## What is wrong with this Fourier serie...

trig_interp3.mw

Hi all

I have this type of generalized Fourier serie: a0+Sum(an*cos(n*Pi*ln(x)/ln(2))+bn*sin(n*Pi*ln(x)/ln(2)), n = 1 .. N)

The coefficients I calculated and the results seems correct. However, the amplitude of Fourier expansion is twice the amplitude of the function.

Find in the attached file my maple code.

Regards

## Rearrange and aggregate inequalities...

Hi, I am very new to Maple and do therefore probably propose a very simple question, so I would kindly ask you to excuse me in advance.

Basically I want so solve a simple and discrete game by comparing expected utility payoffs. There are only three states of the world (0,1,2) and I must determine for what cost-price-ratio what quantitiy is chosen from the same set (0,1,2).

Mathematically it's easy and I solved it, but Maple does not let me present my findings in a way I would like, as presented in my picture (preview from LaTex):

To achieve this I would have to get all w over p and then define it as z (cost-price-ratio). But when I try solving for w/p or respectively z doesn’t work. Additionally, when I try to apply some rearrangements manually (like multiply by 1/p in the first inequality) it doesn't work either, I just receive a '*' in front of round brackets with my equation inside.

So, is there a possibilty to do these simple rearrangement of my inequalities in Maple? And is it possible to aggregate the solutions in the same way as I pictured it for my LaTeX code?

Thank you very much!

## Correctly Plotting a Complex Valued Function...

Hello!

I am currently trying to plot the function: sqrt(x^2+y^2-c), where x & y are variables in cartesian coordinates, and c is an arbitrary real constant. I came across a jagged edged plot when I asked maple to plot:

sqrt(x^2+y^2-c)       *** Code below ***

Explore(plot3d([sqrt(x^2+y^2-c),-sqrt(x^2+y^2-c)],x=-2..2,y=-2..2,numpoints=10000),c=-1..1)

So I entered in the "Re" command to take the real part:

Explore(plot3d([Re(sqrt(x^2+y^2-c)),Re(-sqrt(x^2+y^2-c))],x=-2..2,y=-2..2,numpoints=10000),c=-1..1)

This smoothed the plot out at the ring x^2+y^2=1, but however also added what looks like a solid disc as well. Is there a way I can plot the function correctly without this disc in the middle?

Thanks!

## simplification of Fractional differentiation resul...

Can someone help with the simplification of the result of this code? I am sure the "qs" in the final result should not appear.

