Items tagged with quadratic


 

restart; with(plots); beta := 0.1e-1; Bi := 1; Pr := 3.0; L0 := 1; w = 0.2e-1

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2+beta*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2+0.1e-1*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

(1)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+beta*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+0.1e-1*F(eta)-0.1e-1*(diff(f(eta), eta)) = 0

(2)

Eq3 := G(eta)*(diff(G(eta), eta))+beta*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+0.1e-1*f(eta)+0.1e-1*G(eta) = 0

(3)

Eq4 := H(eta)*F(eta)+H(eta)*(diff(G(eta), eta))+G(eta)*(diff(H(eta), eta)) = 0

H(eta)*F(eta)+H(eta)*(diff(G(eta), eta))+G(eta)*(diff(H(eta), eta)) = 0

(4)

Eq5 := (diff(theta(eta), eta, eta))/Pr+f(eta)*(diff(theta(eta), eta))+(2*beta*H(eta)*(1/3))*(theta[p](eta)-theta(eta)) = 0

.3333333333*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta))+0.6666666667e-2*H(eta)*(theta[p](eta)-theta(eta)) = 0

(5)

Eq6 := G(eta)*(diff(theta[p](eta), eta))+L0*beta*(theta[p](eta)-theta(eta)) = 0

G(eta)*(diff(theta[p](eta), eta))+0.1e-1*theta[p](eta)-0.1e-1*theta(eta) = 0

(6)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(theta))(0) = -Bi*(1-theta(0)), (D(f))(5) = 0, F(5) = 0, G(5) = -f(5), H(5) = w, theta(5) = 0, theta[p](5) = 0

f(0) = 0, (D(f))(0) = 1, (D(theta))(0) = -1+theta(0), (D(f))(5) = 0, F(5) = 0, G(5) = -f(5), H(5) = w, theta(5) = 0, theta[p](5) = 0

(7)

p := dsolve({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, numeric)

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

 

odeplot(p, [eta, f(eta)], 0 .. 10);

odeplot(p, [eta, f(eta)], 0 .. 10)

(8)

``

 

 


 

Download from_net.mw

Hi There,

Im currently on using a trial version of maple for engineering students. I am looking to see how you can view a step by step method of solving equations. I can't seem to find a way of doing so and I keep just getting the final answer. Can you assist?

 

Also I can't find the quadratic equation option.

 

thanks,

 

stuart

consider quadratic equation ax^2+bx+c =0 :
the coefficients vary between -1 and +1 . just like this :
-1<a<+1 , -1<b<+1 , -1<c<+1 ;
how can some one proove that this equation should have real answers ?! can anybody help ? thanks in advance.

What is the right syntax to solve :

min {sum(i=1 to 10) sum(j=1..10) (a_i_j)*(x_i)*(x_j) 

s.t sum(i=1..n) (b_i)*x_i=p and sum(i=1..n)x_i=1 

if a_i_j is a constant, b_i is a constant, p is a constant and x_i, x+j are the decision variables?

I understand that this is a quadratic programming problem and an application of Markowitz optimization. I've tried to use the in-built minimize function but haven't got the right output.

I am trying to produce a worksheet that will give me the two roots of a quadratic equation.

This is what I have:

Maple Worksheet

 

As you can see, It's not giving me the right answers. What do I do?

Thanks,

Paul

 

I have been solved a optimization problem by

Hi, I have read the help files, and many posts in MaplePrime. However, I am struggling to understand how to properly extract a number from a list. I would like to extract only the positive, or the maximum solution of a quadratic expression.I have uploaded the .mw file. (1) (2) (3) (4) With no brackets around A it does no work, Error, incorrect number of extra arguments in select If I extract the positive value I get a list, (5...

Hi,

 

when i tried to solve the following equation, i received ""Warning, solutions may have been lost"":

See attached.  I have stared at this long enough to the point I need some FRESH eyes on this.  Why does MAPLE return FALSE on the last 2 statements

Write a procedure that determines the solutions of a quadratic equation from inputs a, b and c by using the discriminant and the quadratic formula. The quadratic equation procedure should be able to solve all cases: invalid input, linear case, real and complex roots. The procedure should also plot the given equation.

Question :

Write a procedure that determines the solutions of a quadratic equation from inputs ,  and  by using the discriminant and the quadratic formula.

The quadratic equation procedure should be able to solve all cases: invalid input, linear case, real and complex roots. The procedure should also plot the given equation.

I dont understand how to do this can someone please please do it this for me urgently required.

If I run the below code which finds the optimal portfolio weights given a portfolio
target return G then I get a nice solution:

restart:
with(Optimization):
with(LinearAlgebra):

n := 4:
C := 10000:
G := .1*C:

X := Vector[column]([seq(x[i], i = 1 .. n)]):
ER := Vector[column]([0.5e-1, -.20, .15, .30]):
Q := Matrix([[0.8e-1, -0.5e-1, -0.5e-1, -0.5e-1], [-0.5e-1, .16, -0.2e-1, -0.2e-1], [-0.5e-1, -0.2e-1, .35, 0.6e-1], [-0.5e-1, -0.2e-1, 0.6e-1, .35]]):

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