Maple 15 Questions and Posts

These are Posts and Questions associated with the product, Maple 15


I hope my question is not to general. I have a polynomial of 8th order

expression:=a8(z) * x^8 + .... + a1(z) * x + a0(z) = 0

on which I am using solve/RootOf


Now when I plot it against z the solution has a jump, why?

When deriving the polynomial I could as well have used another variable instead of x above, say y. These two are related by a function...Then when I write down the 8th order polynomial in y and use RootOf/solve, then no jump occurs.

Is there a way to handle this because left of the jump the solution is not correct while right of it, it is...


Assume that we hace a set points in the plane, put X:=[a1,a2,...,aN] where each ai is given by its coordinates [x,y]. The commnad "convexhull(X)" give us the points of the convex hull of X, but how I can find to "lower-right" of these points? Please, see the attached image. I need to findo the points A,C,E and F, marked with a solid circle.

Many thanks in advances for your comments.



with(PDEtools); declare(u(x, y, z, t), U(X, Y, Z, T)); interface(showassumed = 0); assume(a > 0, p > 0); W := diff_table(u(x, y, z, t)); E := 6*W[]*W[x]+W[t]+W[x, y, z] = 0; InvE := proc (PDE) local Eq1, Eq2, Eq3, Eq4, tr1, tr2, tr3, tr4, term1, term2, term3, term4, sys1; tr1 := {t = T/a^beta, x = X/a^alpha, y = Y/a^mu, z = Z/a^nu, u(x, y, z, t) = U(X, Y, Z, T)/a^zeta}; tr2 := eval(tr1, zeta = 1); Eq1 := combine(dchange(tr2, PDE, [X, Y, Z, T, U])); Eq2 := map(lhs, PDE = Eq1); term1 := select(has, select(has, select(has, rhs(Eq2), a), beta), a); term2 := expand(rhs(Eq2)/term1); term3 := select(has, select(has, term2, a), a); sys1 := {select(has, op(1, term3), a) = 1, select(has, op(2, term3), a) = 1}; tr3 := solve(sys1, {alpha, beta, mu, nu}); tr4 := subs(tr3, tr2); print(tr3, tr4); Eq3 := dchange(tr4, PDE, [X, Y, Z, T, U]); term4 := select(has, op(1, lhs(Eq3)), a); Eq4 := expand(Eq3/term4); PDE = simplify(Eq4) end proc; InvE(E)

how to find the contour of time series data? and how to find curvature function of this contour?

The representation of the tangent plane in the form of a square with a given length of the side at any point on the surface.

The equation of the tangent plane to the surface at a given point is obtained from the condition that the tangent plane is perpendicular to the normal vector. With the aid of any auxiliary point not lying on this normal to the surface, we define the direction on the tangent plane. From the given point in this direction, we lay off segments equal to half the length of the side of our square and with the help of these segments we construct the square itself, lying on the tangent plane with the center at a given point.

An examples of constructing tangent planes at points of the same intersection line for two surfaces.

i am trying to write the differential equation 

u_{t}=u_{xx}+2u^{2}(1-u) in my maple 15. 

but it shows error,

Error, empty number and  1 additional error.


I need to solve system of 6 non linear equations. 

Down here you can see the code I wrote and at the end used to fsolve function, and it is not running. I get an error about the const 'V': Error, (in fsolve) V is in the equation, and is not solved for.

What is the right way to solve this system?

Thank you very much!



omega1 := 1.562;
omega2 := 2.449;
omega3 := 3.325;
y1 := c1*sin(omega1*t+phi1)+c2*sin(omega2*t+phi2)+c3*sin(omega3*t+phi3);



y2 := .1019*c1*sin(omega1*t+phi1)+.75*c2*sin(omega2*t+phi2)+.4608*c3*sin(omega3*t+phi3);



y3 := .407*c1*sin(omega1*t+phi1)+(0*c2)*sin(omega2*t+phi2)+1.844*c3*sin(omega3*t+phi3);
eq1 := subs(t = 0, y1) = 0;
eq2 := subs(t = 0, y2) = 0;
eq3 := subs(t = 0, y3) = 0;
eq4 := subs(t = 0, diff(y1, t)) = V;
eq5 := subs(t = 0, diff(y2, t)) = 0;
eq6 := subs(t = 0, diff(y3, t)) = 0;



eqs := [eq1, eq2, eq3, eq4, eq5, eq6];
vars := [c1, c2, c3, phi1, phi2, phi3];
fsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {c1, c2, c3, phi1, phi2, phi3});


Dear, I am facing the problem for solvin the attached file. Solution obtained for L=1 successfully but i need the solution for large value of L e.g., L =10. Please find the attachement and fix the problem. I am waiting positive response. Thanks in advance.


Dear I want to solve the system of ODEs in attached file for different values of m1 i.e., 3,4,5 how I will use the value of m1 in dsolve. I am waiting your positive response thanks in advance.



Hope you would be fine. I want to solve the following PDEs by numerically for v[nf]=alpha[nf]=Ec=mu[nf]=C=1 and Pr=6.2

Eq1 := diff(u(x, t), t) = v[nf]*(diff(u(x, t), x, x));

Eq2 := diff(u(x, t), t) = alpha[nf]*(diff(theta(x, t), x, x))/Pr+Ec*mu[nf]*C*(diff(u(x, t), x))^2;

ICs := u(x, 0) = 0, theta(x, 0);

BCs := u(0, t) = 1, theta(0, t) = 1, u(10, t) = 0, theta(10, t) = 0;

and find the values of (diff(u(0, t), x))/(1-phi)^2.5 for different values of phi. Thanks in advace 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

any idea for my problem?


> k1 := sum(X[h, t], t = 1 .. 23) >= 9;
9 <= X[h, 1] + X[h, 2] + X[h, 3] + X[h, 4] + X[h, 5] + X[h, 6]

   + X[h, 7] + X[h, 8] + X[h, 9] + X[h, 10] + X[h, 11] + X[h, 12]

   + X[h, 13] + X[h, 14] + X[h, 15] + X[h, 16] + X[h, 17]

   + X[h, 18] + X[h, 19] + X[h, 20] + X[h, 21] + X[h, 22]

   + X[h, 23], h = 1 .. 6

why 'h' still 'h'. from my textbooks the formula must be like this :

how will i go about solving this problem, i want to return somthing like this (this anwser is from another function that did not contain sin, and therefor did not gave me problems).

thx in advance

I've made a system of two equations:

eq1:= x^2+y^2=0.314

eq2:= y=0.05180967688x

The first is a circle while the second is a line. I use the command fsolve in order to get the intersection and i get:


I need to use these results as the coordinates of a pointplot, how can i do it? Is there a way to isolate x and y?


yVal := 0.01

xVal := 0.01

p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])

I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph. 

Any help will be greatly appreciated :) thanks


Given f(x)=2x^2-4x, how do I define and plot the functions f(x), 2f(x), 4f(x), -f(x) and -4f(x) in maple 15?

Thank You.


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