Recent content by sampahmel

Thanks a lot guys. I think I got it after googling the Jacobian suggested by hunt_mat. I will derive wrt to each variable and evaluate at the point I am trying to linearize. Then I can finally use the matrix product that I am familiar with. Thanks.

Higher Calculus. By the way, do I take logs to linearize it?

This is something new that I have never come across. How can I go about to linearize it?

Exactly. Thank you. This, I know how to solve. But the example I have given where there are sin x(t) and x(t)^2, I don't. Can anyone please enlighten me? \left( \begin{array}{c} x'(t) \\ y'(t) \end{array}\right) =\left( \begin{array}{cc} cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\...

I don't understand how do you "fixed a point". And the sin and cos, calculate them using what?

Or otherwise how do you know how to draw the local behavior as I usually find the eigenvalues and eigenvector to draw phase portrait. But in this case I don't know how to convert them into matrix form.

My matrix product refers to: \left[x\acute{}(t) y\acute{}(t)\right] = \left[1 2 3 4\right] \left[x(t) y(t)\right] I don't know how to write the matrix in two rows, so the x and x derivative are on the 1st row in their respective matrix, while y and y derivative are on the 2nd row. {1,2}...

Dear all, Homework Statement Draw behavior around (0,0) of solutions to the following nonlinear system \left( \begin{array}{c} x'(t) \\ y'(t) \end{array}\right) =\left( \begin{array}{cc} cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\ -x(t) + {y(t)}^2 + y(t) + sin {y(t)}...

Does that mean the maximum is (1-G) where G is the smallest real >0

Hi all, (1.) Can someone tell me the difference between a compact valued and single valued correspondence? (2.) I have been seeing repeating themes of "continuity on a compact set". Does that imply boundedness and thus possible to attain maximum? (3.) What's the difference between...

Homework Statement In Rosenlicht's Intro to Analysis, there is a proposition (p. 52). A Cauchy sequence of points in a metric space is bounded. Proof: For if the sequence is P1, P2, P3, ... and ε is any positive number and N an integer such tat d(Pn, Pm) < ε if n, m > N, then for any...

But I know that in any metric space, an open ball is an open set/ closed ball is a close set. Also, the complement of an open set is a closed set. But then according to you, The complement of an open ball is not closed ball. So an open set is not an open ball?

Homework Statement I am using Rosenlicht's Intro to Analysis to self-study. 1.) I learn that the complements of an open ball is a closed ball. And... 2.) Some subsets of metric space are neither open nor closed. Homework Equations Is something amiss here? I do not understand how...

I am confused with my homework problem in which it asked "If the random variable is normal, specify its distribution". What does it want? sampahmel

Can anyone please answer to the above question?