General Review of Tensors

Part A:

• Summantion conventions, free/dummy indices, no. of equations/terms

• Kronecker delta, alternating symbol

• Changing indices to manipulate equations

Part B:

• Tensors as a linear transformation

• Find components of a tensor given

  • Rotation/reflection about an axis or a plane

  • How some vectors are transformed

• Sum/Products/Transpose/Trace/Inverse of Tensors

• Transformation matrix Q between two base vectors

• Transformation Laws and components of tensors

• Symmetric/anti-symmetric of tensors

• Eigen values/vectors, Invariants

Part C:

• Scalar, vector and tensor fields

• Gradients, divergence and curl of the above fields