Simple Riemann sum

[lorth-2]

I was wondering if anyone can help me out. I am 65 and having difficulty with where to start in mathcad. I am taking an online course in Calculus and they brought up the concept of rieman sums between two functions. I bought prime 3 student edition but I am lost. I am interested in a worksheet that will allow a person to enter two functions, the bounderies, and the amount of subdivisions. and get an output as close to the integrals as one would like. Also if anyone can direct me to a place that I can learn how to use mathcad to make my own worksheets that would be appreciated. If you are willing to show me how, please send the worksheet as an attachment to

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[Werner_E]

What would be the purpose of that sheet you demand?

And we can create those approximating rectangles in different ways, depending on how we would determine their height. It could be the left or the right boundary, the midpoint or the maximum or minumum of left and right. And we can chose that for the first and the second function individually, getting up to 25 different approximations.

See her an applet for just one function (you can type in f1(x)-f2(x) to use it for the area between two curves) http://mathworld.wolfram.com/RiemannSum.html

EDIT: Added the missing link 😉

[lorth-2]

I have used many applets and I didn't mean to sound like I was demanding anything. I would just like to learn how to program mathcad to be able to sum between two curves. When I had mathcad 7 I thought I new how to do it by I do not understand how to do the iterations. I do know that using nurmerical methods you can get as close to the true intervel as you like. If you can show me the way to do this that would be great.

Sincerely,

Larry Orth

[Werner_E]

If you search the net for "Mathcad Riemann sum" you will find some sites you might find interesting. Most (if not all of them) would contain files for older Mathcad versions, which can be opened by Mathcad 15 but not with Prime. Given that, it might be a good idea to install MC15 in parallel with Prime. In the opinion of many people (including myself) MC15 still is the more powerful version (by far), Prime lacks a lot of features which we are used from MC15 for years. Given that you bought Prime you also are entitled to install and use MC15. In fact you will need a full installation of the current MC15 to be able to convert older sheets to Prime format (no guarantee they will work as expected afer conversion, though).

While you may use a programming appraoch with a loop to sum up the areas of the rectangles as you wrote, its also possible to use Mathcads summation along with a range variable to do the job.

Find attached a Prime3 sheet which uses this approach and implemented all five methods to determine the rectangle height. Same method is used on upper and lower end but it should be obvious how to mix to get all 25 variations.

[lorth-2]

Thank you so much. I can study this page and get an idea on how to use range variables. I will figure out how to graph the rectangles.

Thanks again

Larry

[Werner_E]

Drawing the rectangles is easy (at least in MC15 and below, not sure about Prime) if you just are demonstrating the "normal" area between curve and x-axis (e.g.: http://www.math-tech.at/beispiel.asp?id=26), but quite more work if you want it between two curves.

I attach the animation from the file I just linked above (Prime can't do animations).

[Dmitri_K]

Larry, let me suggest my free e-course on calculus with Mathcad Prime labs.Rieman sum coming soon.

In spite of MOOC is in Russian, i am doing english labs both in Prime 3 and XPS format.

Program is based on well-known MIT open course: http://math.mit.edu/classes/18.01/Spring2013/1801_Syllabus.html

1.Intro (slope, secant, tangent line)

2.derivatives

3.limits

4. continuity

5.differentiation rules

6. implicit, inverses

7. exponential, log, hyperbolic

8. linear and quadratic approximations

9. mean value theorem, curve sketching

10. Midterm I

PART II Integration

11. antiderivatives

12. differentials and differential equations (04/14)

13. definite integrals (04/14)

14. fundamental theorems of calculus (05/14)

Link to MOOC: http://tsuefa.ru/eng/
videos in Russian (free, registration on INTUIT required): http://www.intuit.ru/studies/educational_groups/1054/info

[Werner_E · Accepted solution]

Would something like this be what you are searching for? (Click the pic to see the short animation)

[lorth-2]

Hello, yes this is exactly what I have been looking for. You know everytime I see this in action I am amazed. It is so wonderful. When only a few rectangles one cannot see much at all, however, as the number of rectangles approach a large number calculus comes together and with rectanges or squares we can square the circle or curve. And no matter how sharp the turn, with a powerful microscope, one can turn that curve into a straight line. Anyway, it is great.

