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I have a pair of linear functions I want to differentiate wrt time. The first line defines the functions, and thesecond a substitution that tells maple that the variables of these linear functions, are themselves functions of time.

F := Vector([p[1]*p[6]*(p[2]-x[1]-x[2])-p[3]*x[1], p[4]*p[6]*(p[2]-x[1]-x[2])-p[5]*x[2]])
timefull := [x[1] = x[1](t), x[2] = x[2](t)]

This line should give the ith derivative

Fdiffi := [diff(subs(timefull, F[1]), t$i), diff(subs(timefull, F[2]), t$i)]

however maple gives me a responce in terms of the pochammer function. Why is this? How do i avoid it?

diff(F(x,F(x)), x);

 

how to differentiate this?

 

(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))

 

how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?

 

i guess need define new calculus for two variables

Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);
Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);
Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);

 

if inside F(x) is F(x,y)

it seems need to find the basic definition of F(x,y) first

if i define F(x,y) as

F := (x,y) -> min(x,y)/max(x,y);

 

i may be wrong, how to differentiate correctly?

Hello everyone!

Suppose, we have a differential polynomial

P := u(x) + (D@@2)(u)(x)

Given this, I am looking for a procedure which gives coefficients depending on the order given as input, for example, lets say, procedure name is fun_coeff which depends on two parameters, original polynomial P and the order n, then

fun_coeff(P, 3) should give [1, 0, 1, 0]

where each entry corresponds to the coeff of

 [u(x), (D@@1)(u)(x), (D@@2)(u)(x), (D@@3)(u)(x)]

in the polynomial, similarly

fun_coeff(P,4) should give [1, 0, 1, 0, 0]

corresponding to

 [u(x), (D@@1)(u)(x), (D@@2)(u)(x), (D@@3)(u)(x), (D@@4)(u)(x) ]

Thank you all for your time :)

I have functions like

g := (y, t)->sin(y(t))

diff(g(y, t), t) # ok

How to determine the derivative below with maple :

diff(g(y, t), y(t))

Thanks

Hello everybody

In the attached file, as you can see, 'u' is function of 'thet1(t)' explicitly, But when I want to differentiate from 'u' w.r.t 'thet1(t)', maple returns zero as the answer. How is it possible?

Thanks in advance

d.mw

Hello, 

I am trying to get W(x,y,y')=y*y'/x

I am trying 

omega:=(x, y(x), (diff(y(x),x)))-> (y(x)*(diff(y(x), x))/x);

but get 

Error, invalid parameter; functional operators require their parameters to be of type symbol or (symbol::type)

 

Can anyone help me out?

 

thank you

Hi,


This is my first post here, so I apologize for any errors or breaking of posting etiquette. I encountered a strange problem suddenly tonight when I tried running a Maple worksheet I've run succesfully (several times, without changes) in the past. The problem occured on both Maple 18 and Maple 2015, unfortunately I haven't been able to recreate a minimal working example with the same error, since my other worksheets doesn't show the error even though they contain identical caluclations. The problem also persists between copies of the worksheet.

The error I'm recieving is
"Error, (in TypeTools/ac_var_local) unable to handle expressions as (((D@@2)(phi))(theta(t)))(t)"

It occurs whenever I try to differentiate some (not all) expressions containing the above variable. I have no idea what this error even means, and I can't find anything googling. As said previously, I haven't been able to produce the error so I can't really give a concise short example but the flow is as follows:

g0 := simplify(subs(diff(y(t), t, t) = F+N*v(t), lhs(aby)-lhs(aby_y)), 'size');
->Produces an expression containing (((D@@2)(phi))(theta(t)))(t)
diff(g0,t)
-> Gives Error

U := lhs(Vector([1, 0]).subs(subsVhcError, eom));
->Produces an expression containing (((D@@2)(phi))(theta(t)))(t)
diff(U,t)
-> Does not give error

Sorry that I can't be more descriptive, does anyone know have to sort this out, or might give me some more info on what the Error message might mean and how TypeTools are involved? As stated previously, the error just occured today and only affects one worksheet.

Edit: Link to worksheet with error
transverse_linearization.mw

 

I need to replace the "MISSING" in MultiDiff := proc(f,n,x) ---MISSING--- end proc; so that MultiDiff(f,n,x) evaluates as f (n) (x) if f is a suitably differentiable function, n is a positive integer, and x is an undefined variable..F(n) being an nth derivitave..Not sure where to start..Any help appreciated

I want to solve an ODE from Game Theory, the Cournot competition.

It says

p(q1+r2(q1))+p'(q1+r2(q1))*r2(q1)-c2'(r2(q1))=0

 where, I think,

' means diff(,q1),

c2(q2)=c*q2 for a fixed c in [0,1]

and

p(q)=max(0,1-q).

So c2,p and r2 are functions.r2 goes from [0,inf) to [0,inf).

I look for r2, which should be r2(q1)=(1-q1-c)/2 when correctly solved.

However, the command dsolve says Error in dsolve (divison by 0).

 What is wrong? How do I obtain the solution for r2 in Maple?

 

Hello,

 

I am trying to differentiate a matrix containing four variables, alpha, alphaB (representing alpha bar), beta, and betaB (for beta bar). They are are variables with respect to t. I then need to let t=0 and then simplify the result with some initial conitions i have. Could you tell me any useful maple functions which i can use to do this? If you need anymore information let me know and thank you for helping me.

