Items tagged with derivative derivative Tagged Items Feed

 

When I take the derivative of this function wrt p, I am getting this:

 

Why the program gives , instead of only

Sorry for the format, I just copy and paste.

Thanks,

 

 

 

related topic is here

Suppose I have 2 differential equations in vector form, and I want to solve them using dsolve. I am not able to figure the syntax for what I would do for scalar ODE to initial its derivative at t=0, which is D(x)(0)=some_value, but do the same when x is a vector.

Here is an example:

restart;
x := t-> <x1(t),x2(t)>;
eq:=diff~(x(t),t$2) =~ <sin(t),t>;
ic1:=x(0)=~0;

So far so good. Now I wanted to also make initial conditions for derivative at zero to be some value. Only syntax I know is using D(x)(0)=some_value. But this works for scalar ODE. When I tried

ic2:=D(x)(0)=~0;

I got

This does not work:

ic2:=diff~(x)(0)=~0;

any help on the correct syntax to use? I am using Maple 2015

 

Hi, 


     I've been playing around with the Physics package, and I'm confused on evaluaing derivatives of explicit funcitons of the coordinates. This code below doesnt behave as I would think. I'm trying to define z as a function of X[mu]*X[mu], and take diff(z, X[mu]). You can see that each method d_, diff,  disagree and none are satisfactory ansers. (Maple 2015, Windows 8.1 64-bit, Intel i5 Haswell) 

# Declare coordinates for 2 dimensions, flat space

restart:
with(Physics):
Setup(mathematicalnotation = true, dimension = 2):
Coordinates(X):

# Method 1: Using Define and various differential operators
Define(z):
z :=sqrt(R^2-X[mu]*X[mu]);
d_[mu](z(X));
d_[1](z(X));
diff(z, x1);  #This one is correct
diff(z, X[mu]); # off by 2

# Method #2: Using functions
# Off by a factor of 2
z2 := mu -> sqrt(R^2-X[mu]*X[mu]);
diff(z2(mu), X[mu]); # off by 2

 PhysicsDiffBug.mw

In the following, the diff operator calcuates the derivative correctly, but the D operator doesn't.  A bug?

restart;

f := x -> a[1][2]*x;    # the double index on a[][] is intended

proc (x) options operator, arrow; a[1][2]*x end proc

 

diff(f(x), x);

a[1][2]

 

D(f)(x);

(D(f))(x)

 


Here is a worksheet containing the commands above in case you want to try it yourself: mw.mw

Hello everyone!

I'm pretty new with Maple. I think I've understood the way Maple handles differentiation fairly well, but upon a specific request from my PhD tutor I have to perform a task which is giving me a hard time. 

My question is: is in any way possible to express a derivative of a function or expression in terms of the function itself?
I'll try to explain myself with an example: let f(x) and f'(x) be the function and its first derivative:

Instead of expressing f'(x) in the way shown, I'd like to express it as a function of f(x), such as in the following:

I would apply the same process to the higher order derivatives, if possible.

A huge thank you to whoever will help me!

When I take the derivative of abs(x), I use the chain rule and get this

When I ask Maple to differentiate abs(x), I get this:

I read the help file on "signum", and I expected this to work, but it does not.

 

 

How can I represent signum in normal calculus syntax when working the derivative of functions involving abs(x)?

 

 

 

Determine using determinants the range of values of a (if any) such that
f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz
has a minimum at (0,0,0).

From the theory, I understand that if the matrix corresponding to the coefficients of the function is positive definite, the function has a local min at the point. But, how do I get the range of values of a such that f is a min? Is this equivalent to finding a such that det(A) > 0?

 

2.

Now modify the function to also involve a parameter b: g(x,y,z)=bx^2+2axy+by^2+4xz-2a^2yz+2bz^2. We determine conditions on a and b such that g has a minimum at (0,0,0).
By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.

Which region corresponds to a local minimum?

Now determine region(s) in the (a,b) plane where g has a local maximum.

I don't understand this part at all..

I have the function:   f(x,y) = 1/(sqrt(2*Pi)) * e-1/2(x^2+y^2)

I need to take the total derivative of this function in maple, but I don't know the syntax.

I've plotted the graph for this max function. Is there any way I can find the points of discontinuity in general and then use that to compute the derivatives at points where it exists?

Hi Everyone,

I have an expression that contains a second order derivative: EXPR:=ay''(x) + bz'(x) + cf'(x)+... The variable y  obeys an ordinary differential equation, y''(x) = f(y,x). I would like to replace the second order deriavtive in my expression with f(y,x). So far I have tried applyrule([y''(x)=f(y,x)],EXPR), subs(y''(x)=f(y,x),EXPR) and algsubs(y''(x)=f(y,x),EXPR) and nothing seems to work. Any helpful suggestions?

