What are the essential prerequisites for a Calculus I class?

[Angry Citizen]

I'm going to be taking a five-week Calculus I class this summer. It's going to be intensive, but I'm very good at math, so I think I should be okay. However, I'm a little worried about my prequisites. Due to circumstances which I won't go into, pretty much all my formal math education has come from three college classes in intermediate algebra, college algebra, and precalculus.

I found a website which had a series of subjects in precalculus, and I definitely didn't cover several of them (and most of the beginning and middle stuff I'd covered in the other two classes). Here's the website for reference: http://www.themathpage.com/aprecalc/precalculus.htm

Anyway, I identified the following areas in which I had no preparation whatsoever: Factorials, Permutations and Combinations, the Binomial Theorem, Multiplication of Sums, and Mathematical Induction, Sequences and Series (summation), and Matrices (these last two not listed on the site, but I was made aware of my deficiency in them through other means). I am also shaky on my trigonometry, but I have the basics down fairly well, and I can solve simple-to-intermediate trig equations.

My question is, which of these should I try to focus on for the next month? Which will matter most in the first calculus course? Which will I kick myself for not at least brushing up on? I find myself not knowing what it is I need to know; so I hope you folks can help me out.

 

[sponsoredwalk]

Basically none of those things in your list will not come up in your calc class if you're doing the standard calc I class, i.e. from a Stewart or Thomas Calculus book unless they teach you how to deal with them first.

I seriously advise you get your trig and algebra as good as possible, once you have them mastered they make calculus a breeze, that's no joke. You can just focus on the concepts instead of struggling with concepts because every equation looks new because of your weak algebra skills. All of these concepts are really easy, if you've been shown a concept that seems difficult find a different source, the idea is simple you've just been given an idiotic way to look at it

If you don't believe me, watch the MIT videos when you've gotten through some calc concepts & witness calc being taught ridiculously

Up until chapter 11 in Thomas calculus uses pretty much none of the things you've mentioned, and when they do they show you how to use the ideas.

That said, if you want to deal with a proper calc book like apostol or spivak know everything in that list of yours inside out before cracking those books open. You might want to find out what book you're expected to be using, it will say a lot about what is expected of you.

edit: www.khanacademy.org is a great way to prepare, seriously!

 

[Angry Citizen]

https://www.amazon.com/dp/0495014427/?tag=pfamazon01-20

That's my book for Calc I and next semester's Calc II. I hope I won't be mathematically short-changed, as I'm an engineering student who'll need a lot of math.

 

[sponsoredwalk]

Cool, I can't look inside it but judging from the reviews it's just a shortened version of his Calculus book which is well over 1000 pages.

No, you're not going to be shortchanged though, it's probably just reduced the 100+ questions accompanying every chapter & every sub-chapter of the bigger book - nearly all of which are unnecessary anyway...

My advice is to just get your algebra and trig solid, maybe do some study of limits yourself beforehand too.

I think if you watched a few of the videos on calc and any algebra/trig concepts worrying you on www.khanacademy.org[/url], [url]www.justmathtutoring.com[/url] and http://www.5min.com/Thinkwell you'll have absolutely no problems. ( I do advise watching the videos before school starts, to know what to expect!)

If I was stuck with the book alone I would have quit, having them 3 sources literally changed the way I see mathematics - I really do recommend all three!

[SIZE="1"][I](I especially recommend the 5min.com/Thinkwell videos, Ed Burger - the guy in the green and purple shirts - makes every math concept so simple).[/I]

Edit: From reading a few more reviews, I actually think you should [B]definitely [/B]watch the videos too, just to make sure the book doesn't leave you confused as some reiewers say there wasn't enough explanation. That said, it's not going to be too taxing anyway, just work hard & you'll be fine :biggrin:

 

[Angry Citizen]

Cool. Thanks a lot! I was quite worried.

Though I take it as a given that I should learn these before calc II?

 

[Studiot]

Stewart is good for engineers, you won't need anything from Spivak et al.

Stewart has

Apendix A Review of Algebra

Appendix B Review of Trigonometry

So get hold of a copy now and review.

 

[sponsoredwalk]

Matrices = www.sosmath.com

If you're worried about matrices you can learn about them at that link there. TBH, you'll learn enough there to keep you going until you get to study linear algebra, where the proper theory of matrices is actually dealt with. (I don't know why they waste time teaching them before linear algebra)

Sequences and Series (summation)

There should be a chapter called sequence & series in your calc book, around chapter 11 or so, that deals with these things properly. You'll use a rudimentary version in the integration chapter in which they'll show you what to actually do.

Mathematical Induction

That should be taken care of in an appendix, but tbh you won't need this atm and you should find a better soure to learn this concept - it's useful in rigorous calculus (Spivak, Apostol) & analysis (i.e. after calc).

Permutations and Combinations

This is taken up in Discrete Mathematics properly.

If you watch as many videos as possible in the links I've given you before starting classes along with studying up on algebra and trig you'll have no problems

 

[Studiot]

Sorry I was looking at the wrong book by Stewart.

"Single Variable Calculus" is the one.

Does your series and everything else - a wonderful book for engineers.

 

[Quisquis]

About to take calc 3 this semester with that book. You'll be fine with a solid knowledge of trig and algebra. Everything else you listed will be walked through as you come across it.