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POMathematica Index Equation (basic algebra)
 

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  1. POMathematica Index Equation (basic algebra)
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    <p>I am currently working on a Mathematica project to calculate Riemann's sums and put them in a table. I am having trouble printing the row numbers (intervals). (The row numbers are also parameters to the secondary functions). I don't know of any way to just access the index of the iterator in a Mathematica Table, so I am trying to compute them using the function parameters.</p> <p>Here is an example of what I'd like to print, for the integral of x^2 over the range {0, 1}, with 10 subdivisions.</p> <pre><code>tableRiemannSums[#^2 &amp;, {0, 1}, 10] </code></pre> <p><img src="https://i.stack.imgur.com/Oo8UA.jpg" alt="enter image description here"></p> <p>I need to figure out what the index of each iteration is, based on the value of the current subdivision k, the range of the integral {a, b}, and the number of subdivisions, n. Below is the main piece of code. </p> <pre><code>tableRiemannSums[fct_, {a_, b_}, n_] := Table[{'insert index here', leftRiemannSum[fct, {a, b}, 'insert index here'], rightRiemannSum[fct, {a, b}, 'insert index here']}, {k, a, b - (N[b - a]/n), N[b - a]/n}] </code></pre> <p>In the above equation, the line </p> <pre><code>{k, a, b - (N[b - a]/n), N[b - a]/n}] </code></pre> <p>means the range of the table is k as k goes from 'a' to 'b - ((b - a)/n)' in steps of size '(b - a)/n'.</p> <p>In each of the places where my code says 'insert index here,' I need to put the same equation. Right now, I am using 'n * k + 1' to calculate the index, which is working for positive ranges, but breaks when I have a range like {a,b} = {-1, 1}. </p> <p>I think this is a fairly straightforward algebra problem, but I have been racking my brain for hours and can't find a general equation. </p> <p>(I apologize if this is a duplicate question - I tried searching through the Stack overflow archives, but had a hard time summarizing my question into a few key words.)</p>
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    1. USKelly King
    1. USKelly King
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    1. COMaybe [**this Demonstration**](http://demonstrations.wolfram.com/RiemannSums/) can help. You may also want to consider [**this designated forum**](http://mathematica.stackexchange.com).
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      1. POMathematica Index Equation (basic algebra)
      1. USVitaliy Kaurov
 

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