MTH623 Finalterm Quiz solution by taleemi markaz
MTH623 FinalTerm preparation Quiz (Lecture 23-45) with 100% accurate Solution
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Questions:
The Christoffel symbols of first kind 𝚪_𝒊𝒋𝒌 are defined by
In generalized curvilinear coordinates the divergence of vector point function 𝑨^𝒊=𝑨^𝒊 (𝒙^𝒊 ) is defined as
Christoffel symbols of first and second kind include derivatives of
The Christoffel symbols of first kind 𝚪_𝒊𝒋𝒌 are symmetric in
The Christoffel symbols of first kind satisfy the transformation law of a third rank tensor.
The Christoffel symbols of first and second kind are equal in any coordinate system.
In the notation 𝚪_𝒊𝒋^𝒌 of Christoffel symbol of second, the symbol 𝒌 tells
The covariant differentiation of metric tensor is
For a diagonal metric which of the following is true?
The covariant differentiation of a tensor with constant components is zero.
The covariant derivative and partial derivatives coincide when _________ are constant.
In curvilinear coordinates the derivative of a vector also includes
In generalized curvilinear coordinates the gradient of scalar function ∅=∅(𝒙^𝒊 ) is defined as
The covariant derivative of an arbitrary tensor is tensor.
The ordinary derivative of a tensor is a tensor if and only if coordinate changes are restricted to
The covariant differentiation of a scalar is equal to
In any coordinate system 𝒙^𝒊, the covariant derivative with respect to 𝒙^𝒌 of a covariant vector 𝚪_𝒊 is defined as
Which of the following is true for basis vectors in general curvilinear coordinates systems?