Why sinusoids are important
http://www-ccrma.stanford.edu/~jos/r320/Why_Sinusoids_are.html
********GREAT LINK***************
http://www-ccrma.stanford.edu/~jos/r320/Positive_Negative_Frequenci.html
download this site!!
meaning of sinusoids: anything that resonates can be roughly approximated by one...
how we hear -- our ears actually do a Fourier decomposition!!!
hear different frequencies... that's incredible.
sinusoids of same frequency.. make copies, scale them, delay them, add them up... get a sinusoid of same frequency!
exponentials: important. decay/grow at a rate proportional to how much is there. I.e. population... the more people, the faster you grow. disease spread: the more people the faster the disease spreads. bank interest: the more money you have, the more interest you get.
a single sinusoid (at some some frequency and phase) can be decomposed into two components: a sine component and a quadrature (90 degrees out of phase, or cosine) component.
rational exponents and roots.
a single sine wave can be expressed as the sum of a sine and cosine. that is crazy...
If have a question about a derivative, etc. go back to the definition.
limit does not have to equal the actual value!! remember this! (the idea of a line having twice its own length)
e is the number such that as lim o -> 0 (a^o - 1)/o = 1
