Thomas Madden

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17 years, 121 days

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These are answers submitted by Thomas Madden

Use Int with an uppercase I. If you use int with a lowercase i Maple will attempt to do symbolic integration first and then evalf. See help for Int,evalf. Hope this helps, Thomas
The Statistics package has superseded the stats package. The NormalPlot generates a Normal Probability Plot. It is a bit of a misnomer, but it is standard in the literature. It is often used to check for normality in a data set. Some options: In the Statistics package use DensityPlot. For example with(Statistics): X := RandomVariable(Normal(0, 1)); DensityPlot(X, range = -2..2, thickness = 3); Or you can work directly from the definition. If X has a normal probability distribution with mean = mu and standard deviation = sigma, where sigma is assumed to be greater than 0, then the the density function of X is f:=(x,mu,sigma)->(1/(sigma*sqrt(2*Pi))*exp(-(x-mu)^2/(2*sigma^2))); plot(f(x,0,1),x=-5..5); will give you a plot of the standard normal density Hope this helps, Thomas
Some options: as noted above you can use the CurveFitting package. The Statistics (upper case S) package also has regression tools. There are links to example worksheets on the help pages for these packages. Additionally, from the Tools -> Assitants menu you can access maplets for curve fitting or data analysis and if you go to Tools -> Task -> Browse you will find many detailed worksheets including regression under Statistics. Best, Thomas

You can use solve to find the roots. If r is a root, then x-r is a factor.

> p1:=x^2-2*x^2-4*x-8;

Maple Equation

> S:=[solve(p1=0)];

Maple Equation

> (-1)*(x-(S[1]))*(x-(S[2]));

Maple Equation

> expand(%);

Maple Equation

Note I inserted the factor (-1) since solve finds the roots of

> -p1;

Maple Equation

which are the same as the roots of

> p1;

Maple Equation

You can also use

> factor(p1,complex);

Maple Equation

Hope this helps,


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George, I think the user has an obligation to read the documentation provided before commenting on how well documented the software is. Consider the following: "To create a copy of a table that is independent of the original, use the copy command. copy( T ); > c := copy(T6); ..." "To create a copy of an array that is independent of the original, use the copy command. copy( a ); c := copy(a8); ..." "To create a copy of an Array that is independent of the original, use the Array command. > C := Array(A8); ..." All of this is from the Introductory Programming Guide. Many of the topics discussed in this guide are either directly or indirectly related to some of your recent post. For example: "Simplification of Repeated Exponentiation In general, Maple does not perform the simplification (x^y)^z → x^(yz) automatically because it does not always provide an accurate answer. For example, letting y = 2 and z = 1/2, the simplification would imply that √ x^2 = x, which is not necessarily true. ..." If you don't like the index Maplesoft has provided PDF versions for download which you can search with Adobe Reader. You will find a number of references in a search for "copy" directly related to the current discussion. On balance, Maplesoft provides three guides, a large help file system, the application center, and this site where help often comes in minutes. What more could you ask for? Thomas
Here are two of the many ways Maple can do this. restart: f:=exp(x*y*z)*cos(x*y^3*z^2); gradf:=; subs(x=0,y=0,z=0, gradf); or VectorCalculus[Gradient](f,[x,y,z]); subs(x=0,y=0,z=0,%); Thomas
First, the gradient is not 0 it is <0,0,0>. The gradient is a vector not a scalar. It is not really strange. This may indicate a local or global max or min. Look at a 3d plot of the function f(x,y)= x^2 + y^2. The function has a global min a (0,0), and you can check that gradf is <0,0> at (0,0). This is the multivariable version of a critical point for a function from R^n to R. Hope this helps, Thomas
My guess is that the person who wrote the help page made a mistake by implying this could be used for functions from R^3 to R. If you look at the examples and at the DirectionalDerivativeTutor it appears you can only work with functions from R^2 to R. This makes sense since the output can be a plot which is impossible in R^3 to R case. As an alternate the VectorCalculus package has DirectionalDiff and Gradient and many other nice features. Thomas
restart: (x+k)^2=-d: simplify(sqrt(lhs(%)), symbolic) = sqrt(rhs(%)); x+k = sqrt(-d) Thomas
The points you have given do not lie on a line student[slope]([22,100.19],[40,200.19]); 5.555555556 student[slope]([40,200.19],[50,300.19]); 10.00000000 student[slope]([50,300.19],[62,400.19]); 8.333333333 Maybe you are looking for the slope of the line of best fit? Thomas
You can also look at the Introductory and Advanced Programming Guides. Many users prefer these to the User Manual Thomas
duracell0057, Your solution converges just fine. I would only add scaling = constrained, so that it does not look like a circle. plots[display](%,scaling=constrained); Thomas
I may be missing something here, but it seems to me all you want is the interior and border of the following ellipse: restart: g:=4*y^2 + x^2 = 1; plots[implicitplot](g,x=-1..1,y=-1..1,filled=true, scaling=constrained); Hope this helps, Thomas
I am not sure if some command already exist in Maple to do this. If it does not need to be a clean slice you can adjust the ranges. I did pretty well with the following ranges: x=-4.75..4.75,y=-4.75..4.75,z=-4.75..4.75 However, as you can see, you loose some of the plot. If you really need a clean slice then I think you can use a rotation of coordinates so that your plane will be perpendicular to a coordinate axis. Then you can see exactly where to cut off the first plot along that axis. Off the top of my head, this is all I can think of. Hopefully one of the experts will have a look and offer a suggestion. I would also like to know what the best approach is. Hope this helps, Thomas
Increase the range of your variables. The following input will give a plot: implicitplot3d(cos(.5*x)*cos(.5*z)+cos(.5*x)*cos(.5*y)+cos(.5*y)*cos(.5*z)+0.5, x=-2*Pi..2*Pi,y=-2*Pi..2*Pi,z=-2*Pi..2*Pi); Thomas
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