You would not happen to have a copy of this mathcad file you could share and if it comes with explanation of how it works that would be great. I just bought mathcad student prime 3 and downloaded 15 so I can open xmcd and mcdx.

Thanks either way.

Larry

My email is -

[Werner_E]

OK, here are the sheets in MC15 and Prime3 format, but the sheet was created by me in MC15 (easier to use and more powerful) and so the converted file would need quite some formatting. Furthermore we don't have components in Prime, so theay way the functions are sampled would have to be assigned manually. And of course Prime has no ability to create animations.

Attached find the two worksheets along with an animation and a pdf of how the MC15 version looks like.

[lorth]

Dear Werner,

Thanks again for the files. Can you advice me where I might look to get an explanation of how the program works.

I don't know much about mathcad but I would like to learn. Where do I start? I openned up the files you sent. The one in prime three had a lot of programming. I would like to understand it. Do I have to be a programmer to learn how you set up the file Riemann_we.mcdx?

Larry

[Werner_E]

The files all are the same - the Prime3 file was created by converting the Mathcad 15 sheet (xmcdz) and then editing it which is necessary, because the converter ever so often fails and Prime is much less powerful, lacking a lot of features. I prefer working in Mathcad 15 as its more powerful, much speedier and because of its ease of handling. I wasn't sure if you could open Mathcad files and so I create a pdf print of it so you can see what the file looks like.

I don't think that you need a programming background to write small progams in Mathcad, but it sure helps.

Can't advice where to start learning as my way was learning by doing. What helped me most was the built-in help (I am talking of Mathcad, 15 and below) with its quicksheets, etc. and the old Mathsoft collab forum, which was so poorly integrated in this community here. One learns a lot by just listening to others posting and flipping trough their files.

PTC has converted some old (and some very old) files to Prime format and offers them here http://communities.ptc.com/docs/DOC-3621

The conversion was often done sloppily and you will ever so often find references to features not available in Prime, but maybe you find something useful for you there.

If you have any specific questions concerning my file, feel free to come back and ask.

[lorth]

Dear Werner,

I woke up this morning with a fresh point of view and solved the problem with the file I sent to you. I appreciate all your help. It was a formatting issue and I need a lot more practice with mathcad. Unless you think it unwise, I am going to invest my time in learning mathcad 15 since I have a copy of that too.

Thanks again,

Larry

[Werner_E]

I woke up this morning with a fresh point of view and solved the problem with the file I sent to you.

Fine, but at the moment I am not sure which problem and I can't remember you ever would have sent a file?

Anyway, I don't think its unwise to use Mathcad 15, but you have to be aware that this version will sooner or later die and, we may like it or not, Prime will be the future. So you sure will be able to use a lot of what you learn with MC15 in Prime as well, but of course there are differences, not only in the look an feel. But is your decision what you will do when PTC no longer supports Mathcad15 - jump on the Prime bus, keep using MC15 anyway or switch to a completly different software as we will do.

Good luck and fun with Mathcad!

[lorth]

OOk, now I am curious. What software are you moving to.

[Werner_E]

Larry Orth wrote:

OOk, now I am curious. What software are you moving to.

We have not yet settled on a specific software but still are exploring and using Mathcad15 as long as it seems to make sense. Of course we primarily look at the usual big players like Mathematica, Matlab and Maple, but we also keep an eye on free software like SMath (kind of a Mathcad clone, lacking a lot of what Mathcad 15 has to offer, but also has a lot of improvements implemented), Maxima and for some edu demonstration purposes even Geogebra. But whatever software(mix) we will settle at, it will mean starting by zero - thanks PTC 😞