 

Hello,

 

could you help me solve this error ? I don't understand what it means.

 


> eq3:=diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*(x(t)-(diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*x(t)+omega[0]^2*X[0])/omega[0]^2) = -omega[0]^2*X[0]:
> dsolve(eq3);
Warning, it is required that the numerator of the given ODE depends on the highest derivative. Returning NULL.

 

Thanks.

Hello i want to sort according to u derivatives (k) system.  And finding determining equations system and solving this system. Thank you very much.  

restart

with(PDEtools)

[CanonicalCoordinates, ChangeSymmetry, CharacteristicQ, CharacteristicQInvariants, ConservedCurrentTest, ConservedCurrents, ConsistencyTest, D_Dx, DeterminingPDE, Eta_k, Euler, FromJet, InfinitesimalGenerator, Infinitesimals, IntegratingFactorTest, IntegratingFactors, InvariantEquation, InvariantSolutions, InvariantTransformation, Invariants, Laplace, Library, PDEplot, PolynomialSolutions, ReducedForm, SimilaritySolutions, SimilarityTransformation, Solve, SymmetrySolutions, SymmetryTest, SymmetryTransformation, TWSolutions, ToJet, build, casesplit, charstrip, dchange, dcoeffs, declare, diff_table, difforder, dpolyform, dsubs, mapde, separability, splitstrip, splitsys, undeclare]

(1)

U := diff_table(u(x, y, t))

table( [(  ) = u(x, y, t) ] )

(2)

declare(U[])

u(x, y, t)*`will now be displayed as`*u

(3)

pde := diff(U[t]-(3/2)*U[x]-6*U[]^2*U[x]+U[x, x, x], x)+U[y, y] = 0

diff(diff(u(x, y, t), t), x)-(3/2)*(diff(diff(u(x, y, t), x), x))-12*u(x, y, t)*(diff(u(x, y, t), x))^2-6*u(x, y, t)^2*(diff(diff(u(x, y, t), x), x))+diff(diff(diff(diff(u(x, y, t), x), x), x), x)+diff(diff(u(x, y, t), y), y) = 0

(4)

NULL

w := phi(x, y, t, U[])

phi(x, y, t, u(x, y, t))

(5)

w*(-12*U[x]^2-12*U[]*U[x, x])+12*w*U[x]^2+12*U[]*w*U[x, x]+(diff(w, x, x))*(-3/2-6*U[]^2)+diff(diff(w, t), x)+diff(w, y, y)+diff(w, x, x, x, x)-lambda*(diff(U[t]-(3/2)*U[x]-6*U[]^2*U[x]+U[x, x, x], x)+U[y, y])

-lambda*(diff(diff(u(x, y, t), t), x)-(3/2)*(diff(diff(u(x, y, t), x), x))-12*u(x, y, t)*(diff(u(x, y, t), x))^2-6*u(x, y, t)^2*(diff(diff(u(x, y, t), x), x))+diff(diff(diff(diff(u(x, y, t), x), x), x), x)+diff(diff(u(x, y, t), y), y))+(D[1, 1, 1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 1, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(u(x, y, t), x))+2*((D[1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(u(x, y, t), x), x))+(D[1, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(u(x, y, t), x), x), x))+((D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+((D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(u(x, y, t), x))+2*((D[1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(u(x, y, t), x), x))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(u(x, y, t), x), x), x)))*(diff(u(x, y, t), x))+3*((D[1, 1, 4](phi))(x, y, t, u(x, y, t))+(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(diff(diff(u(x, y, t), x), x))+3*((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(diff(diff(u(x, y, t), x), x), x))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(diff(diff(u(x, y, t), x), x), x), x))+(D[2, 2](phi))(x, y, t, u(x, y, t))+(D[2, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), y))+((D[2, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), y)))*(diff(u(x, y, t), y))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), y), y))+(D[1, 3](phi))(x, y, t, u(x, y, t))+(D[3, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), t))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), t), x))+((D[1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))+((D[1, 4](phi))(x, y, t, u(x, y, t))+(D[4, 4](phi))(x, y, t, u(x, y, t))*(diff(u(x, y, t), x)))*(diff(u(x, y, t), x))+(D[4](phi))(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x)))*(-3/2-6*u(x, y, t)^2)+12*u(x, y, t)*phi(x, y, t, u(x, y, t))*(diff(diff(u(x, y, t), x), x))+12*phi(x, y, t, u(x, y, t))*(diff(u(x, y, t), x))^2+phi(x, y, t, u(x, y, t))*(-12*(diff(u(x, y, t), x))^2-12*u(x, y, t)*(diff(diff(u(x, y, t), x), x)))