 

Robbie

restart;

with(DETools, diff_table);

kB := 0.138064852e-22;

R := 287.058;

T := 293;

p := 101325;

rho := 0.1e-2*p/(R*T);

vr := diff_table(v_r(r, z));

vz := diff_table(v_z(r, z));

eq_r := 0 = 0;

eq_p := (vr[z]-vz[r])*vr[] = (vr[]*(vr[r, z]-vz[r, r])+vz[]*(vr[z, z]-vz[z, r]))*r;

eq_z := 0 = 0;

eq_m := r*vr[r]+r*vz[z]+vr[] = 0;

pde := {eq_m, eq_p};

IBC := {v_r(1, z) = 0, v_r(r, 0) = 0, v_z(1, z) = 0, v_z(r, 0) = r^2-1};

sol := pdsolve(pde, IBC, numeric, time = z, range = 0 .. 1);

 

what am I doing wrong?

it's telling me: Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 3, got 2
but i did just as in the example :-/

I have a problem, to which I think the solution is to make ln(x) inert.  I'd like to be able to enter the following

diff(1.5^x,x);

and get back 

ln(1.5)1.5^x

But of course Maple returns 

It seems to me that if I could make ln(x) inert for that might work, but I don't really know much about the ToInert command.  Or maybe this isn't the right approach.  

 

Hello i want to solve the differential equation but i have these problem i don't understand  why !?

restart;
with(LinearAlgebra):
with(student):
P:=180000:
Vt:=P/m;
m:=1.4787880*10^5-t*606.06:
g:=9.81:
T:=176:
pi:=evalf(Pi):

Euler_x := -(diff(lambda3(t), t)) = 0;
Euler_y := -(diff(lambda4(t), t)) = 0;
Euler_Vx := -lambda3(t)-(diff(lambda1(t), t)) = 0;
Euler_Vy := -lambda4(t)-(diff(lambda2(t), t)) = 0;
Euler_theta := lambda1(t)*sin(theta)-lambda2(t)*cos(theta) = 0;
transversalnost:=y(t)-lambda1(t)*Vt*cos(theta)-lambda2(t)*Vt*sin(theta)+lambda2(t)*g-lambda3(t)*Vx(t)-lambda4(t)*Vy(t)=0;

transversalnost:=eval(transversalnost,t=176);

sys:={Euler_x, Euler_Vx, Euler_y, Euler_Vy, theta=arctan(lambda2(t)/lambda1(t)), diff(Vx(t),t)=Vt*cos(theta), diff(Vy(t),t)=Vt*sin(theta)-g, diff(y(t),t)=Vy(t), diff(x(t),t)=Vx(t),x(0)=0, y(0)=0.302, lambda1(0)=0, lambda2(0)=0, lambda3(0)=0, lambda4(0)=0,transversalnost, x(176)=120};

ans:=dsolve(sys, numeric, output=listprocedure):

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

thanks for your help

 

Download 1234.mw

Hi

I wrote a custom recursive procedure to calculate some value (it is an implementation of a recursive algorithm)
During the further calculations derivatives of this procedure occur. Because of the statements in the specific procedure the automatic diff of a procedure does not work (at least I think that is the reason). However this is no problem as the differentiation is far from simple. L'hopitals rule needs to be used when necessary and Maple cannot detect when it needs to be used automatically (because there is another function, implicitly defined involved).
Therefore I am looking to write my own diff procedure as an extension. From the manual I gathered that this can be done as such `diff/name_of_type' =... however my procedure is not a type and I cannot easily write a 'type/name_of_type' function to define it as such. Can someone help me out?

 

I've made a toy example:

toy_example.mw

I know that in the case of this toy example other ways are possible.
What I need is a way to write my own procedure to evaluate the differential (D[1](A))(1,2,3);

Possibly defining procedure A as a type and writing 'diff/A'=proc...

Thanks

 

Dear all;

I need you help for solving this problem, and thanks in advantage for your help.

I have a polynom like  P =x^6-4*x^3+x-2;  and i would like to find an approximate value of the roots in some interval [a,b] =[-2,2] using sturm sequence.

The method is based on:

1) first construct the sturm sequence:

For given polynom P =x^6-4*x^3+x-2;

Let S0=P;

S1=diff(p,x);

let   s:=quo(S0,S1,x);
       S2:=-rem(S0,S1,x);

.... S[k+1-rem(S[k-1],S[k]);

 

S[k] is the sturm sequence.

2) let f(a)= number of change of sign in the sturm sequence and f(b) the same . so f(b)-f(a) give the number of roots in the interval [a,b].

3) If f(b)-f(a) =0 so there are no roots

and if f(a)-f(b)=1 one can find the root

4) if f(a) -f(b) >2  :

given toterance tol=0.001; for example

if the abs(a-b)<2*epsilon we display a message that there are k roots at (b+a)/2

with our error tolerance

5) otherwise if c=(b+a)/2 is not a root of P_k(x)  for any k, ( where p_k is an element of the sturm sequence ) 

we divide the interval into equal halves [a,c] and [x,b] and we run step 2 on each interval

else if c is a root of one of these p_k(x) add any time account to c so that c lies close the middle of [a,b] and not a root

6) Give all the roots ( approximate the rrots with small error epsilon).

 

I kindly  appreciate your help

 

 

 

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