Which Calculus books are recommended for fun and in-depth learning?

[ibmichuco]

Hi all,

I am looking for calculus books that are fun to read. In
particular, I am looking for books that show, say, the
proof of

\int dx/x = log[x]

not just simply state the results. Something similar
to Thompson's Calculus made easy.

Thanks in advance,

Michuco

 

[lugita15]

In my opinion, the best way to learn Calculus for the first time is using infinitesimals, not limits. Absolutely nothing beats Silvanus Thompson's Calculus Made Easy, so if you haven't already read it you definitely should. If you liked it, then I would recommend Calculus Without Limits by John C. Sparks. Just like Thompson's classic text, it approaches calculus using the intuitive notion of an infinitesimal, and its style is very conversational and humorous. It's treatment is more modern, though, and despite its title it does occasionally use the notion of Limits.

If you like to do calculus with infinitesimals but want to do it more rigorously and precisely, then read Elementary Calculus: An Infinitesimal Approach by Jerome Keisler. It's also very easy and understandable, so you might want to take a look if it's for you. But it's not "fun" in any sense of the word.

If you are willing to learn calculus without infinitesimals, but still using a fun and entertaining book, then I would highly recommend Calculus: the Easy Way by Douglas Downing, which is how I was able to learn a large part of Calculus as early as sixth grade! It teaches Calculus in the form of a story, where the characters have to use Calculus to solve various problems. (I know that it sounds dumb, but it has really god explanations.

 

[Frostfire]

Hi all,

I am looking for calculus books that are fun to read. In
particular, I am looking for books that show, say, the
proof of

\int dx/x = log[x]

not just simply state the results. Something similar
to Thompson's Calculus made easy.

Thanks in advance,

Michuco

I don't know if you found what you were looking for but my personaly favorite is the 6th edition of Larson hosteller edwaurds Calculus, its just a textbook, but it does a very nice job of working things out

 

[ibmichuco]

Lugita15 and Frostfire,

Thanks for the suggestions. I am finishing Calculus
made easy and have downloaded a copy of Keisler
Elementary Calculus. Calculus by Larson, Hostetler
and Edwards doesn't look bad, but $170.00? I
paid $23. for my Thompson/Gardner copy.

Cheers,

Michuco

 

[lugita15]

Larson, Hostetler, Edwards is a full-sized textbook, so it's no wonder it's really expensive. But in my opinion, it's probably not best to start off with a big textbook anyway. They may have full-color illustrations, software CDs, and "real world" applications, but they don't substantially increase your understanding.

If you are interested in a big expensive calculus textbook, though, I would recommend the one my Anton. I felt that it was much more instructive than either Larson/Hostetler/Edwards or the book by James Stewart, which is the standard textbooks used in most colleges.

 

[sponsoredwalk]

idk, for me all of these types of books have failings and you need many sources to get by. First off, if you want a follow up to Thompsons Calculus Made Easy (which I thought was okay) would be Thomas Calculus or Stewart Calculus or one of the others mentioned.

Then, the problem with these books is they are alright, they are the minimum in calculus and you need to know this material nowadays. Unless you are capable of more advanced books like Spivaks Calculus, Apostols Calculus, Courants calculus or Fritz&Courant's calculus&analysis all of which require proofs and are a humongous step up from Thompsons Calculus Made Easy (IMO, maybe others don't think so) I suggest getting one of the above books.

Once you have Stewart or something, work through the book as fast as possible, and be 100% sure you can do all types of problems in the book, (not all though jeesh there are thousands) . There was no way, for me, to be able to do everything in those books by using the books material, I needed youtube videos. This is where you learn the material imo, here's three sources. http://www.youtube.com/user/khanacademy http://www.youtube.com/user/patrickJMT & find videos on 5min.com by Thinkwell (which are truly the best for calculus). Unless you've got a photographic memory you'll need to practice questions and I think this is a full frontal assault on calc. It's just the way I did it, it is by no means a method clad in stone & hopefully you'll go through less pain than I did learning this material for the first time (along with all of the prerequisites mixed in for fun )

BTW, don't pay crazy amounts of money. Get the book second hand, either online, on amazon or at a college bookshop. It's worth getting one of those standard books so that you can master it and then throw it in the bin or sell it and be done with it, so that you can move on to either study calc more in depth or study diff eq's etc...

Hope this helps somewhat

 

[Gib Z]

It depends on your experience and mathematical maturity, in which age and practice can be a factor. I first learned calculus roughly from "Calculus for Dummies". Right after I finished it I picked up a copy of Courants "Differential and Integral Calculus, Volume 1" and couldn't make any sense of it at all. I waited about another year whilst I did other mathematics, and then I found it readable and enjoyed the extra rigor, detail and proofs immensely.

Whatever level you are at, my suggestion is rather than doing several of the easy books, think you know the subject and move on to another topic, do at least one "difficult" book first. For Calculus, Courant is great.

EDIT: Also, I directly oppose the notion of using Infinitesimals rather than limits in a first course in calculus. Calculus as most people see it is basically most fundamentally on the concepts of a function and of a limit.

 

[sponsoredwalk]

I don't see where the problem with limits comes from. Especially the epsilon-delta phobia, if anything it's the most intuitive concept. Also, I have Spivak & Fritz/Courant and find them both great but I want to get some discrete math/ proofing down before I re-attempt them, I hate skipping things as you feel you haven't learned anything so they signify a brighter future :p

 

[ibmichuco]

I took calculus many years ago and my work now involves
a fair amount of math, like, I got to play around with
stuff like gamma function (which I found Nahin's An
Imaginary Tale an excellent read), numerical methods,
but nothing fancy.

I discovered Calculus made easy a while ago, and I feel
that I got the short end of the stick when I took calculus
in my first year. Sure, the prof showed us how to do things
like integration by parts, gave us a few examples, exercises,
etc. I encountered these concepts again in later courses, but
no one ever explained it quite like Thompson. The same for
Feynman, we took physics but don't we all wish that the prof
could explain it the way Feynman does.

Reading Thompson or Feynman gives me the joy of
rediscovering things that are somehow ruined by bad profs.
I read Thompson's Calculus made easy in bed and find myself
saying, why on Earth didn't the prof say this to me. Quite a
few Homer moments - "that's where that comes from, doh!"

To make a long story short (kind of late for that now, :-)) I
am looking for books where the authors explore things a bit
deeper, in a leisure pace if possible, and not much of "here
we have the recipes for all possible problems that you may
encounter". The latter ones have their own purpose and are
handy to have, but I am looking for something to read in bed,
against gf's wish, not at my desk.

Thanks for listening to the ranting,

Michuco

 

[Frostfire]

Lugita15 and Frostfire,

Thanks for the suggestions. I am finishing Calculus
made easy and have downloaded a copy of Keisler
Elementary Calculus. Calculus by Larson, Hostetler
and Edwards doesn't look bad, but $170.00? I
paid $23. for my Thompson/Gardner copy.

Cheers,

Michuco

Well ya, but who buys new ;), I bought my sixth edition on amazon for 14 dollars+ shipping,
Anton does another book, but his is really into theory, and assumes you can follow when it skips steps, and the solutions manual isn't worth much especially for the first five chapters, its decent after that