Thanking you in anticipation of your positive responses

```#k=1
restart:
P:=sum(a[k]*x^k, k=0..2):
assume(alpha>0,alpha <= 1):
Q:=fracdiff(P,x,alpha);
e1:=simplify(eval(P, x=q))=y[n]:
e2:=simplify(eval(Q,x=q))=f[n]:
e3:=simplify(eval(Q,x=q+h^alpha))=f[n+1]:
var:=seq(a[i], i=0..2):
M:=e||(1..3):

Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 3 do
a[i-1]:=Cc[i]:
end do:
Cf:=P:
E:=collect(Cf, [y[n], f[n], f[n+1]], recursive):
print():
#y[n+1]=collect(simplify(simplify(expand(eval(Cf,x=q+h^alpha)),size)), [y[n],f[n],f[n+1]], factor);
y[n+1]=simplify(eval(Cf, x=q+h^alpha)):
collect(%, [y[n], f[n], f[n+1]], recursive);```

## Can fsolve in this maplesoft appication be explore...

In the application whose link is below, an error message results when I right click the fsolve command and select explore.

https://www.maplesoft.com/applications/view.aspx?SID=119851

I would like to explore changes to several of the parameters in the equations named "sys", especially the value of Qoutflow. Can this be done and, If so, how can the solved values, Q1, Q2, Q3, and H be graphed as the slider values of individual parameters values are modified?

## Syrup problem for band-pass filter...

I am attempting to reproduce the results claimed by analog.com for a band pass filter.

I have checked the circuit specification and found no errors.

Am I expecting too much or am I doing something wrong?

## www.analog.com/designtools/en/filterwizard/
## Filter Requirements for Band-Pass, 4th order Butterworth
## Specifications: Optimize for Power, +Vs= 5, -Vs= -5
## Gain: 10 dB
## Passband: -3dB at 2kHz
## Stopband: -40dB at 40kHz
## Component Tolerances: Capacitor = 5%; Resistor = 1%; Inductor = 5%; Op Amp GBW = 20%

restart;
with(Syrup); Version;
with(DynamicSystems):

ckt := "*60 kHz Band Pass Filter  \n\
vin 1   0 \n\
R1A 1   2 165k \n\
R1B 5   7 169k \n\
R2A 2   0 976 \n\
R2B 7   0 1k \n\
R3A 6   0 221 \n\
R3B 11  0 226 \n\
R4A 5   6 12.7k \n\
R4B 10 11 12.7k \n\
R5A 4   3 97.6k \n\
R5B 9   8 100k \n\
R98 3   0 1e9 \n\
R99 8   0 1e9 \n\
C1A 2   4 270pF \n\
C1B 7   9 270pF \n\
C2A 2   3 270pF \n\
C2B 7   8 270pF \n\
* \n\
X1A 6  3 5  NonIdealOpAmp \n\
X1B 11 8 10 NonIdealOpAmp \n\
.include Library:-NonIdealOpAmp \n\
.end";

volts, others := Solve(ckt, 'ac', 'returnall');
gain := eval(v[10]/vin, volts);
H := subs({A=80000, f0=15*10^6, Ro=100}, gain);
evalf(H);
tf := evalf(H);
sys := TransferFunction(tf);
PrintSystem(sys);
plotsetup(maplet);
MagnitudePlot(sys);

## How to fix incomplete worksheet?...

An error message during opening a Maple file is seen:

ibb.co/hqOOkJ

I put the file link in below. The Maple file has been saved as Maple 2016.

https://files.fm/u/jpc3k5s4

I will be grateful if you can recover the file. Thanks

## Difficulty with NonlinearFit() : I cannot replicat...

I'm having a hard time trying to understand and use the various fitting functions.

For starters, if I copy and paste the code from the example on the Maple support Help page for NonlinearFit(), I'm not able to successfully execute the code. It gives the error:

Error, (in Statistics:-NonlinearFit) complex value encountered

I've attached my Maple file: testing_nonlinearfit.mw

## Display long formulas...

Hello,

I have a very simple problem. When Maple displays long outputs I can only see a part of them. Here there is an example

https://www.dropbox.com/s/ymp1vdsg80ewu1s/Untitled.jpeg?dl=0

On my previous versions of Maple I had a slider on the bottom of the page. How can I activate it in Maple 2016?

Thanks, Nicola

## Some problem with "uses"...

Hi everybody,

Why f generates the error "... orthopoly is not a module or member"

f := proc(n)
uses orthopoly;
H(n,z);
end proc;

as g works correctly ?

g := proc(n)
orthopoly:-H(n,z);
end proc;

## Calculate Neumann BC from known function...

How to calculate the following at point p=(xo,yo):

n . del(u), u=u(x,y)

from the known function u, where n is the unit outward normal at p and the dot represents the dot product.

The objective is to create example PDE problems with Neumann BCs on irregular 2D domains.

## Can we plot(3D/2D) solution of Nonlinear Schroding...

Can someone help me to find graph of this type of solutions .

finalsol := exp(I*(-k*x+t*(k^2+2*rho^2-2*sigma^2)+theta))*rho*tanh(-2*k*rho*t+rho*x);

sol1 := eval(finalsol, [rho = .5, theta = .5, sigma = .5, k = .5]);

graph1 := plot3d(sol1, t = -5 .. 5, x = -5 .. 5, numpoints = 300, frames = 50, axes = framed, color = x, thickness = 5, axesfont = ["HELVETICA", "ROMAN", 24], labelfont = ["HELVETICA", "ROMAN", 24]);

ContPlot1 := contourplot(sol1, t = -20 .. 20, x = -20 .. 20, frames = 50, axes = framed, thickness = 5, numpoints = 300, a*xesfont = ["HELVETICA", "ROMAN", 24], labelfont = ["HELVETICA", "ROMAN", 24])

plot_solution.mw

## How can I plot a rod with rectangle cross-section...

Dear All

I want to plot A long rod with length L and its cross-section is a rectangle

## Pick the "positive" solution of a quadratic...

Quadratic equation ax^2 + bx + c = 0. Coeff's long and ugly expressions in their own right, but I know that a is nonzero, that there is at least one real solution, and that I want the largest.

So, question: How do I get Maple to return the -b/2a PLUS sqrt((b/2a)^2-c/a) solution?

## How to plots[animate] a HeatMap ?...

Hi,

This is a notional example

1/ I define a matrix through some procedure, for instance
p := k -> Matrix(3, 3, (i,j) -> i+j+k mod 3)

2/ Now I would like to animate the plot of matrices p(k) for successive values of k.
The red commend below doesn't work
N := 5:
plots[animate](Statistics[HeatMap], [ p(k) ], k=0..N, frames=N+1);