Question on Morse and Feshbach's book

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I am interested in moving into the fields of mathematical physics and applied mathematics, and wish to build a solid background over the coming years. My background is a PhD in electromagnetic engineering.

After some research, it seems that the famous book by Morse and Feshbach, 'Methods of Theoretical Physics', is highly and repeatedly cited as a key reference. So, is this a good compendium of the subject that can build a solid background in this field? Are there any other contenders which are as well-regarded and as comprehensive?

Does the book by Arfken (et. al.), 'Mathematical Methods for Physicists', or the book by Jeffreys and Jefferys, 'Methods of Mathematical Physics', compare to Morse and Feshbach?

Any comments on how they compare (level, depth, scope, assumptions of reader background, etc), or suggestions of others, would be appreciated.

Finally, some people suggest that I should first do a course in Analysis, such as using the book of Whittaker and Watson, 'A Course of Modern Analysis'. Is this necessary or can one go staight to the above references?

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