Which Books Explain Calculus Intuitively?

[εllipse]

Understanding Calculus -- books?

I know how to work high school level calculus and such, but I don't feel like I have a very intuitive understanding of it. Can anyone suggest any books that maybe go through the history and explain it in an intuitive manner?

 

[neurocomp2003]

STEWART...i believe its the standard for cdn universitys.

 

[quasar987]

Stew is the man. Though I never looked at the much praised Courant.

 

[εllipse]

Thanks. I assume you are talking about James Stewart's . Do you know which one you're talking about?

 

[neurocomp2003]

Calculus: Early Transcendentals i believe that's the names...or intro to calc...my edition has a integral sign..and black/blue the next edition i think was a bit greenish...

 

[Noxerus]

Thomas' Calculus.

 

[quasar987]

I was talking about concepts & context.

 

[mathwonk]

stewart is a good regular calculus book, and courant is an honors level book. i recommend as old an edition of stewart as you can find, say 2nd if possible, as they are "dumbed down" in every succeeding edition.

 

[Cyrus]

I have 2nd edition and its great! (concepts and contexts) Although I hear some recommend spivak, eh mathwonk

 

[mathwonk]

again, spivak is on another level above stewart, a no nonsense honors calculus book.

honors books: spivak, apostol, courant, kitchen.

ordinary good books: stewart, edwards penney, cooke - finney - thomas, thomas,... lots of others.

then there are inferior ordinary books, whose name is legion...

then there are unpretentious good books with limited objectives: silvanus p. thompson, elliot gootman,...

 

[Cyrus]

But none with such pretty pictures of the guggenheim as stewart

 

[fourier jr]

Can anyone suggest any books that maybe go through the history and explain it in an intuitive manner?

calculus: a physical & intuitive approach by morris kline

 

[quasar987]

I stick by my opinion that if you're going to use an intuitive book, use it simultaneously witha rigorous one. Like spivak, apostol, courant, kitchen, according to wonk.

I got to check out that Spivak book that everyone's talking about as being great.

 

[cscott]

I have 2nd edition and its great! (concepts and contexts) Although I hear some recommend spivak, eh mathwonk

Is it a good first calculus book?

 

[fourier jr]

the spivak text is the most hardcore of any of all the calculus texts i think. if you're not very prepared I would say it isn't a great first book.

 

[shmoe]

I think Spivak is a great start for those aiming for a math degree more challenging than your standard major (specialist, honors, whatever you want to call it), though a very motivated math major might do well with it. I'd be wary of unleashing Spivak on your average beginning calculus student though. It would still be fine supplement for the less dense texts.

 

[MathematicalPhysicist]

stewart is a good regular calculus book, and courant is an honors level book. i recommend as old an edition of stewart as you can find, say 2nd if possible, as they are "dumbed down" in every succeeding edition.

but why the first editions of books are better than the latest ones?
arent the latest editions more updated than the ones from the past century?
im asking specifically about courant's and fritz's classic series which have in the past 5-7 years got its reedition at springer publishing company.

 

[cscott]

Is it a good first calculus book?

by "it" I meant Stewert's Concepts and Contexts... didn't realize I had quoted a sentence with both books named.

So to clarify: Is stewert's book a nice intro textbook?

Thanks.

 

[MathematicalPhysicist]

mathwonk, youre not replying because...?

 

[lurflurf]

but why the first editions of books are better than the latest ones?
arent the latest editions more updated than the ones from the past century?

There is nothing to update. What is in the older books is correct. Some topics might go in or out of fashion. The earlier editions were written with a clear purpose. Newer editions often are not. Often newer books will cite previous editions of themselves something like "I made this hard to understand so I could save ten pages for silly stuff I wanted to add see last edition for clear explanation". If the first edition was quite good tinkering is almost sure to make things worse. Let's play new book old book.

New book:has computer and calculator use tips
Old book:has sliderule use tips or only refers to hand calculations
Nb: Lacks important results
obas a few results of limited use nowdays
nb:Is obscure and bloated
ob:has clear and concise style
nbas many trivial problems (now w/ 10000 exercises!)
ob:has helpful problems
nb:uses 8000 pages when 500 would do
ob:uses 800 pages when 800 would do
nb:has pretty pictures
ob:uses figures as needed
nb:$200 brand new
ob:$5 used
nb:assumes reader is moron (is often right)
ob:assumes reader is not moron (is often right)

 

[SplinterIon]

Apologize if anyone's posted this already, but imho I think

Anton/Bivens/Davis Calculus: Early Transcendentals

is probably the best bet - It starts out ~simple (it's all relative ) and then hits a calc III or higher level by the end. The questions are fairly good and the later ones in the problem sets provide a great challenge. The newer editions do contain fluff in terms of pictures etc but they're of the more interesting variety and actually serve to illustrate some of the points better . Stewart is a waste of time - and before you say that the above might not be suitable for high-school/first year, it's what I'm using and it works like a charm.

Just my $0.02.

Edit: I have to add this is not Spivak or Courant level or anything - it's "introductory"