# How to be prepared for calculus 2?

Just finished taking my calculus 1 final now I'm ready to take calculus 2 in the fall. The question is how should I prepare for calculus 2? What are the important trig and calculus 1 sections I should study beforehand? Thanks.

Matterwave
Gold Member
It would be helpful if you provided a summary of the topics covered in calc 1 and 2. The topics covered are not universal. Typically calc 1 is differential calculus, and calc 2 is integral calculus, but that's not true everywhere.

symbolipoint
Homework Helper
Gold Member
Just finished taking my calculus 1 final now I'm ready to take calculus 2 in the fall. The question is how should I prepare for calculus 2? What are the important trig and calculus 1 sections I should study beforehand? Thanks.

Your grade alone from Calculus 1 is not an indicator of being ready for Calculus 2. What parts of Calculus 1 are your weak parts for you? Review THEM. Also, spend some time on review of basic Trigonometry, since you are likely to deal with differentiation and integration on Trigonometric functions.

If you are good enough (really strong) in what you learned in Calculus 1, then spend the summer studying as much as you can of Calculus 2 on your own, before the fall semester begins; that way, you can be studying Calculus 2 for the second time during the fall, and having spent several weeks on it already, you could be able to learn it better.

verty
Homework Helper
Just finished taking my calculus 1 final now I'm ready to take calculus 2 in the fall. The question is how should I prepare for calculus 2? What are the important trig and calculus 1 sections I should study beforehand? Thanks.

Something that can help is to learn the derivatives of common functions: x^n, ##e^{ax}##, ln(ax), sec(ax), ##cos^{-1}(ax)##, etc. Be able to say, the derivative of tan is sec^2, etc. This will help you solve integrals quickly. Also realize that integration is a lot more difficult, there isn't always a solution and the answer is often complicated. Knowing the derivatives can make it easier.

Also know limits and approximations, be able to calculate them. There are more complicated things coming later and this is a good test of being able to understand complicated topics.

jtbell
Mentor
Something that can help is to learn the derivatives of common functions: x^n, ##e^{ax}##, ln(ax), sec(ax), ##cos^{-1}(ax)##, etc. Be able to say, the derivative of tan is sec^2, etc.

Better yet, be able to say them backwards without thinking about it: "sec2 is the derivative of tan". Integration is basically the inverse operation to differentiation, so if you can see something like sec2 and think immediately, "aha, that's the derivative of tan", it helps a lot.

Better yet, be able to say them backwards without thinking about it: "sec2 is the derivative of tan". Integration is basically the inverse operation to differentiation, so if you can see something like sec2 and think immediately, "aha, that's the derivative of tan", it helps a lot.

Yes! Get a table of basic integrals and memorize it completely. Revise it every day so that you really know them by heart.

mathwonk
Homework Helper
2020 Award
It depends what is the focus of your next course also, computations, theory, and/or applications to problems. Besides just practicing skills like taking derivatives of elementary functions, you should also review the definitions of concepts like the derivative, if you hope to appreciate the proof of the fundamental theorem of calculus, which is often presented in calc 2. The theoretical underpinning from calc 1 lies in the intermediate value theorem, the existence of closed interval maxima and minima for continuous functions, and Rolle's theorem and the mean value theorem, and their corollaries for the behavior of differentiable functions.

One way to study, if you already did well in your course, is to work through a different book on calc 1 from the one you used.

It depends what is the focus of your next course also, computations, theory, and/or applications to problems. Besides just practicing skills like taking derivatives of elementary functions, you should also review the definitions of concepts like the derivative, if you hope to appreciate the proof of the fundamental theorem of calculus, which is often presented in calc 2. The theoretical underpinning from calc 1 lies in the intermediate value theorem, the existence of closed interval maxima and minima for continuous functions, and Rolle's theorem and the mean value theorem, and their corollaries for the behavior of differentiable functions.

One way to study, if you already did well in your course, is to work through a different book on calc 1 from the one you used.

Thanks. I received a b in the class. (Proffesor or also teaches grads school at UC). I understood alot the majority of the material. Work problems being my weakest and also areas of cross sections.
The focus of the next course is integration (parts, trig, etc), Taylor series,polar, and derivatives of ln. So far in 3 days I'm halfway through a trig book. My emphasis is becoming faster at identities, properties of conics, and how to go from polar to cartesian plane and vise versa with ease. I will began to re study calculus 1 using swokoski calculus because I enjoyed his theorem/axiom/proof approach. Our school uses stewart and the layout of the book I do not like.

I think I can do it. I am taking intro to art history in the summer to knock out a ge requirement.

on a second note. I never took a science class in school (9th grade drop out). I was thinking of completing all of my calculus series (2 and 3 are left) so when I actually start physics I can focus on the concept and not the math. Is this a smart move or am I being extremely cautions with intro physics courses at a cc. All my stem classes are taken with the hardest professors.

verty
Homework Helper
Thanks. I received a b in the class. (Proffesor or also teaches grads school at UC). I understood alot the majority of the material. Work problems being my weakest and also areas of cross sections.
The focus of the next course is integration (parts, trig, etc), Taylor series,polar, and derivatives of ln. So far in 3 days I'm halfway through a trig book. My emphasis is becoming faster at identities, properties of conics, and how to go from polar to cartesian plane and vise versa with ease. I will began to re study calculus 1 using swokoski calculus because I enjoyed his theorem/axiom/proof approach. Our school uses stewart and the layout of the book I do not like.

I think I can do it. I am taking intro to art history in the summer to knock out a ge requirement.

on a second note. I never took a science class in school (9th grade drop out). I was thinking of completing all of my calculus series (2 and 3 are left) so when I actually start physics I can focus on the concept and not the math. Is this a smart move or am I being extremely cautions with intro physics courses at a cc. All my stem classes are taken with the hardest professors.

My gut instinct is that taking the math in a row like this will be more difficult but better in the sense that you can focus on doing problems in the best way. I'm convinced that this is the best way to learn math: to focus on methods of solving problems, being as efficient and general as one can be.

The other direction is to learn the math at the same time as you try to use it, there is always a danger that people focus on the theoretical concepts and bomb in exams because there was not due emphasis on doing the math.

So you can do either but I think this is a good way to proceed. One thing though, Stewart is not a particularly good book, I find the language to be not very accurate. You say you are going over the calc 1 material again, this is very good, one thing though, do problems while you do that. Get good with the problems of calc 1 if you aren't yet, and I think you'll do fine.