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diff --git a/Fourier Series.page b/Fourier Series.page index 8ef6bd3..ab344fd 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -1,8 +1,8 @@ -##Why Fourier series possible?</b> +#Why Fourier series possible?</b> We first begin with a few basic identities on the size of sets. Show that the set of possible functions representing sets is not larger than the set of available functions? -##Why Fourier series is plausible?</b> +#Why Fourier series is plausible?</b> To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: $1.\quad\sin^2(x) = ?$ @@ -78,9 +78,9 @@ Summing these two functions we get the following: <center></center> -##What is the Fourier series actually?</b> +#What is the Fourier series actually?</b> Now, to begin proving that the Fourier series is a true fact let us begin with the following hypthesis: -Let f ____ be a continuous, periodic function where I is some the time interval(period of the function). Then it can be expressed as +Let f ____ be a continuous, periodic function where I is some the time interval(period of the function). Then it can be expressed as : $$ \begin{array}{ccl} @@ -88,5 +88,6 @@ f & = & \Sigma e^{inx}\\ & = & a0 + \Sigma a~n\cos nx + \Sigma b~n\sin nx\\ \end{array} $$ - -##Why is Fourier series useful? </b> + +#Why is Fourier series useful? </b> +Applications will be covered on Monday July 5, 2010. See you all soon!
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