MaplePrimes Questions

 

Hi,
I want to plot an equation, but I couldn't. Who can guide me?

Ra.mw

Suppose that a function f  has derivatives of all orders at a.  The the series

 

∑=(f(k)(a)/(k!))*(x−a)^k (limits are infinity and k=0, i donot how to insert that)

is called the Taylor series for f  about  a, where  f(n) is the n th order derivative of  f.

 

Suppose that the Taylor series for e2 x sin(5 x) about 0 is

a0+a1x+a2x2+⋯+a8x8+⋯

 

Enter the exact values of a0 and a8  in the boxes below.

      a0=   Preview   

     a8=   Preview   

Use Maple to find the solution of the initial value problem

y*(d^(2)*y/d*x^2)+(dy/dx)^2=0 0 with initial conditions y(0)=5and y'(0)=8.

Using Maple syntax, type in your answer in the box below, or copy (Ctrl-C) from your Maple worksheet and paste (Ctrl-V) in the answer box the solution. Do NOT enter the y(x)= part of the Maple output.

Why is pdsolve's 'generalsolution' option giving the particular solution u(x, y) = 0 instead of the general solution u(x, y) = A sin(x) sin(2 y) + sin(2 x) sin(y) for the attached problem?

Problem.mw

Is there a way to convert a Fourier series (from the OrthogonalExpansions package) automatically into the sum of odd/even terms if the even/odd terms are 0 respectively?


 

restart

with(OrthogonalExpansions)

FourierSeries(x-2*Pi, x = 0 .. 4*Pi, infinity, series = cosine); simplify(subs(i = n, %))

Sum(8*((-1)^n-1)*cos((1/4)*n*x)/(n^2*Pi), n = 1 .. infinity)

(1)

Sum((-16*cos((1/4)*(2*k-1)*x))*(1/((2*k-1)^2*Pi)), k = 1 .. infinity)

Sum(-16*cos((1/4)*(2*k-1)*x)/((2*k-1)^2*Pi), k = 1 .. infinity)

(2)

``

Download FourierSeries.mw

what is the most elegant way to get coefficients of a series that contains negative powers.

for example in this:

tt := a*N__s^3 + N__s + CSxSx__0 + CSxSx__1/N__s + CSxSx__2/N__s^2 + CSxSx__3/N__s^3;

i would like

fancy_coeff(tt, 1/N__s, 3)

to give me `CSxSx__3`

while

fancy_coeff(tt, 1/N__s, -3)

give me `a`

(the standard coeff call doesn't work with this, as would be known to people here)

thanks!

 

Hi,

The black circle below is vanishing at the peak. How do I make the entire  circle visible?

Transparency=0.5 is not a good solution.

 

 

 

 

 

A1 := -12; A1 = log*sigma[matrix];
print(`output redirected...`); # input placeholder
                              -12
                    -12 = log sigma[matrix]
sigma[matrix] := 0.1e-11;
print(`output redirected...`); # input placeholder
                                -12
                            1 10   
A1 := 6; A1 = log*sigma[CNT];
print(`output redirected...`); # input placeholder
                               6
                       6 = log sigma[CNT]
a := phi;
print(`output redirected...`); # input placeholder
                              phi
sigma[CNT] = 0.1e7;
print(`output redirected...`); # input placeholder
                                        6
                       sigma[CNT] = 1 10 
eq := log10(sigma[CNT]*a+(1-a)*sigma[matrix]);
print(`output redirected...`); # input placeholder
             /                     -12       -12    \
           ln\phi sigma[CNT] + 1 10    - 1 10    phi/
           ------------------------------------------
                             ln(10)                  
plot(eq, phi = 0.15e-1 .. 0.21e-1);
%;
Warning, expecting only range variable phi in expression ln(phi*sigma[CNT]+.1e-11-.1e-11*phi)/ln(10) to be plotted but found name sigma[CNT]

How can i solve that please ?

How to find the values of unknown parameters for these equations with initial and  boundary conditions

where Pr=6.2,M=2,nu=0.3,phi=0.05 and lambda=Sc=Ks=1

Could some one help me out to find the exact way to find the values of unknown parameters

Hello everyone,


I'm trying to generate plots in Maple so that I can export the image and be easily read in a document. I usually use the plots [display] command as I often reuse "subplots". The main problem appears when entering a legend, as it disrupts the proportions and I have to rescale everything manually. In doing so I sometimes get small, hard-to-read images or captions. Is there any way to resize the image and caption other than manually? Even better, is there a way to scale both to a certain image size and to make the caption legible at that size (e.g. image 7 cm wide and font equivalent to 10 pt in Word)?

Thank you so much in advance

A is a 2 x 2 matrix with eigenvalue, eigenvector pairs:

5,<4,1> and 1,<3,4>.

1. Find an invertible matrix M and a diagonal matrix D such that A=MDM^(-1).

M=   Preview                                       D=   Preview   

2. For any integer n, find the matrix A^n   as a single matrix (i.e. explicitly entry-by-entry). Use Maple notation for a matrix.

   An=   Preview    

(Hint: compose your answer in Maple to make sure your syntax is correct and your answer is what you think it should be.)

Something goes wrong with the DE   : de  
Error, unexpected single forward quote

I solved this by converting this : de  to a 2 D Math input 
Something must be chanced
in the configuration settings ? 

Ch05Sec03Prob19.mw

 

 

 

Let A be an m×n matrix. The image of A  is the set of vectors

 

im(A)={y:y=Ax for some x∈Rn} ,

 

which is a vector space.

The dimension of im(A)  is called the rank of A, denoted by rank(A) .

(a)  Find the rank of the matrix 

v1:=<-146, -84, 28, -154>

v2:=<-203, 106, 34, -181>

v3:=<-94, -4, 106, -154>

v4:=<-36, 152, -86, 50>

v5:=< 173, 122, -390, 435>

A:=<v1|v2|v3|v4|v5>;

and enter in the box below.

rank(A)=    

(b) For the matrix A in (a), select all the statements below which are true.

(1) <97,-8,-49,-66> is in im(A)

(2) <-65,74,10,-52> is in im(A)

(3)im(A) is subspace of R^4

(4) <2,-2,-4,4,-2> is in im(A)

(5) <0,0,0,0> is in im(A)

(6) <0,0,0,0,0> is in im(A)

(7) <-1,-2,1,-2,1> is in im(A)

(8) im(A) is a subspace of R^5

Let A be an m×n matrix. The kernel of A  is the set of vectors

ker(A)={x:Ax=0} ,

which is a vector space.

The dimension of ker(A)  is called the nullity of A, denoted by nullity(A) .

   (a)  Find the nullity of the matrix 

v1:=<136, 40, 124, -94>

v2:=<-74, -54, 150, 99>

v3:=<-104, 68, 196, -134>

v4:=<-38, -142, -108, 280>

v5:=<342, -326, -634, 635>

A:=<v1|v2|v3|v4|v5>

and enter in the box below.

nullity(A)=     

      b) For the matrix A in (a), select all the statements below which are true.

 (1)  <71, -37, 44, 73> is in ker(A)

 (2) <-1,1,2,-2,1> is in ker(A)

 (3) <0,0,0,0> is in ker(A)

 (4) <0,0,0,0,0> is in ker(A)

 (5) ker(A) is a subspace of R^5

 (6) ker(A) is a subspace of R^4

 (7) <95,-72,-85,-12> is in ker(A)

 (8) <2,4,-2,4,-2> is in ker(A)

 

 

 

Hi there,

What is the algorithm implemented in Maple's function modp1(('Resultant')(...)?

Thank you.

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