I don't know where to start to solve for c.. that is my problem...
I don't understand where the 1 comes from... I know O(logn) < O(sqrt(n)) so I can get that but where is the (1+srt(n)) comes from?
yes well I don't know how to go from f(n) to g(n)... the examples I have seen were just that you would multiply so part of f(n) until you could group everything together to get c* g(n) but this time I don't see how I can multiply anything to get anything that looks like g(n)...
f(n) is O(g(n)) if and only if there exists an n_0 part of natural numbers and a constant C that is part of rational numbers for which f(n) <= that c*g(n) for all n >= n_o
I know the def just don't know how to get g(n)...
Homework Statement
Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).
Homework Equations
n/a
The Attempt at a Solution
I really don't know what to do else I wouldn't be here :? Some hints would be appreciated!
Homework Statement
A particle is attracted toward the origin by a force proportional to the cube of it's distance from the origin. (...)
What would be this Force equal to (in xy plane)?
The Attempt at a Solution
So distance is Sqrt[x^2+y^2]... and from here I don't know what to...
Homework Statement
I have to find the solution of (1) and show that it is not unique if y(0) = 0.
I can prove it is not unique by using Picard's theorem but I don't know how to find the non trivial solution.
Homework Equations
(1) y(t)' = Sqrt(y(t))
The Attempt at a Solution
I...
e^ix
first
i*e^ix
second
i^2*e^ix
e^-ix
first
-i*e^-ix
second
i^2*e^-ix
p.s. I've read about the Cauchy-Riemann equation but just not sure how to apply it... should I split the exponential in a sin and a cos?
p.s.s. There are probably rules, like exponential function are always derivable or...
I have to solve an ODE with variation of coefficient technique. It's pretty easy but I have no clue what is the first and second derivative of e^ix and e^-ix.
Homework Statement
I have a project for one of my class and I have been given a sheet to do the statistical analyst of my data. I am not convince this sheet is proper and I need someone to look over it it. I don't understand where my Delta R goes...
Homework Equations
\chi^2...
Ok well I guess my intuition was bad. I made a few search on books.google.com and found a couple of proofs. One is pretty easy and I actually though of that solutions before but didn't know how to generalise it. My only problem now is that I'm not familiar with one notation in the proofs.
I...