Should one focus on just the ability to DO the math or also the theory behind it? Would a the book " ISBN-10: 0521679710 " suffice or should I do something to the effect of Spivak's or Apostol's calculus?
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Kreyszig is a good choice, I think. At least it was for me when I did my B.S. in the 80s in EE. We did have Apostol as a reference in our freshman calculus class, but it's going to be too formal and proofy and really meant for math majors and not suited for what you want. Same for Spivak.