"Ordinary Differential Equations" by V Arnold
Hello,
I recently bought "Ordinary Differential Equations" by V I Arnold to study differential equation. In that book he assumes we know basic topology. I want to know which subfield of topology should I know, in order to study this book...
Hello Niles,
I think it should give (0,0,√2)
The point (1,0,1) lies on XZ plane. So its distance from origin is √ (1 + 1) = √2
As per the image you have attached.
It makings an angle of 45° CCW with Z-axis.
Now you are rotating the point CW 45°.
i.e you are moving the point about...
Hello Niles
I don't know how you got (0, 0, 1/√2).
I multiplied your rotation matrix with (1,0,1) & got the right answer, which is (√2, 0, 0)
cos(-45) = 0.707
sin(-45) = -0.707
Thanks everyone for replying. I will refer some other books & try to dig some more.
In meantime I will try to put my question in other words.
In Pg 26 he says "more loosely, we may say that elements of any countable set can be "arranged in a sequence""
So I am assuming that, if anything...
Thanks for the reply DonAntonio. You say
So,since th. 2.14 is true for 1's & 0's, it has to be true for any natural/rational numbers.
And set of all sequences is Union.
If th 2.12 says a countable union of countable sets is countable.
so can i say that th 2.14 states union of all...
Please help me in understanding the difference between theorems 2.12 & 2.14 of Rudin's Principles of Mathematical Analysis.
Both are sets of sequences.
Set S in Th.2.12 is union of countable sequences
While set A in Th 2.14 is set of "all" sequences.
Is set A uncountable only because it has...
Please have a look at the book "Dynamics for beginners" by John Bascombe Lock.
This is a very old book(1890).
It can be freely downloaded from the below link.
http://www.archive.org/details/dynamicsforbegin00lockuoft
Concepts are explained & developed very neatly.