Exercises on Fourier Series

Question

unklerhaukus · Answer

attachment

unklerhaukus · Answer

attachment

unklerhaukus · Answer

have i made any mistakes

perl · Answer

hey uncle, looks good

unklerhaukus · Answer

$$\large\color{teal}{\ddot\smile}$$

perl · Answer

how did you get these on pdf? very nicely done

unklerhaukus · Answer

a program called TeXShop

perl · Answer

very nice, are you a professor?

perl · Answer

i am stumped on a question, freaking book of mine , 
Prove that if there is an injection f : A -> A which is not surjective, then A is not a finite
set.
. . . . . . . . . .

unklerhaukus · Answer

im a only a student

perl · Answer

wow

perl · Answer

is this a differential equations class >?

perl · Answer

i never learned fourier series :(

unklerhaukus · Answer

yeah from DE class

anonymous · Answer

uncle is there an exercise on proving trigonometric identities?

unklerhaukus · Answer

|dw:1356168122187:dw|

experimentx · Answer

@perl the difference between fine and infinite set is that the infinite set is that the infinite set will be equivalent to some proper subset of itself. i.e. if there is injection f:A->A ... means the set is equivalent to some proper subset (due to surjective). Which means the set A is not finite.

experimentx · Answer

@UnkleRhaukus do you have Mathematica ( i bet you have matlab)? 
Plot these infinite series, if these infinite series is equal to your function, then your work is right!!

unklerhaukus · Answer

i do not have Mathematica
i do have Matlab

i checked these on a program called Grapher, and they turned out right , but that dosen't mean i haven't made mistakes

experimentx · Answer

if you have identical function ... except at the point of discontinuity then your work is correct!!