Which Calculus Textbook is Best for Self-Studying?

[david.aloha]

Hi, while I see this question has been beaten to death I don't feel I know the answer for myself. I've been looking at picking up a calculus text of Apostol or Spivak while I go back this fall. I'll be taking the second half of first year calculus starting september (integration, diff. equations, infinite sequences and series) and then courses in linear algebra and discrete mathematics in January. I previously went to university for a year and a half and did the first class in first year calculus (fall of 07), but the program I was in at the time didn't have any other math classes (much to my regret). Prior to that I had completed Calculus AP AB (06) and really enjoyed math.

I'd been lost for awhile as to what I wanted to do and study. I decided to take a distance course on "Finite Mathematics" which was pretty simple (although some aspects of linear programming and game theory that it covered were incredibly tedious since it was all done by hand), but it taught me how to work with matrices (my high school curriculum never went beyond simple linear systems despite being in the "pure" math stream). Most importantly, it made me realize just how much I'd missed math plus it got me self-teaching linear and more advanced algebra concepts and helped when I started working with transformations in programming 3d graphics (something I've been working on).

My calculus is more than a bit rusty at this point, but I opted to go back and start with the second calculus course anyways. I realized though when I went back to my text (Thomas Calculus 11th ed.) how frustrating it is to read through topics that are explained half-heartedly and run into all kinds of poorly defined assumptions. I need to know and work out the nitty-gritty details or it doesn't stick. I need to turn it inside out, and this text doesn't help me do that with the way it's presented. I'm currently reviewing epsilon-delta notation and it jumps around and just seems to throw things in. It has nice diagrams which help on the intuition side, but the way it approaches many things just seems so arbitrary - it's like I'm trying to form this mental mindmap and rather than being this logical web it's a mishmash of concepts that are thrown together (frankly I suck at memorization without the deeper logical/intuitive side to back it up).

I know it's getting pretty close to the start of classes, but my instructor recommends Stewart and from what I understand it's no better than Thomas (I'm taking the class at a small institution with a bunch of people who are mainly engineering transfers). I intend on continuing on in mathematics and would like a really good foundation, especially since I feel like the previous university course I took didn't do the topic much justice, and the high school course had major holes. I'll also be taking physics both semesters.

At first I was leaning towards Spivak, but after reading the way the material is presented I'm thinking about Apostol. Starting with integration would fit better with the course I'm taking anyway. I'm still not entirely sure though. Anyone with any suggestions?

 

[thrill3rnit3]

no no no to Spivak and Apostol if you're calculus is "more than a bit rusty at this point"

Go back to Thomas or Stewart

 

[david.aloha]

Thanks for responding, and I understand your concern, but I'm at least looking for a better textbook. Thomas is not working for me. I need to know things on a deeper level, I've always been that way. I'm terrible at memorizing things for the sake of memorizing. I was previously in a Kinesiology program where I did a bunch of anatomy and even more physiology. I appreciated the importance of anatomy although it was incredibly challenging for me (still did all right in it, but it was tough). I did excellent in physiology though and found it easier because I could associate with concepts like function, biochemical make-up, etc. It was more fundamental. What I remember best now from anatomy is not the naming, but the functions underlying different muscle groups, bone structures, etc (despite names being such a huge part of the class). Physiology on the other hand I remember in great depth (I spent a lot of time studying it, but I did the same for anatomy).

I'm craving something that goes into important topics in calculus on a deeper level. I'm not satisfied with "just remember it, you'll understand it better later" because I'm not going to "remember it" at the level I should without that understanding.

 

[thrill3rnit3]

Yeah I understand, but you need to have a better foundation to gain deeper insight before delving into more advanced textbooks.

If epsilon delta seems "arbitrary" to you at this point, then you still need to develop intuition about the limit process, for example.

Try William Chen's lecture notes. They're more rigorous than your run-off-the-mill textbooks.

http://rutherglen.science.mq.edu.au/wchen/lnfycfolder/lnfyc.html

Then tell us what you think about it.

 

[david.aloha]

No, epsilon-delta doesn't seem arbitrary, the book's way of explaining it does. I know that it opens up potential for more substantial proofs and gives more specificity to the definition of a limit and I already had a basic understanding of the concept (although I wanted to review it since it's been awhile since I last looked at it). I've been finding that the way I saw it presented in the book had me jumping back and forth a lot and seeing many things being assumed without definition.

The book, as many seem to do, takes the approach of "do repetitious examples and you'll memorize the way of doing it." I don't mind spending a lot of time doing problems, but if I do then I want to do ones that truly expand my understanding, not stamp out boilerplate solutions. I enjoy doing proofs (frustrating as they can be sometimes) because I feel like I get a better understanding and appreciation of whatever I'm proving, plus I find it very satisfying to prove something.

I really like that link you gave me though. Considering price (that being free) it's definitely the winner in that regard (Apostol was making me cringe, I have enough texts to buy). Also, I actually prefer reading from the computer screen over paper. It's more rigorous than my text, as you said, but that's exactly what I'm looking for. It's clear, defines what is written, and doesn't try to mask more complicated concepts (which I always find just makes them more complicated). Thanks.

 

[yungman]

I study a lot of calculus on my own. I have many books include (Anton, Bivens), (Thomas, Finney), ( Sherman Stein), Varberd.

Sherman Stein is a very easy book to understand. It is very good until the last two chapters of vector fields, line integrals, Green's, Stoke's and Divergence theorem. The book is pretty bad on that. But for the first two classes, this is the best for easy understanding.

Over all Anton, Bivens is the best book. Not the easiest one, but it is the book that is most complete, tighter and more logical than Stein. Now when ever I reference back, I only use Anton.