I want to teach myself Calculus

[Azrioch]

To what length do you have to know Algebra in order to begin teaching yourself the basics of Calculus? How much trigonometry is required? I am in Math 11 on the Canadian system which I am finding very easy. I am going to a summer program in Cornell university and taking Calculus is an option but is is university level and they have a warning that it is a very demanding course. Because of this I wanted to get a head start and try to teach myself some. What background is required? Is it anything like algebra or totally different?

Thanks in advanced.

 

[drag]

Greetings !

I'd like to add some more questions on this :
Can you advise the best way/best material
to learn calculus ?
Thanks.

Live long and prosper.

 

[Zefram]

I started to teach myself last summer which was the summer between my high school geometry class and algebra II (which I'm in now). I would say know how to work with trig and be reasonably comfortable with it (know all the identities and that junk); as for algebra, it helps to understand logs and e. Being weak in trig and logs was what hurt me the most when I first started but if you've mastered those it shouldn't be too hard to work your way into calc (as long as you work hard). I would recommend not starting off with rigorous books and textbooks at first, start off with a fun one or two that shows you what you're doing and why (like The Complete Idiot's Guide to Calculus, Calculus the Easy Way, or Calculus Made Easy). Once you're reasonably confident you have some idea that you know what you're doing (i.e. you can take derivatives and antiderivatives, etc) then move on to something more rigorous. And remember, as that Calc Made Easy book says, "What one fool can do, another can."

 

[Azrioch]

Ok. I do not yet know the identities yet. That is later on in the 11th grade course. I taught myself logarithms but I do not know what e is. I know it is something for natural logarithms, right? Ln with base e is 10 or something like that. Not too clear. Unfortunently I am unable to procure a fun textbook as I am in boarding school in Italy. I only have the dry one that I brought with me.

I suppose I will have to teach myself the identities first then.

Thank you for your help.

 

[damgo]

OK, my 2c:

Algebra-wise, you need to be very comfortable with the basics: solving equations, powers, etc. Trig is optional, not essential; though later on of course you will need to know it.

Also, there are two types of calculus classes: the first is the usual high-school class (in the US). Here they teach you what integrals and derivatives are, and how to do them. It is sort of a cookbook-like approch: "to integrate blahblahblah, this is the trick you use."

The second is more abstract; you are taught how to define calculus concepts rigorously, how to derive the formulas used in the first type of class, and so on. This requires much more mathematical smarts, but not background.

It sounds like the Cornell class is going to be of the second type... in which case learning the basics will help you a ton. So I would learn what integrals and derivatives are, the chain/multiplication rules, and how to find integrals/derivatives of basic functions.

 

[Sting]

Calculus is a blend of algebra, trigonometry, arithmetic and geometry.

I prepared for my first Calculus course by going out and purchasing several Calculus textbooks and going through the first few chapters (some Calculus textbooks like Bittenger's Calculus have an algebra and trig review before you get into the Calculus part.

 

[lethe]

oddly enough, i learned algebra, analytic geometry, trigonometry, and logarithms/exponentials for the first time in my calculus book. if you are patient, and have a nice book, you don t need many prerequisites. i managed it with just a bit of 7th grade pre-algebra under my belt.

my textbook was edwards and penny. most calc textbooks i ve seen look pretty much the same though.

 

[Sting]

oddly enough, i learned algebra, analytic geometry, trigonometry, and logarithms/exponentials for the first time in my calculus book. if you are patient, and have a nice book, you don t need many prerequisites. i managed it with just a bit of 7th grade pre-algebra under my belt.

I don't find that hard to believe because I only adapted to logarithms/exponentials in my intro Calculus course.

I'm making a "theory" here: The reason why a lot of people find Calculus initially difficult is because before Calculus, there were four major operations. Once you get into Calculus, there are two new types of operations (differentiation and integration) so the difficulty is the mental adjustment.

It's only my lousy theory though.

my textbook was edwards and penny. most calc textbooks i ve seen look pretty much the same though.

Edwards and Penny is good. My personal favorite is (Thomas and Finney).

 

[Mulder]

Originally posted by Sting
My personal favorite is (Thomas and Finney

I think I have the same one. Great for reference and practise questions.

 

[Nicool003]

Well I am not an expert but there are TONS of books and a few good websites you can go to. If you want to find a good one then just try google. But I suggest that you get a book too if you use a website...

 

[Sting]

I think I have the same one. Great for reference and practise questions.

Yes, great overall layout. I went by T & F when I was in Calculus.

If there is one author to avoid, avoid anything written by Anton. He wrote the Calculus book I used for Calc I - III and the Linear Algebra book I'm using now and I have to resort to other textbooks to learn because of the ambigious nature of the book.