Best Introduction to Calculus Book

[StonedPanda]

Teeehehhehe I was kidding about Div Grad Curl and all that--- I am taking vector calc and I have trouble with that book.

Me too. Vector Calculus by Marsden and Tromba, right? The T.A said that it made things overly complex and didn't explain things enough. Alas, this is what our teacher uses =p

A pretty awesome introduction to calculus book, and it's also pretty definitive is Calculus by Anton. He later included some co-authors, Bivens and Davis. Anton is a legend in the calculus textbook writing world =p

 

[mathwonk]

what about an honors calc book?

I am teaching honors calc this fall and cannot find a good book. I do not mean Spivak or Apostol, those are too hard for my "honors" course. There only seem to be really weak books for non honors, or really hard books for super honors courses, Any good plain old intermediate honors books out there?

I don't want to be difficult but I also dislike heavy books, and space wasted on technology, or bundled CD's. I want clear explanations, some rigor, and a logical sequence of ideas, intelligently written.

I have considered the old Courant, but it looks a bit unattractive on the page for todays kids. I once liked Stewart, and Thomas Finney, but subsequent editions have been dumbed down.

 

[mathwonk]

You need to look at some books to see what you like. I suspect you are not going to learn about Maxwell's equations from "Calculus for blondes".

Calculus Made Easy, by Thompson was written by a fellow of the royal society of engineers, about 80 years ago for average people to learn methods of calculus, without theory [quote: what one fool can do, another can"]. What he says about calculus is correct, and I loved that book, but it was impossible for me to understand WHY what he said was correct from the presentation there. It is short and cheap, and light.

A book like Stewart, is a step up. it is a good standard, long, heavy, expensive, calculus book that hits all the bases, but without extensive theory. In my opinion it has deteriorated in quality as new editions come out, so i would recommend an old edition, like the second edition, as better and also cheaper used.

If you are a budding mathematician or theoretical physicist, a real no nonsense honors level book by a master, that really explains deeply all the ideas of calculus, is the book of Apostol (2 volumes). Many people will say it is too hard, but I used it successfully with a class of returned high school teachers, none of whom were mathematicians. One of them liked it so well, she decided to go into graduate school in math afterwards.

Probably the best overall calculus book on one and several variables, including physics applications and enough mathematical rigor for most people is the 2 volume set by Richard Courant. It is a classic, has been in print over 60 years and has never been surpassed. Go online at Amazon.com and read the raves about it from users to see for yourself.

To go straight to the several variables stuff you need for physics without waiting for years, there are cheap excellent books on the partial differential equations of physics, by excellent pedagogues that explain the ideas without the mathematical baggage.

I would not be afraid to look at Div Grad Curl and all that. As I recall it was written in the 60's by a physicist who wanted to help his students, possibly at MIT, get to the material quicker than they were doing in their math courses. The famous books by Feynman as I recall made using calculus seem easier than my math courses did.

 

[mathwonk]

I realize it may be way too late for the original questioner, but here is a great deal on the excellent 9th edition of thomas and finney:

THOMAS/FINNEY
CALCULUS 9TH ED BY THOMAS/FINNEY
0201531763*
ISBN: 0201531763
Bookseller Inventory #T8029-15
*


Price:*US$*3.90 (Convert Currency) Shipping:*Rates & Speed


Bookseller:*SUBtext, Student Union Building, University of Victoria,, PO Box 3035, Victoria, BC, Canada, V8W 3P3


That's right, only $3.90. The good thing here is that this edition is actually better than later editions, but is so cheap because of the policy of textbook publishers of releasing new editions every year to kill off the used book market.

You can't beat this. To find such bargains occasionally, look on the excellent used book site, ABEBOOKS.com.

 

[BobG]

I would second two previous suggestions for an initial introduction:

David Berlinski's "A Tour of the Calculus" - It does introduce Calculus, plus the info on different math legends is great.

Any Michael Kelley book, including "The Complete Idiot's Guide to Calculus". He also wrote a very readable "Master the AP Calculus AB and BC Tests". He even has a nice website - www.calculus-help.com . The highlight of site has to be Michael Kelley's hit song, "Quadratic Formula Song".