chwala's latest activity

For ##f_n(\theta)=e^{-n\sin \theta} ## on ##[0,π]## three cases to consider. Case 1 consider interior values, ##\sin \theta >0##...

A generalization is to fix ##g: [0,1] \to \mathbb{R}## and let $$f_n : [0,1] \to \mathbb{R} : x \mapsto \begin{cases} ng(nx) & x < \frac...

Will definitely look at it...

I was going to append this to @chwala's thread here, but thought it deserved a new thread. For ##n \geq 1##, define $$f_n : [0,1] \to...

I meant for uniform convergence, this must hold ##\lim _{n→∞} sup |f_n (x) - f(x) | =0## and in our case, ##\lim _{n→∞} sup |f_n (x)...

Thanks @WWGD , getting analysis slowly, in any case analysis is not that difficult as i had earlier thought, ... For uniform convergence...

Notice the limit function is discontinuous, which shows convergence isn't uniform. The limit of a sequence ##f_n \rightarrow f##...

Consider also ##e^{-n\sin \theta}## for ##\theta \in [0, \pi]##.

You should try to prove the non-uniformness of the two examples @WWGD and I gave to see that you cannot choose N independently of the...

clearer now, For ##f(x)=x^n ## on ##[0,1]## three cases to consider. Case 1 consider ##0 ≤x <1## ##x^n → 0, ∀ 0 ≤x <1 ## further...

Note that ##\sin(\frac{n\pi}{2}) = 0## if ##n## is even and alternates between ##\pm1## if ##n## is odd. Using the alternating series...

Clearly, the equation ## 4x^5u''+12x^2u'-4u=0 ## is not a Cauchy–Euler equation, and it cannot be solved by the standard method, which...

Doing some reading ... I want to analyse my problem further by firstly looking at existence and uniqueness. Re-writing it as a first...

ok man, I read that. The only thing remaining is for me to get to learn some analysis on this type of problem...

I’ve been exploring the limits of Cauchy–Euler type methods and constructed the following equation: ##4x^5 u'' + 12x^2 u' - 4u = 0##...