Messages

1

MAT244 Math--Lectures / Re: How to find the eigenvector and determine type, special case.

« on: December 07, 2014, 03:28:50 PM »

Also what is the type of critical point?  proper or improper node? And how to draw pic?( I don't think this is as usual as we draw (im)proper node picture)

2

MAT244 Math--Lectures / Re: How to find the eigenvector and determine type, special case.

« on: December 07, 2014, 02:45:56 PM »

I mean forλ1=0, matrix is A=(0 1)  *(x1) =(0)
                                           (0 0)   (y1)    (0)
the eigenvector is (1,0) which is horizontal.

and since λ is repeated, i.e λ1=λ2=0,
we solve (0 1)  *(x2) =(1)
              (0 0)   (y2)    (0)
so, another eigenvector is (0,1), which is vertical.

Am I correct?

3

MAT244 Math--Lectures / How to find the eigenvector and determine type, special case.

« on: December 07, 2014, 01:50:12 PM »

I got a question like this,
As I solved, I find the critical point is (0,0) and A= (0                 1)
                                                                          (-6x^2+8     0)
after plug(0,0) into, it becomes (0, 1)
                                              (0, 0)
so, λ1=0=λ2, how to solve eigenvector and determine the type of critical point?

Thanks for help.

4

MAT244 Math--Lectures / Re: Particular Solution Question

« on: December 06, 2014, 09:55:50 PM »

Prof, why you make the particular solution Y1=(Acos(t)+Bsin(t))t^2?
I think for this question, the particular solution multiplies by t is enough, i.e Y1= Atcos(t)+Btsin(t).
Thank you.

5

MAT244 Math--Lectures / Textbook 7.8 Q3

« on: November 19, 2014, 01:00:30 AM »

Is answer of ch7.8 Q3 a) the solution manual wrong?
I think the answer should be clockwise.