Use the Gram-Schmidt process to transform the basis
 
           {Vector(3, {(1) = 0, (2) = 1, (3) = 1}), 

             Vector(3, {(1) = 1, (2) = 1, (3) = 1}), 

             Vector(3, {(1) = 1, (2) = 2, (3) = 3})}

for the Euclidean space R3 into an orthonormal basis for R3

                               
Show 3D result.

I am having a great deal of difficulty with this exercise.

Clues are

>irem(floor(evalf(K*10^n,N)),10) can be used to find the nth digits of the decimal expansion of K

A given process.

The following procedure P(n) counts the number of prime numbers ≤ n.
> P:=proc(n) local c,i;
c:=0; # initialize the counter c=0
for i from 1 to n do
if type(i,prime) then c:=c+1;
end if; # increase c by 1 if i is prime

I have a multivariate polynomial equation, in that somehow I know the coeffcients, using this information, I want to extract the variables. This will be the opposite of coeffs function.

for e.g. I have 3*x3 + 5*x4

Given 3 and 5, I want to extract x3 and x4.

Thanks in advance.

Satya

I believe this is a result of my ignorance rather then the flaws of the system. Can anyone teach me how to do this question?

Given 

>sum(1/n, n = 1 .. N)

I want to find the value of N such that sum(1/n, n = 1 .. N) is greater then 20.12.

>solve(sum(1/n, n = 1 .. N) > 20.12, N)

Warning, solutions may have been lost

Help please! Thanks.

Hi, experts,

I have an equations:

How to solve a, and b? It's easy to know that a = 2, b =5 though.

Many thanks! 

In the name of God

Any one knows how I can summerize this:

v1:=Vector(3):v2:=Vector(3):v3:=Vector(3):v4:=vector(3):v5:=Vector(3):

these 5 are independent.

Maybe some help page of maple helps me.

Hossayni

How can i solve for G(p,q,r,t) in the following pde

diff(G(p, q, r, t), t) = {lambda*(p-1)+gamma*(r-1)}*G(p, q, r, t)+delta*(1-p)*(diff(G(p, q, r, t), p))+kappa*(N*r-q)*(diff(G(p, q, r, t), q))+mu*(1-r)*(diff(G(p, q, r, t), r))+beta*(q*e^(-`ρτ`)-p*r)*(diff(G(p, q, r, t), r, p))

Dear All

I trying to solve the following in MAPLE, the code works fine in MATLAB but I am not sure why it doesn't give me values in MAPLE

n:=3: alpha_p:=1: p:=2: mu0:=4*Pi*1e-7: Br:=1.12:

A1:=unapply(sin((n*p+1)*alpha_p*Pi/(2*p))/((n*p+1)*alpha_p*Pi/(2*p)),n):

A2:=unapply(sin((n*p-1)*alpha_p*Pi/(2*p))/((n*p-1)*alpha_p*Pi/(2*p)),n):

M1:=unapply((Br/mu0)*alpha_p*(A1(n)+A2(n)),n):

M2:=unapply((Br/mu0)*alpha_p*(A1(n)-A2(n)),n):

How can i solve for X(t) in the following equation

diff(mean(X(t)), t) = lambda-delta*mean(X(t))-beta*mean(X(t)*V(t))

and how can i plot X(t) against t.

Here is what I tried.

I need to get the sum of all the real roots of 3*sin(x^2) = x

So I tried this. 

>solve(3*sin(x^2)-x = 0, x, AllSolutions)

Which gaved me this 3*sin(RootOf(_Z-9*sin(_Z)^2))

Then >sum(3*sin(RootOf(_Z-9*sin(_Z)^2)), _Z = -infinity .. infinity)

Which gives me this answer which I cannot make sense of.  signum(sin(RootOf(_Z-9*sin(_Z)^2)))*infinity

I'm trying to solve for n in a simple sum() function:  Here is the function.

I have a question regarding on how to graph and prove that csc ^2(theta)-cot ^2(theta)=1 our professor provided us with a very poor example, i have to graph the left side of the equation first with a 0 to 2*Pi x-axis and then graph the right side on the same plot. 

I examined some rules to verify that if a certain function for example f(x)=x^2+5 is a 1-1 function or not.

What I did after defining the function was as follows:

[> assume(x>0,s>0);

[> solve(f(x)=f(s),{x,s});

OR

[> solve(f(x)=f(s),{x,s}) assuming x:: positive;

They didn't give me just

s=x

at all. Thanks so much.

Could anyone help with solving this integral?

> evalf((∫)[-infinity]^(infinity)((∫)[-infinity]^(v)( uv)/(sqrt(2 Pi))(1/2+1/2 erf((1 )/2 sqrt(2) u))(1/2-1/2 erf((1 )/2 sqrt(2) v))(e)^(-((u^(2+v^(2))))/(2)) ⅆu )dv);

thanks,

Hi!

I have a piecewise defined function alpha. Its functional directives are stored in a vector A. But when I call up the command

alpha:=(x1,x2,x3)->piecewise(
    x1 < 0 , A[1],

   0< x1<1 A[2], ...):,

the result (x1,x2,x3)->piecewise(.... , A[1], ...) remains symbolic. What can I do that the entries of A[i] appear in the functional directive?

Thanks!