## Draw a line through all maxima...

I have a family of functions characterized by

f:=x^2+b*x+b*3;

I plotted some of them:

graph1:=x->subs(b=0,f):
graph2:=x->subs(b=2,f):
graph3:=x->subs(b=4,f):
plot([graph1(x),graph2(x),graph3(x)],x=-10..3,y=-5..15);

And now I want to draw a line through all maxima into the same diagram. The maxima have the coordinates (-1/2*b | -1/4*b^2+3*b). I managed to create a pointplot:

## How to assign a number explicitly?...

Hi friends,

It is a simple question but I got confused... The best way to explain the problem is the example below (I modified my example to make it more clear and easier):

gCount := 1;

hCount := 5;

dCount := 10;

lineCounter := 1;

for k to gCount do

for i to hCount do

for j to dCount do

## How to create For (do) loop in maple 13.02 in a de...

Hello everyone,

I want to create a loop in descending order like this: for i from 100 by -0.01 to 0 do ....

I wrote functions trying this logical solution but nothing, please help, it's very important to me to get the answer as soon as possible.

Steve

## Point Plot in Maple...

I am trying to add a point to an existing 2d plot, I understand how to plot functions and points but I can't seem to combine them into a single plot.  I am new to maple and still getting use to the functionality.  Any suggestions will be appreciated.

## 9 functions 9 unknown variables strange answer...

Hallo, I have 9 functions and 9 unknown variables. I want to solve these 9 variables. I tried this by defining al the 9 functions and the known variables in maple and the 'solve({Fx1,Fx2....Fxn},{N1,N2.....Nn})' commando. I get an answer but I don't understand what it means: {Fb = 825., Fc = -675., Fd = -2025.-3.Fm, Fe = -2025.-3.Fm, Fj = 1200.+2.Fm, Fk = -2.Fm-1350., Fl = Fm, Fm = Fm, Fr = 250.}. I don't know what they mean with 'Fd = -2025.-3.Fm.' Tanx, Olivier

## Sumfunctions of power series ...

with convert and FormalPowerSeries one can find power series of some functions. WIth the function int one can sum / make integrals of expressions.

I am new to Maple and have tried finding the sum function of the product of two power series :

in both cases sum of n from 0 to infinity

how to program Maple to find the sum function of f(x), g(x)
and g(x)*(f(x) ?

## ODEs & Maple: graduate-level textbook ...

Dear All,

I am looking for a textbook which could be used as a supplementary text for a graduate-level course on ODEs and Dynamical Systems. Ideally, such textbook would feaure numerous examples in Maple, mostly symbolic but with some numerical as well, illustrating certain more advanced topics in the theory of ODEs. Such topics could include stability theory with Lyapunov functions, stable and unstable manifolds, hyperbolic theory, center manifolds and nonlinear stability, periodic orbits and limit cycles, Poincare-Bendixcon theory and phase spaces.

On 4th May I submitted Ploting 10 functions to plot mentioning codes with with Mapple.

BR and thanks

mathstudentdk

## differential equation...

How can I solve the following differential equations  by using Maple functions and boundary conditions in a parametrical manner(obtaining x)?

## Ploting 10 functions with Mapple...

What Mapple code for ploting these ten functions ?

Plot these functions. I need urgwent help with these functions :

A=\sum_{n=[1,infinity]}(3n^{2}+7n+1)^{-n}

B=\sum_{n=[1,infinity]}(-1)^{n}(3n^{2}+7n-1)/(3n^{5}+4n+1)

C=\sum_{n=[1,infinity]}(-1)^{n}(n^{2}+n-1)/(3n^{2}+n)

D=\sum_{n=[1,infinity]}sin((phi/2n)+n(phi))

IF n is uneven E=\sum_{n=[1,infinity]}a=(2/n)

IF n is nevenF=\sum_{n=[1,infinity]}a=(-1/n)

G=\sum_{n=[1,infinity]}(n^{-4)}

H=\sum_{n=[1,100]}(1/3)n^{-3}+\sum_{n=[1,100]}n^{-4}

1. For n = 5 plot I=\int e^{\frac{1}{(1+exp((n(2-x))}}

## 'accessing data' of 3D plot ?...

Testing a numerical implementation I want to access data, which are
suggested as maximal errors through plotting (with care) to examine
that in more detail (so plotting is considered just a help)

For univariate functions I am aware how to look into data pairs for
the command plot.

My function is bivariate and real valued.

P:= plot3d( f(x,y), ...) lets me save the result and

op(P);
op(1,P);
arr:=op(3, %);

arr; Arr:=convert(%, Matrix);
plots[matrixplot](Arr, axes=boxed);



## a contour integral...

Hi,

I try to calculate a contour integral(in fact it is the contour integral defined in the principle argument theorem) with a function that was given in my earlier entry here

y:=2.0;W:=(2^(z+3/2)*Pi)/(GAMMA(-z/2)*GAMMA(1/2-z/2)):V:=1.0;
f:=1+((abs(V))^2/W^2)*(CylinderD(z,y)^2)*(CylinderD(z,-y)^2-CylinderD(z,y)^2);

I try to use this f in this contour integral as:

phi:=t→exp(I*t);

g:=(diff(f(phi(t)),t)/f(phi(t))) * diff(phi(t),t);

here I give f  (z)/f(z) is g. And

## pde system...

I have a set of PDEs & I tried to solve it. First of all I defined some functions as:
H := (diff(a(t, y), t))/a(t, y), Hy := (diff(a(t, y), y))/a(t, y), H1 := diff(H(t, y), t), a1 := diff(a(t, y), t), a2 := diff(a1, t), Hy1 := diff(Hy(t, y), y), ay1 := diff(a(t, y), y), ay2 := diff(ay1, y), n1 := diff(n(t, y), t), n2 := diff(n1, t), ny1 := diff(n(t, y), y), ny2 := diff(ny1, y), pef := -2*n(t, y)^2*Hy1-3*n(t, y)^2*Hy^2-n(t, y)*ny2-2*n(t, y)*Hy*ny1-2*H(t, y)*n1/n(t, y), ρef := 3*n(t, y)^2*Hy1+6*n(t, y)^2*Hy^2, ωef := pef/ρef`,

## Assigning and disconnecting the relation between t...

Hi every body I have two functions which are aold(x) and anew(x). I am using them to update a function as: For example: aold:=x-> x^2; for i from1 to 5 do anew:=x->aold(x)+x; aold(x):=anew; end do; But it does not work because it cause loop in assigning the function. Also, if I unassign the aold(x) as aold(x):='aold(x)', also anew(x) got unassigned automatically. I am looking for a way to assign anew(x) as anew(x)=aold(x) and after that disconnect the relation between the two functions. Thanks Hamidreza.

## How to integrate...

I need to find value of integrals ratio:

int(f2(t),t=0..5.5)/int(f1(t),t=0..5.5),

where the functions f1(t), f2(t) are result of numerical solution of differential equations system:

> restart; with(plots):
> sys:=diff(f1(t),t)=piecewise(t<=4,3*exp(-2*t),-1),
diff(f2(t),t)=sin(t):
init:= f1(0)=1, f2(0)=1:
> F:=dsolve({sys,init}, {f1(t), f2(t)}, numeric);
> Result:=odeplot(F, [[t,f1(t)],[t,f2(t)]], 0..5.5):
> display(Result);

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