{"id":6,"date":"2016-12-15T20:27:37","date_gmt":"2016-12-15T22:27:37","guid":{"rendered":"http:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/?page_id=6"},"modified":"2021-05-20T15:23:04","modified_gmt":"2021-05-20T18:23:04","slug":"calculo-vetorial-e-tensorial","status":"publish","type":"page","link":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/","title":{"rendered":"C\u00e1lculo Vetorial e Tensorial"},"content":{"rendered":"

Recomenda\u00e7\u00f5es:<\/strong> Fun\u00e7\u00f5es de V\u00e1rias Vari\u00e1veis<\/a><\/p>\n

Ementa<\/h2>\n

An\u00e1lise Vetorial: Campos vetoriais, operadores gradiente, divergente e <\/span>rotacional. Integrais de Caminho e Superf\u00edcie. T<\/span>eoremas de Green, Gauss & Stokes. <\/span>Teoria de Potenciais, Teorema de Helmholz. Introdu\u00e7\u00e3o ao c\u00e1lculo tensorial, derivada <\/span>covariante e operadores diferenciais em coordenadas curvil\u00edneas. Aplica\u00e7\u00f5es do <\/span>c\u00e1lculo tensorial aos meios cont\u00ednuos, relatividade e grav<\/span>ita\u00e7\u00e3o.<\/span><\/p>\n

Objetivos<\/h2>\n

Os objetivos da disciplina C\u00e1lculo Vetorial e Tensorial s\u00e3o de capacitar o <\/span>aluno a: entend<\/span>er e resolver problemas de C\u00e1lculo Diferencial e Integral para Fun\u00e7\u00f5es <\/span>de V\u00e1rias Vari\u00e1veis; entender e resolver problemas de C\u00e1lculo Vetorial; entender e <\/span>resolver problemas de C\u00e1lculo Tensorial; fazer uso destas ferramentas para resolver <\/span>problemas de f\u00edsic<\/span>a em mais de uma dimens\u00e3o. Por exemplo, problemas de <\/span>Cinem\u00e1tica, Mec\u00e2nica, Fluidos, Eletromagnetismo, Relatividade e Gravita\u00e7\u00e3o.<\/span><\/p>\n

Programa<\/strong><\/h2>\n

An\u00e1lise Vetorial:<\/strong> Limites e Derivadas de Fun\u00e7\u00f5es Vetoriais. Matriz do Jacobiano. Operadores gradiente, divergente e rotacional.<\/p>\n

Integrais de Caminho e Superf\u00edcie:<\/strong> Curvas e Superf\u00edcies. Integrais de Caminho e Superf\u00edcie. Teoremas de Green, Gauss & Stokes. Teoria de Potenciais, Teorema de Helmholz.<\/p>\n

C\u00e1lculo Tensorial:<\/strong> Introdu\u00e7\u00e3o ao c\u00e1lculo tensorial, derivada covariante e operadores diferenciais em coordenadas curvil\u00edneas. Aplica\u00e7\u00f5es do c\u00e1lculo tensorial aos meios cont\u00ednuos, relatividade e gravita\u00e7\u00e3o.<\/p>\n

Bibliografia B\u00e1sica<\/b><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \n
  • APOSTOL, T. M. C\u00e1lculo II: c\u00e1lculo com fun\u00e7\u00f5es de v\u00e1rias vari\u00e1veis e \u00e1lgebra linear, com aplica\u00e7\u00f5es \u00e0s equa\u00e7\u00f5es diferenciais e \u00e0s probabilidades. Waltham: Revert\u00e9, 1996.<\/span><\/li>\n<\/ul>\n
      \n
    • ARFKEN, G. B.; WEBER, H. J.; HARRIS, F. E. Mathematical M<\/span>ethods for Physicists. <\/span>6th. ed. <\/span>Amsterdam: Elsevier Academic, 2005.<\/span><\/li>\n<\/ul>\n
        \n
      • BRAGA, C. L. R. Notas de F\u00edsica Matem\u00e1tica: equa\u00e7\u00f5es diferenciais, fun\u00e7\u00f5es de Green e <\/span>distribui\u00e7\u00f5es. S\u00e3o Paulo: Livraria da F\u00edsica, 2006.<\/span><\/li>\n<\/ul>\n
          \n
        • STEWART, J. D. Calculo, v. 2. S\u00e3o Paulo: Cengage, <\/span>2005.<\/span><\/li>\n<\/ul>\n

          Bibliografia Complementar<\/b><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

            \n
          • BUTKOV, E.; F\u00edsica Matem\u00e1tica. Rio de Janeiro: LCT, 1998.<\/span><\/li>\n<\/ul>\n
              \n
            • COURANT, R.; HILBERT, D. Methods of Mathematical Physics, v. 1. <\/span>New York: Wiley, 1989.<\/span><\/li>\n<\/ul>\n
                \n
              • GUIDORIZZI, H. L. Um Curso de C\u00e1lculo, v. 3. Rio de Janeiro: LTC, 2001.<\/span><\/li>\n<\/ul>\n
                  \n
                • MARSDE<\/span>N, J. E.; TROMBA, A. J. Vector Calculus. <\/span>5th ed. New York: W. H. Freeman & Company, <\/span>2003.<\/span><\/li>\n<\/ul>\n
                    \n
                  • MATTHEWS, P. C.; Vector Calculus. New York: Springer<\/span>–<\/span>Verlag, 1998.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                    Recomenda\u00e7\u00f5es: Fun\u00e7\u00f5es de V\u00e1rias Vari\u00e1veis Ementa An\u00e1lise Vetorial: Campos vetoriais, operadores gradiente, divergente e rotacional. Integrais de Caminho e Superf\u00edcie. Teoremas de Green,…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_mi_skip_tracking":false},"_links":{"self":[{"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/pages\/6"}],"collection":[{"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/comments?post=6"}],"version-history":[{"count":19,"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/pages\/6\/revisions"}],"predecessor-version":[{"id":105,"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/pages\/6\/revisions\/105"}],"wp:attachment":[{"href":"https:\/\/gradmat.ufabc.edu.br\/disciplinas\/cvt\/wp-json\/wp\/v2\/media?parent=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}