Ementa
Breve revis�o de An�lise Vetorial � operadores gradiente, divergente e rotacional. Teoria de Potenciais, Teorema de Helmholz. Transforma��es de coordenadas. Matrizes de rota��o, introdu��o ao c�lculo tensorial, derivada covariante e operadores diferenciais em coordenadas curvil�neas. Separabilidade de EDPs. Aplica��es do c�lculo tensorial aos meios cont�nuos, relatividade e gravita��o.
Bibliografia B�sica
Spivak, Michael. Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced CalculusApostol, Tom. Calculus: Multi-Variable Calculus and Linear Algebra with Applications to Different Equations and Probability, Vol. 2Faraoni, Valerio. Cosmology in Scalar-Tensor GravitySternberg, S. (Ed.). Differential Geometric Methods in Mathematical Physics
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Bibliografia Complementar
Cartan, H. Differential FormsBott, Raoul; W. Tu, Loring. Differential Forms in Algebraic TopologyDas, Ashoke. FIELD THEORY A Path Integral ApproachWesson, Paul S. FIVE-DIMENSIONAL PHYSICS Classical and Quantum Consequences of Kaluza-Klein Cosmology
Cosmology in Scalar-Tensor GravitySternberg, S. (Ed.). Differential Geometric Methods in Mathematical Physics
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