dharr

Dr. David Harrington

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18 years, 153 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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I am a professor of chemistry at the University of Victoria, BC, Canada, where my research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

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These are replies submitted by dharr

I have had success in the past with providing an approximate solution. Something like 'approxsoln' = [F(eta) = 1+eta-(1/6)*eta^2, G(eta) = 0, H(eta) = 1-(1/3)*eta]. Presumably you know something about what the solution looks like roughly. Particularly there is not much information about G, only that it is zero at both boundaries.

It's not really an answer, but I do this with a coloured 3-D contour plot where I specify the exact contours I want and then colour the plot according to height using shading =zhue. For example

plot3d(S(X, Y), X = 0 .. X3, Y = 0 .. 1, axes = boxed, orientation = [-90, 0], scaling = constrained, style = surfacecontour, contours = [seq(i/(10.)+0.5e-1, i = 0 .. 9)], shading = zhue, thickness = 3, tickmarks = [6, 4, 3], labels = ["", "", ""], grid = [150, 50]);

You can then have a colour key using

plot3d(X, X = 0 .. 1, Y = 0 .. .2, axes = boxed, orientation = [-90, 0], scaling = constrained, thickness = 2, font = [Times, normal, 20], style = surfacecontour, shading = zhue,thickness=2, tickmarks = [0, 0, 0], labels = [" ", " ", " "],contours=[seq(0.1*i+0.05,i=0..9)]);

 

I can't see the right-hand side of your screen, but two problems come to mind. To define a1 as a function, you need a1:=(r,theta)->sum( etc And for plotting a function you need either plot(a1,0..infinity,0..Pi/2) or plot(a1(r,theta),r=0..infinity,theta=0..Pi/2)

I didn't save yesterday, but did it again, with a smaller number of solutions this time (263), though I believe I entered the equations identically. Many of the solutions have many variables zero, so there is a lot of structure here.

View 127_eqns.mw on MapleNet or Download 127_eqns.mw
View file details

I didn't save yesterday, but did it again, with a smaller number of solutions this time (263), though I believe I entered the equations identically. Many of the solutions have many variables zero, so there is a lot of structure here.

View 127_eqns.mw on MapleNet or Download 127_eqns.mw
View file details

I found this also. Specifically after entering with the maple button, the code previewed with an image (but not well). When I made the post, the image wasn't there. Looking at the source showed the text had been moved out of the maple tags and put after the closing one. I moved it back in source mode, but it ended up outside again. This behavior was different I think from a few days earlier. Definitely strange.

David

I see the half plane for x less than 1/2 as red, which is as it should be, since the function is -1 there. For x greater than 1/2 and y negative the function is x*y which is negative and again red. For x greater than 1/2 and y positive, the function is x*y which is now positive and shows yellow. This all seems right to me, and is a little clearer if you try contourplot3d(f(x,y),x=0..1,y=-1..1,contours=[0],filled=true,axes=boxed); and rotate around until you see the 2-D view. As for your first question, I am not so sure... David.
I did play about with some ways to work with the derivatives (mainly using D) without success; but turning them into derivatives later is a workable solution
I did play about with some ways to work with the derivatives (mainly using D) without success; but turning them into derivatives later is a workable solution
Others have addressed the need Sci. Workplace, especially for LaTeX. Sci Workplace has meant I can produce LaTeX without knowing (much) LaTeX. I could live with some other way of producing nice documents (MathML for example) but the bottom line is I submit papers with math to Journals that can directly typeset from the LaTeX. I use Sci Wrkplace for quickly making notes to myself or for my classes, and use it for simple math to help me make those notes. But for any significant math, I use Maple. Maple is a better math tool, SciWorkplace is a better document production tool.
Others have addressed the need Sci. Workplace, especially for LaTeX. Sci Workplace has meant I can produce LaTeX without knowing (much) LaTeX. I could live with some other way of producing nice documents (MathML for example) but the bottom line is I submit papers with math to Journals that can directly typeset from the LaTeX. I use Sci Wrkplace for quickly making notes to myself or for my classes, and use it for simple math to help me make those notes. But for any significant math, I use Maple. Maple is a better math tool, SciWorkplace is a better document production tool.
A float can be converted to a rational, so the following does something similar (note the decimal point to convert the fraction to a real) convert(77/45.,rational,3); # gives 12/7 convert(77/45.,rational,2); # gives 5/3
A float can be converted to a rational, so the following does something similar (note the decimal point to convert the fraction to a real) convert(77/45.,rational,3); # gives 12/7 convert(77/45.,rational,2); # gives 5/3
try nops (number of operands). I would have expected it to be under ?list, but I see it isn't (in v. 10), which does seems like a serious omission.
And yet, a/bc is usually interpreted in typeset notation as a/(b*c). In the International Union of Pure and Appled Chemistry rules: "In evaluating combinations of many factors, multiplication takes precedence over division in the sense that a/bc should be interpretaed as a/(bc) rather than (a/b)c; however in complex expressions it is desirable to use brackets to eliminate any ambiguity" Usually the IUPAP (physics) and IUPAC (chemistry) rules are in agreement, and when I write papers with my mathematics colleagure, we also use this convention, so I think it is fairly universal. (I am thinking as it it written on the page, i.e., output, here; I am not suggesting input a/b*c be interpreted this way, since (a/b)*c is the standard programming interpretation of input.)
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