Recent content by ams2990

Alright, let's go from example problem to the real problem. No point in coming up with increasingly complex examples. So initially, I calculated my A0...C2 constants with a step size of 1, so stepping through each function at {360, 361, ..., 829, 830}. Then step sizes of .1, so {360, 360.1...

This seems to be somewhat violating the spirit of using an integral. It seems we're kind of "hacking on" some Riemann sums to our nice continuous integral in order to get it a little closer to what we'd expect. No? Also, my final answer via integrals (both with and without those adjustment...

So, I picked an arbitrary example, but in my real problem, I only have data within a certain range (360-830), so while I can theoretically integrate my spline interpolation from 360.5 to 830.5, it's not going to be very reliable past 830. Is there another way?

Example time! f(i)=5x g(i)=x^2 \displaystyle \sum_{i=1}^{10}{f(i)g(i)}=15125 \displaystyle \int_{1}^{10}{{f(i)g(i)} di}=12498.8

So kind of like this thread, I'm looking to convert a discrete sum to an integral. My idea thus far has been to arrive at a function via spline interpolation. I'm doing a few different types of sums, but the first ones look like \displaystyle a=\sum_{i=1}^{100}{data[1]*data[4]} where data...

I am trying to get subequations numbered nonsequentially. I have \begin{subequations} \begin{equation} ... \end{equation} \begin{equation} ... \end{equation} \end{subequations} which gives me (1a) ... (1b) ... Instead, I want (1c) instead of (1b). I have no clue whether...

Sorry if I'm being incredibly dense, but if you only had one parameter, then it would be R \Rightarrow R \times R, right? Like a parametric function?

I was thinking about a good way to traverse the points. The obvious solution of choice are sine and cosine. I'm not sure how to create a function from what would seem like R \times R when the relation is only defined on R. Can I "pretend" it's R \times R because I have a,b \in R? That was...

Uh, really vague question, but I'm assuming you're asking what the contents of the class are. For any a and b \in Z, the contents will be a + b, for all b. Stated another way, the class will be a + every integer value. So if a = 1.5, [a] will be \{...,-1.5,-.5,.5,1.5,2.5,3.5,4.5,...\}

Not really sure what you're asking...the equivalence class of a \in A is [ a ] , which is the set of all elements equivalent to a.

Homework Statement Define a relation on R as follows. Two real numbers x, y are equivalent if x - y \epsilon Z . Show that the set of equivalence classes of this relation is bijective to the set of points on the unit circle. Homework Equations N/A? I don't think there are any special...