Linear, Bilinear and Multilinear functions, tensors, rank of a tensor, Cartesian tensors, Transformation properties, Tensor notation: free indices, repeated indices, Einstein summation.
Lecture 3: Physical Applications of Tensors
Moment of Inertia tensor, dielectric constant tensor of a birefringent material, electrical conductivity tensor of a crystal, Maxwell stress tensor, Four vectors and Covariant form of (i) Charge continuity equation (ii) Maxwell's equation (iii) Klein Gordon equation and (iv) Dirac equation.
Lecture 4: Tensor Calculus
Tensor fields, Differentiation of tensor fields, Tensor fields in Curvilinear coordinates, Derivatives of basis vectors and Christoffel symbols, Covariant differentiation, Gradiant, Divergence and Curl in tensor notation, Geodesics.
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