5. Find ds² in spherical coordinates by the method used to obtain (8.5) for cylindrical coordinates. Use your result to find for spherical coordinates, the scale factors, the vector ds, the volume element, the basis vectors ar, ao, ao and the corresponding unit basis vectors er, ee, ep. Write the gij matrix.

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Chapter2: Second-order Linear Odes
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Mathematical Physics 2 Topic: Tensor Analysis Please answer it in full details and show your solutions clearly.
5. Find ds² in spherical coordinates by the method used to obtain (8.5) for cylindrical coordinates.
Use your result to find for spherical coordinates, the scale factors, the vector ds, the volume
element, the basis vectors ar, ao, ao and the corresponding unit basis vectors er, ee, ep. Write the gij
matrix.
Transcribed Image Text:5. Find ds² in spherical coordinates by the method used to obtain (8.5) for cylindrical coordinates. Use your result to find for spherical coordinates, the scale factors, the vector ds, the volume element, the basis vectors ar, ao, ao and the corresponding unit basis vectors er, ee, ep. Write the gij matrix.
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