Math Is Fun Forum

I was just thinking of some ways you could compute maclaurin or taylor expansions as quick as possible. Consider the maclauren expansion for sin(x)

or in sumation:

note that

(2n -1)! = (2n-1)(2n-2)(2n - 3)! and (2n - 3)! is the factorial of the preceding term.

Also

or if we allow n to move up in increments of 2 and shift the starting point, then we have

thus we could compute the sum as follows:

double xSquared = x*x; // compute x squared ahead of time

double sum = x; // add the first term to the accumulated sum
double previousTerm = x; 
double currentTerm;

for (int n = 3; n < INFINITY; n+= 2) // continue on from the second term
{
// compute this term using the previous term
currentTerm = -previousTerm*xSquared/( (n*(n-1)); 
sum += currenTerm; 
previousTerm = currentTerm; 
}

return sum;

what do you think? Any ways we could make it even faster?

Java is, in my opinion, a ridiculously easy language to learn. C++ on the otherhand, can be rather confusing for a while, and there are many more pitfalls and slight differences which are easy to overlook if you're used to using java.

But really the differences between C++ and java aren't that staggering in terms of essentials (am I not correct?)

what i'm thinking of doing is writing a short tutorial called C++ programming for java programmers. It would ignore all similarities and instead deal with the major differences. It would be a useful resource to me and perhaps other people.

note the tutorial would only assume you know java and teach you the essentials and not the whole of C++.

So what kinds of thing should I discuss? so far i intend to include:
• from reference variables to references and pointers
• from free store objects (always the case in java) to locally declared objects, pointers and references to objects, objects on the free store
• memory leaks
• arrays and strings
• multiple inheritance

any more suggestions?