler-Tricomi, 869, 878evolução temporal de um estado Gaussiano, 2258exemplos básicos de álgebras de Lie, 106expansão binomial, 771expansão de multipolos, 810expansão em frações parciais da função cotangente, 310, 327, 1785expansão geodésica, 1676expoente de Lyapunov, 1285expressão local de um tensor, 1572extensão, 44extensão canônica de uma forma quadrática, 2165extensão de formas quadráticas, 2163extensão de Friedrichs, 2169, 2170extensão de operadores, 2141extensão linear, 1953Extensões de funções, 44

fórmula da cotangente de Euler, 310, 327, 1785fórmula de Koszul, 1632, 1634fórmula de Plemelj-Sokhotsky-Weierstrass, 1861fórmula de adição das funções de Bessel, 830fórmula de adição das funções harmônicas esféricas, 809fórmula de adição de funções harmônicas esféricas, 807Fórmula de Baker, Campbell e Hausdorff, 587Fórmula de Baker-Campbell-Hausdorff, 557, 587fórmula de Baker-Campbell-Hausdorff, 583, 1156, 1819, 1820fórmula de Binet, 298

fórmula de Breit-Wigner, 1859fórmula de Cauchy, 401Fórmula de Duhamel, 557, 592fórmula de Duhamel, 593Fórmula de Duhamel para derivadas de exponenciais, 558fórmula de duplicação, 729fórmula de duplicação da função gama, 328fórmula de duplicação da função Legendre, 328fórmula de duplicação da função seno, 328fórmula de inversão de Möbius, 306, 307fórmula de Jacobi, 455, 1633fórmula de Jensen, 328fórmula de Koszul, 1631fórmula de Leibniz, 1942fórmula de Leibniz para o determinante, 213, 442Fórmula de Lie-Trotter, 557, 574fórmula de Lie-Trotter, 574fórmula de Mehler, 816fórmula de Mercer, 960fórmula de multiplicação da função gama, 333fórmula de multiplicação de Gauss da função gama, 333fórmula de produto de Euler, 356, 359fórmula de reflexão a função Γ, 316fórmula de reflexão de Euler, 324fórmula de reflexão para a função Γ, 324fórmula de Rodriges, 1053fórmula de Rodrigues, 792fórmula de Rodrigues dos polinômios de Hermite, 812fórmula de Rodrigues para as funções de Hermite, 814fórmula de Rodrigues para o grupo SO(3), 1038fórmula de Rodrigues para os polinômios de Laguerre, 818fórmula de Rodrigues para os polinômios de Legendre, 768, 795fórmula de Rodrigues para os boosts de Lorentz, 1103fórmula de soma de Poisson, 1838fórmula de Wallis, 304, 306, 327fórmula do complemento da função gama de Euler, 318Fórmula do comutador, 557, 574fórmula do comutador, 574fórmula do produto de Wallis, 304fórmula do produto Wallis, 306fórmula do resto da expansão de Taylor, 1747, 1752Fórmulas de Girard, 309fórmulas de inclusão-exclusão, 1324fórmulas de prostaférese, 1758fórmulas de recorrência para os polinômios de Laguerre, 820fórmulas de recorrência para os polinômios de Laguerre associados,

823fórmulas de Rodrigues para o grupo SO(3), 1038Fórmulas de Viète, 309fórmulas do crivo de Poincaré-Sylvester, 1325fórmulas do crivo de de Moivre, 1324fórmulas dos determinantes de Fredholm, 984fósseis, 65famı́lia de conjuntos, 42famı́lia equicont́ınua de funções, 1491famı́lia equilimitada de funções, 1491famı́lia globalmente equilimitada de funções, 1491famı́lia normal de polinômios trigonométricos, 855fase de Condon-Shortley, 805fator, 2027fator integrante, 633fatores primos, 354fechado, 1221fecho, 1306fecho convexo, 263fecho de um operador, 2144fecho de uma forma quadrática, 2165fecho normal, 126fibrado, 1597fibrado coordenado, 1596


fibrado cotangente, 1560fibrado principal, 1597fibrado tangente, 1558fibrado vetorial, 1597fibrados, 1596fidelidade quântica, 2471, 2472filtro, 74filtro de Fréchet, 75fineza de uma partição, 1389flexibilidade, 104fluxo Hamiltoniano, 2439fluxo induzido por um campo vetorial, 1575fluxos d

referências bibliográficasdenebola.if.usp.br/~jbarata/notas_de_aula/arquivos/nc-cap46.pdf ·...

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