Calculus: an intuitive and physical approach

In summary, the book recommends reading Lang, Allendoerfer, Burnside, and Spivak simultaneously. It is important to read them cover to cover and work every problem. The book is helpful for self-study, but it is not the only resource needed to succeed in calculus.f
  • #1
I'm currently enrolled in precalculus and I'm finding that almost everything we've learned so far is just Algebra 2 review. I've been looking for a book where I can self study Calculus and move ahead, and I stumbled upon
Calculus: an intuitive and physical approach by Morris Kline.

I am curious as to what you guys here on PF think of the book.
The reviews on Amazon were extremely positive.

I'm tired of the shenanigans and plug-in-chug methodoligy tought in school (although I can't really blame them, they're given such little time to teach so much).
That's why I'm really looking for a book that explains the WHY behind the math, but at the same time I'm not looking for graduate level analysis or anthing of that sort (not yet), just a really solid level understanding of Calculus.

I'm really fine with overexplanations of topics, as long as it helps me understand them.
You might even say that I'd like a 'hold your hand" book that really walks you through all the concepts, but at a deeper level than what is taught in Highschool.

  • #3
Since you asked the WHY question.

Woods: Analytic Geometry & Calculus,
The first 130 pages have plenty of early 20th century style pre-calculus to shake you up.

Burnside: Theory of Equations,
Will (most likely) explain a lot of the things from your algebra classes & way more.

Chrystal: Algebra,
Will (most likely) explain a lot of the things from your algebra classes & way more.

Allendoerfer: Principles of Mathematics,
The ultimate pre-calculus book, including some calculus, more on this book

Serge Lang: Basic Mathematics,
offers a slightly different perspective, often times better.

These books, either all of them (recommended) or some combination (at least 3) will
more than prepare you for the best calculus books I know of: Courant, Apostol & Spivak.
A bit of self-study with this discrete math book before reading those tough
calculus books would be immensely helpful as well.

All this said, you could just pick up Kline's calculus book read as far as you can if all you
want to do is read calculus stuff, from personal experience I can tell you that every time
you're going to get stuck or not be able to predict ahead of time where things are going
is only because you're missing some knowledge contained in one of the above books, so
you could also just use the above as references for when you get stuck.
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  • #4
@ sponsoredwalk: When you say 3 of those books are recommended, which 3 have the least amount of overlapping material?

Also, in what order should they be read in? Like is one of the books more introductory and then after you finish it you can move to the next level and then the next level?

And with these books would you recommend reading them cover to cover and working every problem? How long would that take with 3 books?

  • #5
I would say read Lang, Allendoerfer & Burnside simultaneously & dip into Kline's book &/or a calculus-based physics book (&/or one/all of the 3 hard books I mentioned!) for motivation. Also can be insanely helpful at times. As for overlapping material, well I think treat you should this as a good thing, for example Lang treats trigonometric angles in that book by geometrically deriving cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with an intuitive & memorable picture, & hints at how you can derive nearly everything else from this, while other books will show different derivations of each formula as it comes & you might miss the power of simplicity as regards a certain topic. As for the problems, read the problem & if you can't do it in your head put pen to paper :biggrin:

Once you learn some of the material test yourself by reading some of Chrystal & Woods, hopefully you'll be skimming,
stopping only at the interesting sections (of which there are some) & doing the interesting problems.

Also, if you have trouble with proofs at some point, consider the first few chapters of the discrete math book I mentioned.
  • #6
Thanks sponsoredwalk for the great list of books

Do you (or anyone else) know if Calculus: an intuitive and physical approach can be used as a supplement for calculus I/II/III classes? or at the very least, Calculus BC?

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