Given the following functions, graph them and identify relative and absolute extrema (if any).

f(x)=3x^3-2x^2+5x-7     [-3,6]

Hello

for Example

A is vector A[r[= x+y , this is the equation generating multiple values. some are real and some are imaginery like,20,133, 2+3i,3+3i. I am interested the value which ilies within certain limits like 10-30. Here in this example 20 fits. So A[r] vector should store 20 only. How to do it.

Please help me on that. 

Thanks 

I'm doing a statistic analysis on a lot of data which i have imported from Excel into a matrix. I've got about 2880 data points and i'm trying to use regression and its giving me an error which i do not know how to deal with.

How would i execute the following calculate? I know i could use the statistics package but i want to do with with the formula. I'm trying to find the standard deviation. Look at the attached picture so see. I've also attached a copy of the calculations in maple format.

Download Test.mw

Also another little side thing, but not necessary. Is it possible to have a matrix with empty spaces in it and return it?

Is there any Maple code that allows to view a complex function using the "domain coloring" technique?

This technique is described for example in Wikypedia: https://en.wikipedia.org/wiki/Domain_coloring

How I can determine a function that satisfy these boundary and initial conditions.

Thank you

S2

Maple Worksheet - Error

Failed to load the worksheet //convert/S2
 

Download S2

How I can do ?

Thank you.

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and .

\where the elements of the vector, are the time-dependent generalized coordinates.

L_Maple
 

Download L_Maple

How come maple doesn't support symbolic matrix calculus?

For example, I'd like to differentiate or simplify expressions with relation to general vectors and matrices. Besides simpifying the expressions, in runtime (e.g. optimizing a function in matlab) my vector and matrix size change according to the data, so deriving specific expressions element-wise would only be valid for a specific case.

A simple example (A is a matrix, x is a vector):

f(x) = ||Ax||^2

df/dx = 2A'Ax

Recently, I stumbled into this

http://www.matrixcalculus.org/

where you can try my example above: norm2(A*x)^2

I was wondering how come that mature symbolic softwares on the market (maple and mathematica) can't do it?

An hour or two ago, I answered a question in which it was a question of plotting a complex-valued function of 2 real variables. But the question itself and also my answer to it disappeared somewhere. Therefore, I send my answer here below.

There are two options for plotting:
1. Graphs of real and imaginary parts (as 2 surfaces in 3D).
2. Graph of the absolute value of this function (one surface in 3d) .

restart;
f:=(1+cosh(2*x))*exp(-4*I*t):
plot3d([Re,Im](f), x=0..1, t=0..1, color=[red,blue]);
plot3d(sqrt(add([Re,Im](f)^~2)), x=0..1, t=0..1, color=green);

I define the spherical Bessel function with j([n, z]) := sqrt(2)*sqrt(Pi/z)*BesselJ(n + 1/2, z)/2.  Then I attempt to plot with

Digits := 20;
plot(j([1, z]), z = 0 .. 25);

I get an empty plot and an error message: 

Warning, expecting only range variable z in expression j([1, z]) to be plotted but found name j

which makes no sense to me.

(I am using Maple 2019.)

Hi

I would like to solve the non-linear system to obtain rho1 and rho2 .

But when i use solve i get the following error
Error, (in solve) cannot solve for an unknown function with other operations in its arguments

system.mw

many thanks

>SIRvector := [op(SIRvector), op(evalf(solve(eval({Yeqnx(1), Yeqny(1), Yeqnz(1)}, SIRvector), {JJ(1), RR(1), SS(1)})))];

I have a picture. I tried to find the formula of the curve
My code

t := proc (x) options operator, arrow; b*x^10+c*x^9+d*x^8+e*x^7+f*x^6+g*x^5+h*x^4+i*x^3+j*x^2+k*x+l end proc

And solve
solve([t(-2) = 2, t(0) = -2, t(1) = 0, t(2.5) = -3, t(3.5) = 0, t(-1) = 0, eval(diff(t(x), x), x = -2) = 0, eval(diff(t(x), x), x = 0) = 0, eval(diff(t(x), x), x = 2.5) = 0, eval(diff(t(x), x), x = 1) = 0, t(2.8) = 0], [b, c, d, e, f, g, h, i, j, k, l])

[[b = -0.2688965311e-1, c = .1687428810, d = -0.3166922031e-1, e = -1.490599337, f = 1.885667707, g = 3.845330330, h = -6.939129440, i = -2.523473874, j = 7.112020606, k = 0., l = -2.]]

I ploted

plot(-.2688965311*x^10+.1687428810*x^9-.3166922031*x^8-1.490599337*x^7+1.885667707*x^6+3.845330330*x^5-6.939129440*x^4-2.523473874*x^3+7.112020606*x^2-2, x = -3.5 .. 4.5)

The result too far with picture. How can I repair?

I want to made a comparison via plots of RK-4, NSFD and LWM.

Restart

eqn1 := diff(x(t), t) = x(t)*(2-(1/20)*x(t))-x(t-tau)*y(t)/(x(t)+10)-10;

eqn2 := diff(y(t), t) = y(t)*(x(t)/(x(t)+10)-2/3);

bc := x(0) = 40, y(0) = 16,tau=0;

sol := dsolve({bc, eqn1, eqn2}, numeric);

plots[odeplot](sol, 0 .. 10);

I got the plot Vertically x and horizontally t but i need vertically y and horizontally x, Please help me, how can i write the code for ploting, thanks in advance.

I am trying to calculate the contour integral of exp(-z/A)/z^{2+n}, for constant A and integer n. Here is the Maple code (forgive me, very beginner Maple user here!):

restart;

f := exp(-z/A)/z^(2 + n);
                                 /  z\
                              exp|- -|
                                 \  A/
                         f := --------
                               (2 + n)
                              z       


op~([singular(f, z)]);
                            [z = 0]
poles := [0];
                          poles := [0]
C := z -> is(abs(z) < 1);
assume(2 <= n);
(2*Pi)*I*add(residue(f, z = a), a = select(C, poles));
                              /   /  z\       \
                              |exp|- -|       |
                              |   \  A/       |
                2 I Pi residue|--------, z = 0|
                              | (2 + n)       |
                              \z              /

You can do this by hand by simply expanding the exponential, but how do I make Maple actually do the calculation? (instead of just answering with "residue...".