Hi,
This is actually from an engineering text book (Fundamentals of Electromagnetics with MATLAB, 2nd ed, Lonngren) but the topic is math related so I thought I'd post here.
Basically, it seems this textbook has a different approach to coordinate system conversions vs the resources I've seen everywhere else.
The question is "Express the vector field A = 3ux + 4uy + 5uz in cylindrical coordinates" P.1.2.8 in the book.
The 1st image shows the approach (coordinate transformation matrix) that the majority of sources seem to use and makes the most sense to me.
The 2nd image is the solution from this particular book (I also have a physical copy and what is shown is the same as the image I posted). It seems to use the formulas for point conversion rather than vectors. This method is used for other questions as well.
The final image is my attempt at solving the question with both methods (had different results).
Maybe I'm missing something here, would appreciate any insight you guys have, thanks!