Recommendations on number of exercises to do from Thomas Calculus 15th ed

Question

So I wanted to review my calculus (1, 2, and 3) in prep for upcoming classes (starts Aug 2025/Fall since taking 2 gap semesters starting Dec 12th for personal reasons) like stats, diff eq, real analysis, etc. and Thomas Calculus (15th ed) is the textbook I'm deciding to use (since my uni uses it). I've already taken these classes btw, but I feel my understanding of the material is shoddy (mainly with Calc 3 with triple integrals and such) and I feel I need to review it a bit more thoroughly (than how I did when taking Calc 3) by working through the textbook chps 1-16 (chps 1-11 is Calc 1 & 2, and chps 12-16 is Calc 3). Since there's a bunch of exercises for each chapter (more than 100 sections total and usually 70+ questions per section), what would y'all recommend for me in terms of which and how many textbook exercises I should do? Would there be an external question-bank/test-bank source y'all would recommend instead that would be more efficient but still comprehensive?

Obviously common sense would say to just try doing the problems that seem to address my weak-points, but it's kind of hard for me to figure that out (esp. since it's been a while since I took the Calc classes). I kind of have the habit of wanting to do all the exercises but I fear that'll make it difficult/near impossible to finish reviewing all the chapters. I still want to review the chapters throughly/comprehensively tho. So if anyone could give me some advice on how I should go about it I'd be grateful. Ideally I want to review everything in span of 1-2 months (and I won't have much to do per day so I can spend at least 12 hours per day).

In fact, if anyone who worked through the Thomas Calc textbook could give me some advice that would be very helpful too!

Sorry if this is a dumb question I'm asking, but I just really need some advice here.

Answer 1

This, and your nearly-identical linear algebra question, are the wrong way of going about this. No one is going to ask you to grind out a bunch of basic computations or regurgitate the theorems from Thomas again unless you are teaching them. (In real analysis or some other higher math class, you might revisit the topics, but it will be in greater generality and memorizing the old proofs won't be much help.) You passed the class; it is time to move on.

What you want to do is to work on something that uses this stuff and which actually interests you. Maybe there are some questions in the book where this is the case (often there will be a few more interesting questions towards the end of a set) but maybe you will have to find something from your own interests.

tldr: Look forward, not backward.

Answer 2

My advice would be just to revise calc 3 to mastery. Just run through that entire part of the book, do all those exercises. (If they only have answers for odds, than just the odds.)

I feel you on the 3rd semester calculus. I crushed calc 1/2, getting a perfect score on the AP BC (I think). But then I was much more interested in freshman year activities in college and didn't get 3rd semester calculus mastered the same way.

There are a few topics in that course, that are crushingly easy (partial differentiation). But then others that are arguably covered too briefly. With both those in mind, I would just do all the problems. Since partial differentiation is easy, you'll just go fast, doing the drill problems. Conversely, since Stokes theorem is too briefly covered, you'll at least be doing 100% of the drill.

If there's something else in calc 1 or 2 that you realize (as you work calc 3, or just in back of head)...then fine revise that specific chapter and do the drill. But I wouldn't bother doing much drill otherwise.

FWIW, for all three topics, I think you will find that the amount needed in later classes (diffyq's, stats, etc.) is not that extreme. Usually you'll use the more common techniques of integration for instance. So even if didn't revise, you'd probably be fine. I think the goal is really mastery of the topics themselves...not because if you are not perfect in them, you can't handle the later classes. (Not everything is like this in life, but in this case, it applies.)

I would make the goal mastery of the third semester calc (div, grad, curl and all that). Still remains sort of mysterious to me in a way that doing a partial fractions integration does not. [This argues for doing more drill to build familiarity...analogous to the saying about quantum mechanics... "It doesn't make sense, you just get used to it" in a way very converse to how straight line kinematics is blindingly all is right in the universe.] There is a benefit if you ever take junior year physics E&M (even some in the harder parts of electrostatics in a good calc-based intro physics course).