Div, grad, curl, and all that

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1. bikenagaApr 2024
   I got "Calculus Made Easy" back in high school, and it helped when I first took calc in 10th grade, and then BC Calc in 12th grade. It gave me some confidence to have seen the basic ideas presented in a gentle way. Actually, once you get past the old-fashioned language and layout many math books from the early 1900's are pretty good. They don't have a lot of the abstraction that came later, some of which makes you feel like you're trying to do surgery while wearing boxing gloves. Anyway, there are other calc books which have similar intents, though different styles. Here are two:

   Daniel Kleppner and Norman Ramsey, "Quick Calculus" - We used this for math background when I was taking AP Physics in high school. The physics textbook was Resnick and Halliday, which uses calc throughout. It is not particularly intuitive, but the "programmed learning" approach makes it very easy to pick up enough basic computational ability to do applications. (The phrase "programmed learning" is so old that maybe I should clarify that it has nothing to do with computers.)

   H. M. Schey, "Div, Grad, Curl, and All That" - This might be helpful for people taking vector calculus, or using it in an electromagnetism course in physics. In fact, a lot of his examples are from E-M. Very good at providing intuition without too many technicalities.

   I think the best uses for books like these are: (a) You want to get the "big ideas" without worrying too much about technical facility (maybe because you won't ever need it - e.g. you're just learning for your own interest); (b) To provide a fair amount of the math you'll need in (say) a physics course; (c) As prep before taking a standard calc course, or maybe as a refresher. Books like Thompson, Kleppner and Ramsey, or Schey will help with the big picture and to boost confidence but it's best to read them before taking the "real" calc course - since once the "real" course is running you'll be too busy with the work in the course to read something else on the side. But do whatever works for you. Calculus really is wonderful - have fun!

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2. mp05Dec 2023
   > You want Strang.

   Hell yeah you want Gilbert. Watching the guy's MIT lectures is a joy and the gumby-colored book reads like a narrative. I wish my calc books were as well written, else I'd not be reviewing vector calc with some intensity in my 30s.

   That said, I have to recommend "Div, Grad, Curl, and All That" as I believe that I found it through someone's random comment here and it was a stellar find. I've realized I'm rather rusty on these topics and this book is very assertive of its target audience.

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3. deepsquirrelnetAug 2023
   Even though Susan Rigetti says you don’t need to learn calculus first, I would recommend it -— or learn it concurrently with the introductory mechanics course. Mechanics is so much more enriching when you learn the mathematical language that was created to describe it.

   You’ll already be one step ahead by the time you get to the second course, which is good, because you can strongly benefit from learning vector calculus at that time. I really enjoyed the text “Div, Grad, Curl and all that”.

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4. lamontcgJan 2023
   Div Grad Curl and All That

   https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161

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5. dudeinjapanNov 2022
   "Div, Grad, Curl, And All That: An Informal Text On Vector Calculus"

   This was "optional" reading in my Undergrad Calculus class at Brown, I probably was the only student who bothered to read it, and it made most of engineering a breeze for the next 3.5 years, whether electromagnetism, fluid dynamics, etc.

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6. nborwankarNov 2022
   Div, grad, curl and all that - H.M. Schey Excellent intuitive and visual introduction to vector calculus.
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