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Hi, I want to build recursively defined, piecewise functions.

I first defined my zero-order functions

N40(xi)=piecewise(0<xi and xi<=1);

N50(xi)=piecewise(1<xi and xi<=2);

and I can plot them with desired result

but, how do I combine them, to make first order functions?

 for instance, I want to have a function matematichally defined by:

N41 = (xi-1)*N40 + (2-xi)*N51


Chain Rule ...

February 02 2010 rpcroke 104

How do I get Maple to recognize the Chain rule symbolically?

I have an ODE that looks like this:

u = a[0] + a[1]*w(q) + a[2]*w'(q) + a[3]*w(q)^2

where u,a[i],q are all functions of (x,y,t), so W is really W(q(x,y,t)).  W' is d/dq(W).  I am having trouble figuring out how to get Maple to recognize W' and still being able to take derivatives with respect to x,y, or t.

I want to get the following:

diff(W',x) = W''*q_x or in words: two derivatives of W with respect to q times q_x.

How can I do this?


I have problem with following question:

"You are given two functions: h(x) = (x+2)^2 - 15x - 30 and L(x) = qx, where q is any real number. Find the value(s) of the parameter q such that the area of the region enclosed by these two functions is equal to 1000."

Here is what I have done so far:

1) declare (and display) both functions:

h := proc (x) options operator, arrow; (x+2)^2-15*x-30 end proc; L := proc (x) options operator, arrow; q*x end proc; plot([h(x), subs(q = 5, L(x)), subs(q = -25, L(x))], x = -20 .. 20, y = -200 .. 500)


I have


-Copy full precision

-Copy as MathML

-Why am I able to use whatever strange copy method I have the feeling is useless to me but no simple, plain Copy? Why? Why were you able to implement strange copy functions but not one like the simple one of Windows Notepad.exe's and whatsoever? Or what am I doing wrong?

I've got a system of ODEs I need to solve for dependant variables phi(t) and a(t) with independant variable t.(appologies, it's a bit messy; the maple tag isn't making things render nicely)

dsys := {(D(D(phi)))(t)+3*a(t)*(D(phi))(t)/(D(a))(t)+dOm(phi(t), a(t)) = 0, a(1000) = sqrt(2*sqrt((8*Pi^3*(1/45))*To)*1000), phi(1000) = 12*M^(alpha+4)*alpha*g^2*sqrt(8*Pi^3*(1/45))*To^((1/2)*alpha-1)*10^(1/(alpha+2)), (D(a))(t) = sqrt(RhoDE(phi(t), a(t))+RhoM(a(t))+RhoR(a(t)))*a(t...

How to find functions


F(x) = f(x) / g(x)

G(x) = f(x) * g(x)


so that the third derivative of F(x) and G(x) = 0.


For m=1,2, how do I show with Maple that the first two moments of the Borel-Tanner distribution are simple functions of k and lamda, e.g., k/(1-lambda) for the mean? How do I get the closed-form expressions with maple? Code:

simplify(sum(x^m*k*x^(x-k-1)*lambda^(x-k)*exp(-lambda*x)/factorial(x-k), x = k .. infinity)) assuming lambda > 0, lambda < 1, k::posint; evalf(subs(k = 1, lambda = .8, %))

To judge results of functions coded in double precision against precise results (as they may be given by Maple) one has to respect decimal presentations on one side and IEEE on the other side.

For that one can use routines developed by Florent de Dinechin, which are worth to be better known.

Here is a Maple sheet showing how one can do it (looking at the complex valued power function using evalhf versus using MS VC2005 as an example).

may i know functions for which the computational cost of evaluating their first derivative is higher than the function it self.

I would like to know if it possible in Maple 12 to efficiently compute recursive procedures with two variables.

A simple example would be: f(a,0):=1 for all a>=0, f(0,b):=1 for all b >=0 and f(a,b) :=f(a-1,b) + f(a,b-1) for

a>0, b>0 (which defines the binomial coefficients). In trying to do this in a straightforward way i get

the error message "too many levels of recursion". Using 'trace' I see that Maple doesn't seem to be

creating a remember table for functions of two variables. Am I missing something?


I am new to Maplesim and I would like to multiply 2 voltage-time functions ( mixing in time-domain), but I have no succes with the (Mathematical-Operators-) Product component ( I can't connect it to the voltage sources). How can be done this? Thanks for your help in advance.


I want to learn more about ImpulseResponse functions and the ImpulseResponsePlot in Maple.
Could anyone please explain how it works ? I want to start with a simple example ie
a simple transfer function which is very easy to understand.

sys1 := TransferFunction(s*(s-1)/((s+2)*(s+4)*(s+6))):
ImpulseResponsePlot(sys1, 2);

I realized the other day that I had not mentioned the Threads:-Add, Threads:-Map, Threads:-Mul and Threads:-Seq functions.  These are parallel implementations of the standard Maple functions, add, map, mul and seq.  They expect the sam

I want to solve a system of 2 equations and 2 variables with solve functions.But,I receive invalid argument error.the problem is following:

 R11 := {(200*(-0.8e-1*t+0.8000000000e-1))/p^2-(120*(t-0.3999999999e-1*t^2+0.3010e-1*t^2.5))/p^3-25.0000*t^1.5/p^3-(46.67*(-5.760000000+6*t-.24*t^2))/p^3-(100*(0.8000000000e-1+0.50e-1*t^1.5))/p^3 = 0}

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