What are the prerequisites for starting calculus?

[WORLD-HEN]

Hi, I am 15 years old, and want to start doing calculus. What exactly are the prerequisites for doing calc? And what is a good textbook for it( yes, I've seen a lot of people say "spivak's" in many threads, is it an introductory book or advancded?) And by the way, i live in India and calculus is taught in 12th grade here, just wondering when they start calc in other countries like UK and USA etc.

 

[devious_]

Does your school offer one of those "precalc" classes? I believe they cover all the prerequisites. If you don't, then I'd recommend you have a solid grasp of algebra, geometry and trigonometry.

Spivak's textbook is definitely not for beginners. There are several threads here that have introducty calc book recommendations. I suggest you do a search.

In Jordan, most decent schools start introductory calculus in the 11th grade and finish it up in the 12th grade. My school, however, offered an optional introductory class in the 10th grade and an accelerated class in the 11th. In the UK, I believe they start calculus in the 12th and finish in the either 12th or 13th, depending on the college (senior high school) and student.

I hope that helped.

 

[arildno]

Just adding to devious:
Perhaps even more fundamental, you need to understand the concept of a "function".

 

[bross7]

I can't think of any prerequisite courses for a HS Calculus other than previous year mathematics. I wouldn't suggest calculus without those, although that would be kind of odd anyway to be taking a higher math course without the previous years math.

Having a solid foundation in trig, algebra and function would really be all that you need to get going.

In Canada it is also a Grade 12 course, although it is possible to take it earlier if you can.

 

[Zurtex]

Having a good understanding of trigonometry (and trigonometric identities), basic algebra (completing the square that sort of thing), what a function is, the binomial theorem will allow you to progress through most of basic calculus.

 

[mathwonk]

here is an example of what throws many students: factoring polynomials.


to prove that the derivative of x^2 is 2x, you have to know that x^2 - a^2

= (x-a)(x+a). amazingly many college students in US do not know this stuff.


similarly to prove that the derivative of x^n is nx^(n-1) one must either know that

x^n - a^n = (x-a)(x^[n-1] + ax^[n-2] + ...+a^[n-2]x + a^[n-1])

or know the binomial theortem, again most college students do not know anything like this.

in general, all the drivative does for you is starting from an equation for the height of a graph, provide you with an equation for the slope of the graph.

to aply this and find where the graph has its hgihest and lowest poiunts, one must soilve the derivative equation set equal to zero.

so if one cannot solve an algebraic equation, calculus does you no good in analyzing the graph.

also the main application of calculus in beginning courses is to max min problems, which are written in words. so one must be able to read with comprehension. this is also a big stumbling block for many.

 

[gravenewworld]

I would have to say that you have to be able to do Algebra 1 and Algebra 2 in your sleep to be prepared for Calc. I never took trig in high school and have never taken it, yet I did fine in calc and all my other "advanced" math courses. I don't really think you need trig at all to do calc, the trig you do need you can teach yourself easily in less than one day.

 

[mathwonk]

interestingly, one cannot actually understand trig until after (or during) calculus, as it is impossible even to define the functions sine and cosine without calculus.

I.e. sin is the inverse function of the arc length function on a circle, a concept that makes sense only with integral calculus. So to define sin rigorously one must either define the arclength as the integral of 1/sqrt(1-x^2), or use the power series

x-x^3/3! + x^5/5!- + ... and this too generally uses integration to prove it is differentiable term by term.

So those of us who never had trig in high school were actually lucky to get a better treatment in college (or later!)

 

[gravenewworld]

After taking complex analysis, I am glad I never wasted my time with trig in high school. It seems so pointless to learn trig identities and trig functions when you can just use complex numbers.

 

[WORLD-HEN]

Thanks for the help everybody