(6)

k := simplify(%)

-(3/2)*(D[1, 1](phi))(x, y, t, u(x, y, t))+(D[1, 3](phi))(x, y, t, u(x, y, t))+(D[2, 2](phi))(x, y, t, u(x, y, t))+(D[1, 1, 1, 1](phi))(x, y, t, u(x, y, t))+4*(D[1, 1, 1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)+6*(D[1, 1, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+4*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1, 1](u))(x, y, t)+2*(D[2, 4](phi))(x, y, t, u(x, y, t))*(D[2](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[2, 2](u))(x, y, t)+(D[3, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)+(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 3](u))(x, y, t)-3*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)-(3/2)*(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)-lambda*(D[1, 3](u))(x, y, t)+(3/2)*lambda*(D[1, 1](u))(x, y, t)-lambda*(D[1, 1, 1, 1](u))(x, y, t)-lambda*(D[2, 2](u))(x, y, t)+6*(D[1, 1, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2+4*(D[1, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^3+(D[4, 4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^4+3*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)^2+(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[2](u))(x, y, t)^2+(D[3](u))(x, y, t)*(D[1, 4](phi))(x, y, t, u(x, y, t))-(3/2)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2-6*(D[1, 1](phi))(x, y, t, u(x, y, t))*u(x, y, t)^2+12*lambda*u(x, y, t)*(D[1](u))(x, y, t)^2+6*lambda*u(x, y, t)^2*(D[1, 1](u))(x, y, t)+12*(D[1](u))(x, y, t)*(D[1, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+6*(D[1](u))(x, y, t)^2*(D[4, 4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)+4*(D[1](u))(x, y, t)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1, 1, 1](u))(x, y, t)+(D[3](u))(x, y, t)*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)-12*(D[1, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)*u(x, y, t)^2-6*(D[4, 4](phi))(x, y, t, u(x, y, t))*(D[1](u))(x, y, t)^2*u(x, y, t)^2-6*(D[4](phi))(x, y, t, u(x, y, t))*(D[1, 1](u))(x, y, t)*u(x, y, t)^2

(7)

frontend(coeff, [k, U[x]^2]);

0

(8)

frontend(coeff, [k, U[x]*U[x, x]])

Error, invalid input: coeff received O*O, which is not valid for its 2nd argument, x

 

NULL


Download det.eq..mw

 

with(plots):

a:=polarplot(3-3*cos(theta),theta=0..2*Pi):

c:=plot((3*sqrt(2)+3)/2 + ((-3*sqrt(2))/(-3*sqrt(2)-6))*(x+((3*sqrt(2)+3)/2)),x=-10..10):

display(a,c,view=[-10..10,-10..10]);

 

a:= is the polar plot of the cardiod (3-3cos(theta)


In order to plot the tangent line to the cardiod in theta= 3Pi/4, I find the point (x,y) in rectangular coord x=(3-3cos(theta)cos(theta) and y=(3-3cos(theta)sin(theta); then I find the derivative of dx/dy=

[(3-3*cos(theta)*cos(theta)+sin(theta)(3sin(theta)]/[-(3-3cos(theta)sin(theta)+cos(theta)(3sin(theta)]and from here I get the slope.So I can plot c:= tangent line to the cardiod in 3Pi/4.

How can I avoid having to convert everyting to rectangular coords, and plot the tangent line in polars?

 

 

Hi All,

I have a problem with regard to partial differential equations. I am using Lagrangian dynamics for a problem. First i have a function First i defined a function with two speeds of angles (first derivatives):

ODE := 5*(diff(theta1(t), t))+diff(theta2(t), t). This gives:

Now this gives an output. Lagrange (just a simple example now) demands that i now derive the obtained function with regard to the first derivative of theta1. In this case, the answer i want is 5. Now, if i give the command: 

diff(ODE, diff(theta1(t),t)), maple says go home. Does anybody know how to solve this? I have been searching for a solution all afternoon.

 

Thnx in advance!

Hi everyone,

I have a question regarding the derivation of tensors/matrices.
Let's assume for simplicity, that I have a vector (6x1) s and a matrix A (6x6)defining Transpose(s)*Inverse(A)*s. From this function I want to calculate the derivative w.r.t. s. My approach would be

restartwith(Physics):
with(LinearAlgebra):
Define(s,A)

Diff(
Transpose(s)*Inverse(A)*s, s)

As a result I get

though I'd rather expect something like Inverse(A)*s + Transpose(s)*Inverse(A)

Now as I'm pretty new to Maple, I can imagine that my approach is wrong, but I don't know any better and can't seem to get any information out of the help documents.

Thanks in advance for any of your suggestions!

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