Advanced calculus demystified

Advanced calculus demystifiedMost of my time recently was spent in completing a self-review of vector calculus using the text Advanced Calculus Demystified.  This study refreshed my knowledge of the mechanics and added a couple new tricks.  I completed nearly 75 of the problems in about 3 weeks of study.  (This book was particularly good, because all the problems were not just answered but worked out in the back of the book).

I learned a couple meta-lessons for me in this.

  1. There is no substitute for doing the problems.  I picked up on tics in my approach, and it was confidence building to get the correct answer.
  2. Almost all mistakes came from hasty leaps in the math (or combining leaps), and almost all hasty leaps were dictated by space on the paper!  (Emotional issue here, not wanting to waste paper, or shortcuts because “only sluggards have to write out the details”).
  3. I actually (half) remember more than I thought – my judgment of my current ability was a mistake in perception.

A lot of these still condense down to the maxim I was holding close a year ago – no more shortcuts.

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