I am interested in finding the lower Riemann sum for a partition of unequal width.

The points of the partition are P = { -1, -1/4, 1/4, 3/4, 1} , and the function is f(x) = x^2.

My attempt:

restart: with(Student[Calculus1]):
RiemannSum(x^2,x={[ -1,-1/4],[-1/4, 1/4],[1/4,3/4],[3/4,1]},method=lower)

It said error range must be specified. I looked at the help page but I didnt find a specific command for entering partition points manually.

can anyone help me to calculate the exact  value of the eigenvalues of this matrix:
 

Download mat.mw

 Evaluate, to 10 significant figures

 integration of (e^(-x) *sin(x^2/2))/(3+x) with the limits of infinity and 1.

Dear all

I solve the first-order PDE with a boundary condition contains a parameter  s

When I run the code there is no solution displayed using pdsolve

Many thanks for your help

PDEBCS.mw

with(Maplets[Elements]);

Button("Deduct", Evaluate(f = 'work(3)'))

Here I run fucntion 'work()' when click the button. Is there a way to run several functions when I click the same button?

I have a matrix as follows.

How do we equalize this matrix to zero matrix and solve it?
 

A:=Matrix(2, 2, [[-0.0001633261895*z[1, 2]^2 + 0.0002805135275*z[1, 2]*z[2, 2] - 0.0001200583046*z[2, 2]^2 + 0.0006934805795*z[1, 1]^2 - 0.001190280265*z[1, 1]*z[2, 1] + 0.00007689977894*z[1, 1]*z[1, 2] - 0.00009937418547*z[1, 1]*z[2, 2] + 0.0005090615773*z[2, 1]^2 - 0.00003303758400*z[2, 1]*z[1, 2] + 0.00005683264925*z[2, 1]*z[2, 2] + 0.7021232886*z[1, 1] - 0.3171553245*z[1, 2] - 0.08291569324*z[2, 1] + 0.04647270631*z[2, 2] - 0.1436869545, 0.0002939068385*z[2, 1]^2 + 0.4237544799*z[1, 1] - 0.03129537402*z[1, 2] - 0.06276282411*z[2, 1] + 0.02529757039*z[2, 2] + 0.0004003811990*z[1, 1]^2 + 0.0002177682527*z[1, 1]*z[1, 2] - 0.0006872086309*z[1, 1]*z[2, 1] - 0.0001976167183*z[1, 1]*z[2, 2] - 0.0001764013184*z[2, 1]*z[1, 2] + 0.0001600777394*z[2, 1]*z[2, 2] - 0.1237363898], [0.00006763201108*z[2, 1]*z[1, 2] - 0.0001020812322*z[1, 2]*z[2, 2] - 0.00001554113990*z[2, 1]*z[2, 2] - 0.00003577693711*z[1, 1]*z[1, 2] + 0.0004330743651*z[1, 1]*z[2, 1] - 0.00001941220415*z[1, 1]*z[2, 2] - 0.01736180925 + 0.5623450996*z[2, 1] - 0.2353707048*z[2, 2] - 0.0003226356619*z[1, 1]^2 + 0.00007598605473*z[1, 2]^2 - 0.0001392051452*z[2, 1]^2 + 0.00003283047567*z[2, 2]^2 + 0.04653058230*z[1, 1] - 0.03026711709*z[1, 2], -0.00008037012799*z[2, 1]^2 + 0.03994641178*z[1, 1] - 0.02291248064*z[1, 2] + 0.3140461555*z[2, 1] + 0.01853659924*z[2, 2] - 0.0001862737861*z[1, 1]^2 - 0.0001013147396*z[1, 1]*z[1, 2] + 0.0002500356011*z[1, 1]*z[2, 1] + 0.00005403916772*z[1, 1]*z[2, 2] + 0.00008206914192*z[2, 1]*z[1, 2] - 0.00004377396755*z[2, 1]*z[2, 2] - 0.01370765196]])

And then, I want to select the roots in which 0<z[i,j]<1. 

Finally, I want to create matrix Z from these roots as follows   

Z:=Matrix(2, 2, [z[1, 1], z[1, 2],z[2, 1], z[2, 2]]);

2.22 *10^(-87)

2.55 *10^(-90)

would like to get 2.22 and 2.55 only by ignoring any power

how to do this?

How can I plot the contours with label for the following?

The Code is as follows:

z := -y + sech(x - 3*t);

w := 10*sech(x - 3*t);

with(plots);

P1 := plot(eval(w, t = 0), x = -10 .. 10):
P2 := contourplot(eval(z, t = 0), x = -10 .. 10, y = -eval(w, t = 0) .. eval(w, t = 0), contours = 5, grid = [101, 101]):
display(P1, P2);

Thanks

I assume I'm missing the verb here, but how does one display the elements of a vector and an array?

I can only do it with browsing or changing the "number format". 
 

Download Vector_Display_Problem.mw

I get error on Maple code 

N := 4

f(x):=sum(p^i*fi, i = 0 .. N);

HPMEq := (1-p)(diff(f(x), x$3))+p(diff(f(x), x$3)+(1/2)(diff(f(x), x, x))*f(x));

for i from 0 to N do equ[2][i] := coeff(HPMEq, p, i) = 0 end do

Error, unable to compute coeff

I'm trying to solve this schrodinger equation for a quantum oscillator:

E = n + 1/2 where n = 0,1,2,3,4

If I just use dsolve then I get a bunch of Bessell functions and I'm not sure why.

Can anyone point me in the right direction?

Thanks.

How can I analytially evaluate the following definite integral ?

int(1/(c*x + d), x = a .. b)

My Output is as follows:

Thanks.

is there any library or tools to design index of Grassmannian and its k and n for Schubert use?

is there any library to relate poset with index of Grassmannian and its k and n for Schubert use

RandomMatrix(n, 1);

does not seem too work with Vectors of dimension d in elementwise multiplication ;/ Even though it is an nx1 matrix = an n vector.

This seems like a limitation maple!

RandomVector(n);

Does seem to work with Matrix and Vector.

Matrix(5,1)*~Vector(5);

Both have the same dimensions and should be possible to multiply them pointwise!