Need help, being taught calculus with stewart, what to do

[Cannon00]

Hey guys, I'm so glad I found this forum, so many interesting things to read.

I have a problem. I'm currently going into my 3rd university calculus course, all of which use the Stewart textbook. We only have 1 version of the calculus courses, so I don't have the option of switching into a course using a better text. I've read on here that Stewart was terrible. I've read on amazon it was terrible. And in my experience, it's pretty terrible.
Being that I've already gone through most of the Stewart book within these courses, should I just stay the course until I get into analysis, or should I go through calculus from the beginning using Apostol, Spivak, or both?
Thanks guys, I've seen similar threads to this, but haven't found one with the exact situation of still being enrolled in full time classes, and having gone through a lot of the calculus stream already with Stewart while worrying about the quality of knowledge obtained.

 

[MATLABdude]

Go to class and take notes?

Then again, I only ever used mine for reference and the problems assigned out of it. Can't really comment on how great of a text it was, but I thought it was at least better than Spivak (in the sense that you didn't need to derive everything for later use)

EDIT: And welcome to Physicsforums!

 

[qntty]

Stewart's not an exceptional book but I don't think it's bad. It's a typical college textbook. You can get more out of it if you read the proofs and do the "problems plus" sections. For me the decision to pick up Spivak came down to enjoying the challenge, so I guess that, ideally, the decision should justify itself. If you're asking whether it would be a waste of time to do so because there will be too much overlap, then there is a lot of overlap with the two books especially in the beginning but Spivak has a near flavor to it and as long as you do the problems you'll still learn a lot.

 

[mbisCool]

Essentially your level of expertise relies on your own efforts. The book is not the most rigorous with regards to the problems; however, you can still master calculus if you use it effectively.

Also, as qntty already metioned, the problem plus section at the end of each chapter is quite useful. The problems there are not so much plug and chug like the problems found throughout each chapter. The problem sets in texts such as spivak are very different from what you generally encouter in stewart. They require much more thought.

I would say you don't need to worry that using stewart will leave you with a subpar mastery so long as you take the initiative to do more than the assigned plug and chug problems.

If you are truly intersted in learning the subject with substantial rigor then I would recommend Spivak or Apostol; however, they are not the only way to achieve this.

 

[Cannon00]

Well a large part of the reason I'm worried is: I don't feel that I truly understand calculus. I've gotten high marks in both completed courses, but that doesn't equate to really understanding the subject. I find myself wondering why certain calculus techniques work, and how each was derived in the first place.
Despite the fact I know the proofs are constructed from axiomatic reasoning and clearly ingenious, they seem contrived when taught by my professor as: "This is the proof to integration by parts, this is how you get the proof, remember how I did this proof," with no explanation as to how one would derive that proof. As of now I do understand said proof, from self study, but there are many proofs I do not.

Looking through Stewart, I've wondered if Spivak or Apostol would explain calculus at a deeper level in essence being more difficult but making the concepts more clear, and comprehensible at the same time.

I have trouble sometimes wrapping my head around concepts because I'm distracted by questions concerning how and why they work, I ask my prof and he just tells the class to do what he's doing. The memorization sometimes seems silly to me, because I want to be able to prove them on my own, without any "guide" or steps to follow, or without ever having seen anyone else prove them or a concept similar. I'm considering other texts with the hope that they're more intensive, giving me a complete view of calculus rather than "this guy said use this technique to solve this problem, he was pretty clever, let's just do what he says."

From the responses so far, it's up to me to really understand calculus, and if my courses don't teach it thoroughly, that's no big deal.
So the question changes to: I have to do most of the detailed study of calculus on my own, to really understand it at the level I want to, and at the level more math intensive universities would teach it. So, would I be better able to learn these on my own by just working more thoroughly with Stewart, or should I pick up a copy of Spivak or Apostol?

 

[Flat]

Despite the fact I know the proofs are constructed from axiomatic reasoning and clearly ingenious, they seem contrived when taught by my professor as: "This is the proof to integration by parts, this is how you get the proof, remember how I did this proof," with no explanation as to how one would derive that proof. As of now I do understand said proof, from self study, but there are many proofs I do not.

Are you being tested over the proofs?

I like the stewart book myself. Note that we were not required to be able to do proofs, just the mechanics.

 

[mbisCool]

Have you considered taking analysis?

Your experience in your first calculus sequence is not all that uncommon. Two of my instructors were like yours, fortunately I have more demanding ones now :). If you truly want to learn the theory behind calculus then I guess spivak or apostol would be a good place to start, especially with your backround. With a good work ethic, these texts offer a lot more than stewart in my opinion.

 

[Cannon00]

We are tested on specific proofs. But not for understanding. In fact we've been told to memorize certain proofs should we encounter them on exams.

I have considered, and will be taking analysis sometime after this last calculus course. Just trying to decide if the investment into a more thorough understanding of calculus will be beneficial, or if it will be compensated for when I take analysis.

 

[Howers]

Spivak and Apostol will give you all the proofs and teach you why calculus works based on the axioms of algebra and a few definitions. However, do not expect that you will memorize the proofs as most are very unintuitive and highly technical. For your current course I do not recommend you get these books, as they will prove largely useless to your course.

Stewart proves most important results of calculus. The techniques of both differentiation and integration are mostly algebraic substitutions, barring of course change of variables. I suggest you learn what you can from your course and look at Spivak over the summer.