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've got the following matrix :

A:=[<a,a-1,-b>|<a-1,a,-b>,<b,b,2a-1>] where <> are the column elements of A, a is  a real number defined on [0,1] and b^2=2a(1-a) 

a) to show A is an orthogonal matrix, I understand that I need A.Transpose(A)=Identity(3*3) but is there a way in which I can let a take a random real numbered value between 0 and 1? The rand() only returns an integer within a range. Directly multiplying A and Transpose(A) will return an expression in a, so what's the right approach?

b) from a) we can infer that A is a matrix that describes a rotation in e1,e2,e3 where these are the standard bases vectors in R3. How can I determine the rotation axis? The hint I've been given says I need to consider the Eigenvalues and eigen vectors but I don't quite understand how.

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.

When plotting a continous function that looks something like a square wave, for example like this:

f:=x->piecewise(0<x<Pi,0,Pi<x<2*Pi,Pi);
a:=0: b:=2*Pi: p:=b-a:
fp:=f(x-floor( (x-a)/p)*p);
plot(fp,x=-6*Pi..6*Pi,discont=true);

Is there some way to show dashed vertical lines at the points of discontinuity?

So i got a procedure test, she is kind of numeric, i whant to optimaze test([.5, .5, .5], 1, 3, 100, 100, true, [x, 0, 0, 0, 0])=0 by x. But optinization substitutes x like a symbol, i tryed all methods but they all do the same.

f := proc (x) options operator, arrow; abs(test([.5, .5, .5], 1, 3, 100, 100, true, [x, 0, 0, 0, 0])-.4) end proc; Minimize(f(x));
%;
Error, (in test) cannot determine if this expression is true or false: 0 < -43.0+100*x

Can i some how use optinization on such procedure?

file link  - >    primset.mw

A created an overly complicated worksheet thaI can no longer open.  It's about 17 Mb, has several interactive plots and equations in it.  Is there a way to force Maple to open a worksheet without executing it?

(Lesson learned:  split this up into separate worksheets next time.)

I wish to use closed Newton-Cotes with n=2, also known as Simpson's Rule to numerically integrate an improper integral.

If it matters the integrand is (cos(2x))/(x^1/3), integrating between x=0..1

I've tried a few different (but similar) code but to no avail. Here is some stuff I've tried:

1.

with(Student[NumericalAnalysis]):

with(Student[Calculus 1]):

Simp1 := ApproximateInt(cos(2*x)/x^(1/3), x = 0 .. 1, method = newtoncotes[2]);

This gives me an output message that says "Float(infinity)".

2.

with(Student[NumericalAnalysis]):

with(Student[Calculus 1]):

Simp2 := int(exp(-x)/sqrt(1-x), x = 0 .. 1);

This doesn't have Simpson's rule as an option.

I think I'm on the right track with my first try, since I guess it wasn't tecnically an error message, but I'm not sure how to alter the code accordingly to get a numerical value instead. Thanks for any help.

I am trying to numerically double integrate x^2+sqrt(y), with the bounds y=0..x and x=1..1.5.

Then I tried the following code:

int(int(x^2+sqrt(y),method=trapezoid,y=0..x),method=trapezoid,x=1..1.5);

I know how to write the code if instead of a 'x' in my upper limit for my integral, I had a real number, but I'm not sure how to remedy to code in order make it work. Any help would be appreciated. Thanks!

Thanks.

Download dsolve_question.mw

Hi,

I got the Real and Imaginary of an expression J1 

assume(d,real):

Gamma:=0.04:tau:=10*Pi:j:=0:

J1:=(exp((1-I*d)*Gamma*tau)-1)/((1-I*d));

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)

################

but when I change the expression  for J1 to be

J1:=((2*e^(-2^(-j-1)*(1-I*d))-e^(-2^(-j)*(1-I*d))-1)*exp((1-I*d)*Gamma*tau)-1)/((1-I*d)):

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): 

J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help

Thanks

Hello everybody,

can somebody tell me how to use subscripts in textmode? 

Thanks for your help!

Picard

OK, what am I doing wrong here?

This polynomial can be factored by almost anyone who knows algebra:

factor(x^2+y^2+2*xy);

but Maple refuses:

 x²  + y²  + 2 xy

but if I pose the question this way:

ans := expand((x+y)^2);

factor(ans);

(x + y)²

I get the expected result.  What is wrong with how I am using the factor?

If we have a piecewise continous 2*Pi-periodic function

h(t)=e^(2*t) when 0 < t < 2*Pi

How can we plot it? It should look something like this:

I.e. I want to be able to just set an interval and then it automatically plots the function with the specified periodicity.

Hi,

I am new to maple. I want to write the following codes in Maple in a file and execute it. I am writing the code in matlab. thanks

for i =1:1:5

for j=1:1:5

M(i,j)=i+j;

end

end

thanks

I am working with a package that is not entirely stable and which can sometimes corrupt Maple's state. I would like to "sandbox" the risky operations, executing each of them in another kernel thread that I can destroy (or somehow reset), getting back just the return result of each operation (each return result involves only global names, numbers, and strings). What would be a good way to achieve this?

I see the Task model, but it is not clear to me that each kernel used is effectively restart()'d for each Task Start(). At the moment I would have a bit more confidence in manually using Thread Create(), except that I do not see any information on how to destroy a thread (just to destroy Mutex and Condition Variable resources.)

This is, I suppose, a kind of security, but it is not covered by EngineSecurity. (Not unless I need to process[popen] to achieve this.)