Top Books for an Introduction to Calculus: Reviews and Recommendations

[theoristo]

Remarks on kline 's book??

I've been reading Morris Kline calculus book for an intro to calculus ,although I like the applications and the intuitive stuff,my preference would be a tiny bit more rigourous,I've found the following book and would like to ask for your opinion on them(which is the best for a good introduction to calculus):
1.Durell and Robson, Elementary Calculus (which was suggested at the end of W.w.sawyer calc book)
2.Calculus L.V. TARASOV Basic Concepts for High Schools(also suggested by W.w.sawyer calc book)
3.Differential and Integral Calculus by Clyde E. Love
4.Calculus by Henry Charles Wolff Herman William*
5.Introduction To Calculus by Kuratowski Kazimierz.*
6. Piskunov Differential and Integral Calculus.*
7.Elementary Calculus by FREDERICK S. WOODS
Thanks in advance.

 

[verty]

You need to pick a book and learn from it. Calculus books will very similar to each other. If you want all the rigor, get a real analysis book. Any advanced calculus book that is fully rigorous will assume you already know calculus, so you might as well just get a real analysis book instead, once you know calculus, if that interests you.

I think Kline should be fine to learn from, and if you need to, have a look at MIT's course.

 

[theoristo]

You need to pick a book and learn from it. Calculus books will very similar to each other. If you want all the rigor, get a real analysis book. Any advanced calculus book that is fully rigorous will assume you already know calculus, so you might as well just get a real analysis book instead, once you know calculus, if that interests you.

I think Kline should be fine to learn from, and if you need to, have a look at MIT's course.

Thanks ,do you know any of the books I listed?

 

[verty]

I don't know them at all. But from the recommendations I've seen on this site, Kline's book is highly regarded.

 

[micromass]

If you want a rigorous book, then go through Spivak.

 

[theoristo]

If you want a rigorous book, then go through Spivak.

I don't know enough proof to go through all of it.

 

[Theorem.]

I don't know enough proof to go through all of it.

You can learn along the way :) It is a very valuable thing to have, and will improve your problem solving skills.

 

[theoristo]

You can learn along the way :) It is a very valuable thing to have, and will improve your problem solving skills.

So what's the best book for proof and fundations?

 

[micromass]

I don't know enough proof to go through all of it.

OK, but that's the problem, I guess. Either you do it rigorously, and do Spivak. Or you have to settle with books that are a bit less rigorous. Kline and Lang are very good books in this category: not entirely rigorous, but not completely without rigor either.

So, I'm afraid that if you want more rigorous books, then you need to brush up your proofs. Or learn it along the way.

 

[micromass]

So what's the best book for proof and fundations?

Velleman has always been a popular proof book. I don't think you can find much better.

 

[Theorem.]

Velleman has always been a popular proof book. I don't think you can find much better.

I agree. It covers all the basics quite nicely.

 

[theoristo]

Thanks velleman be it.

 

[reenmachine]

Interesting thread for me as I'm about to use Kline to learn calculus myself.I wish I could get Lang but it's much more expensive than Kline unfortunately.I'm also thinking about the possibility of going directly to Spivak , but it's just hard to judge for yourself if you are really ready to go through such a rigorous book.

Kline is not reader friendly though in my opinion , it's a brick and the writing is small on the pages.It looks like you're reading a dictionnary.

 

[theoristo]

Wait, I have this other book A Course of Pure Mathematics by Hardy ,what is it about? I can't find any thread about it here,although everybody claim it to be one of the best ...but the best on what subject?

 

[Theorem.]

http://en.wikipedia.org/wiki/A_Course_of_Pure_Mathematics

 

[theoristo]

Thanks.

 

[QuantumCurt]

I'm starting calculus in a couple weeks, and I've been planning on picking up the Kline book. I've gotten a couple of recommendations for it here, and most of the reviews I've read for it online have been pretty good. It sounds like it reinforces a lot of the intuitive aspects of calculus. I'm also planning on picking up the Lang book, which sounds like it has a bit more rigor, and focuses more on the theoretical/formal aspects of calculus. I think the combination of the two should make for a good supplement. The required text for my Calculus sequence is Larson's Calculus, and the reviews are mixed. I can't say I've been very fond of the Larson books I've used in the past. The College Algebra book was pretty good, but the Trigonometry book was downright awful.

I'm also planning on picking up the Spivak book sometime down the line, though I'm going to hold off on that for a while.

 

[theoristo]

A Course of Pure Mathematics by Hardy is recommended for people studying calculus says wikipedia ,well I'll use it now,should I ?

 

[micromass]

Sounds like you guys can work together :tongue:

 

[lurflurf]

If in doubt read simultaneously through a book a little easier and another a little harder. As far as rigorous calculus books go stay away from Rudin. In print I recommend Courant, Undergraduate Analysis by Lang, or Elementary Real and Complex Analysis by Shilov, Spivak is alright but a bit eccentric and lacking in motivation and completeness. Out of print there are many options either in calculus one books and calculus two books readable as a first book.

Durell and Robson, Elementary Calculus and Elementary Calculus by FREDERICK S. WOODS are fine books Wood's advanced calculus book is famous and expensive because Richard Feynman mentioned it.

Loomis and Sternberg excellent but perhaps a bit too hard, but you should look through it as it is free online.

^If you have Hardy you should know what it is about. It basically a great rigorous calculus book staying away from harder topics like interchanging limits and Lebesgue integration.

 

[theoristo]

thanks ,I'm going to read Hardy and then Spivak or courant after that.

 

[theoristo]

Just read a few pages of Hardy's book it's a bit hard ,so it's going to take me a while to get used to it(use something else to supplement it).

 

[theoristo]

Although I'm not going to use it INTRODUCTION
TO CALCULUS by KAZIMIERZ KURATOWSKI has been said to be better than Spivak on amazon

 

[theoristo]

Although I'm not going to use it INTRODUCTION
TO CALCULUS by KAZIMIERZ KURATOWSKI has been said to be better than Spivak on amazon

It's also free online legally