Homework Statement
R = { (X,Y) \epsilon P(A) x P(A) / (X\DeltaY) \subseteq B}
(X\DeltaY) \subseteq B - what does delta mean?
Homework Equations
The Attempt at a Solution
x'= rx- sxy/(1+ tx)= 0
x(r-sy/(1 + tx)) = 0
x= 0 and (r-sy/(1 + tx)) = 0
since x = 0 r-sy = 0
therefore, y = r/s
similarly we do that for y'= sxy/(1+ tx)- wy= 0 and we get y = 0 and x = w/(s-w)
when I substitute y= (r/w)x into x'= rx- sxy/(1+ tx), x' is NOT zero. So how...
So the discussion in this thread is really advanced and here I come with a simple question:
say we have the system
x' = x
y' = y
How do we find a first integral for this?
I know that f(x) = e^x and f(y) = e^y are solutions for this system...
But I have no idea where to start with...
I have been working with the equations:
x' = rx - sxy/(1+tx)
y' = sxy/(1+tx) - wy
I find that the only singular point is (0,0)
is this correct?
I got another point, ( w/(s-w) , r/s ), however, that cannot be a critical point because when substituting, x' and y' fail to be 0.
Homework Statement
Find the singular points for:
x' = ax - bxy
y' = bxy - cy
Homework Equations
The Attempt at a Solution
ax - bxy = 0
bxy - cy = 0
implies
x = 0 or y = a/b
y = 0 or x = c/b
the the critical points are (o,o) or (c/b, a/b)
why is (0, a/b) and...
Hi everyone,
I am currenly finishing my undergrad in math, and am currently submitting applications for my masters.
One school is asking me to "describe my reasarch interests, briefly"
Now, I have no idea what i want to research - i know which particular field i want to go into...
Hi,
My school offers this new course called Quantum Computing - it's offered by the Math Department.
Can somebody please explain to me what Quantum Computing is? What kind of math would be involved in this course? Number Thoery? Algebra? Etc..
Homework Statement
Can somebody please veryify for me that (47/14) = 1 (mod 11)
Homework Equations
The Attempt at a Solution
What I did was:
(47/14)
=(14)^-1(47)
=(3^-1)(3)
=1 (mod 11)
Homework Statement
Let a be a generator of F_q
Prove that a^i is a generator if & only if i and q-1 are relatively prime.
Homework Equations
a is a generator of F_q means that a^(q-1) = 1 and a^i cannot be 1 for all i not q-1.
relatively prime means that gcd(i,q-1)=1
fermats...
by the way, i never like linear algebra...i allways hated it..its awefull.
I only took it because it was an Applied Mathematics Specialization requirement.
Here is my situation;
I am currently in my 3rd year.
My first term, I had an A+ A A- and B+ in all my math courses (real analysis, advanced diff, stocastic, and modelling)
Those are okay grades, not bad.
This term, I have all math courses again (4th year real analysis, complex...
Homework Statement
Apply the Gram-Schmidt orthogonalization procedure to the canonical basis 1, x, x^2, x^3, x^4 in order to find an orthonormal basis for the space P4([0, 1]) with respect to the inner product <p(x), q(x)> =int(0,1) p(x)q(x) dx
AND USE THIS BASIS TO FIND THE ADJOINT OF...
Your explanation was very very clear.
When I see "If ..then" problems, I allways try to write it out as "suppose so and so..." and see where I can get...and if i get lost, i go for the contrapositive.
I guess my method fails here.
Thank you for your explanation.