Selecting the Right Calculus Book for University Prep

[Chewy0087]

Hey again, I just posted a thread yesterday about University preparation and I was recommended to consolidate and expand my calculus knowledge and in light of that I would like help in choosing a calculus book;

While looking at these forums there's been a lot of praise for Michael Spivak's book "Calculus", but I'm not sure if it's at the right level for me;

I've already studied derivatives, differentiation and simple integrals, as well as differentiating/integrating trigonometric functions and differentiation/integration of e. After looking at the index on Amazon of the book, it seems to me that the book spends almost 1/2 to 2/3 of the book on these things, which I feel relativity confident on.

Therefore do you think it's worth me buying this book? Is there sufficient detail in it to warrant me buying it?

To be honest the price is not a HUGE issue as it's Christmas anyway and since I'm usually given some money a good calculus book would be good (i know that sounds sad =P) and a good investment.

If this book isn't right could you please recommend on that would be more suitable?

Thanks a lot again.

 

[Chewy0087]

After further investigation i found the book;

"Calculus" by James Stewart

now THIS book seems to be almost perfect for me, and it goes into all of the depth i think i'd need (possibly ever!)

however! this book is a whole £40.00 (perhaps around $65.00) is that worth it?

 

[Nabeshin]

Stewart is pretty much the watered down version of calculus. If you already know the mechanics of differentiation/integration/etc. why are you considering buying another book?

The point of Spivak is to make a transition into calculus beyond mere computation. To that end, Spivak almost serves as an introductory analysis text in some respects.

 

[Chewy0087]

Stewart is pretty much the watered down version of calculus. If you already know the mechanics of differentiation/integration/etc. why are you considering buying another book?

The point of Spivak is to make a transition into calculus beyond mere computation. To that end, Spivak almost serves as an introductory analysis text in some respects.

Hmm could you then recommend a book that isn't "watered down" as such, and will likely lead me through all of the calculus that i'll need? For example differential equations (first and second order), vector calculus, infinite series, partial differentiation, and multiple integrals?

I agree that I'm happy with the mechanics of simple differentiation and integration but I understand there's so much more to calculus i'll need in time, and am looking for a really good book to use

 

[naele]

Stewart is fine for multivariable and vector calculus. You should consider the book by Gilbert Strang. It's freely available from MIT OCW http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm

There's also a free associated solutions manual, and it covers the calculus you're looking for. For differential equations consider a separate text such as Pollard and Tenenbaum https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20

 

[xristy]

A nice single and multi-variable straddle between calculus and analysis is https://www.amazon.com/dp/354065058X/?tag=pfamazon01-20 reissued by Springer in 3 volumes. There are chapters on Calculus of Variations, Differential Forms and so on as well as solutions for the original volume 2 (now split into 2 volumes).

 

[Nabeshin]

Hmm could you then recommend a book that isn't "watered down" as such, and will likely lead me through all of the calculus that i'll need? For example differential equations (first and second order), vector calculus, infinite series, partial differentiation, and multiple integrals?

I agree that I'm happy with the mechanics of simple differentiation and integration but I understand there's so much more to calculus i'll need in time, and am looking for a really good book to use

I don't mean watered down in terms of content -- Stewart's book has all the topics you mention. It's just I (and undoubtedly others) feel that it's at a very mechanical level with little or no underlying theory. I haven't read your other post, but if this is what you're looking for, then stewart appears to be a popular choice. Depending on why you're learning calculus and what you hope to get out with it, a more theoretical approach like Spivak might be completely useless. Sorry if I came down harsh on Stewart -- it can be a good book, but just evaluate it on the basis of what you need and expect to get out of the text.

Also, like naele notes, usually one uses a separate book for differential equations, but you will undoubtedly have to take that later in university so the brief intro in a book like Stewart should be sufficient.

 

[Chewy0087]

Hmm i see, well the main reason I want to learn calculus is simply to give me the tools to do university physics, sad to say it but I have little or no interest in the pure math side of it =P, do you think Stewarts book would give me that?

Thanks a lot for the advice, it's much appreciated! :D

Thanks for the links as well, the book by Gilbert Strang looks great but unfortunately I don't have access to a computer all the time and would need a paper-copy of it :/, which costs even more! than Stewart...

 

[qspeechc]

Stewart is ok for the single-variable stuff, but I feel the chapters on vector calculus are poor, but that's just my opinion. For vector calculus I prefer the book by Marsden & Tromba, which gives more explanation and theory, but is not proof-heavy.

 

[yungman]

I am mostly self studying on Calculus. I have books by Stein & Barcellos, Thomas & Finney, Anton & Bevens & Davis, Varberg & Purcell and a lot of older book from my college days.

I think the best one is Anton Bevens & Davis. It is slightly more advance than the other few. But it is the most logical, well explained. Some books like Stein & Barcellos is easy to understand at the beginning BUT when it come to the more advance portion, it started to get confussing because the author try too hard to keep it simple and the concept got loss. This is particular true in the last 2 chapters on Green's, Stokes, Divergence theorems, line, surface and volume integrals. I end up have to restudy the Anton book. It might take a little time to follow, but once you get into the detail, Anton really shines.

I have the student manual for both Anton and Stein. I bought it used on Amazon for really good price. My secret of self study is to get multiple books so you can see different point of views. Also no books are good in all topics, my experience is all books are good in some sections, some are just better in more sections.