diff options
| -rw-r--r-- | Fourier Series.page | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index 90a64f1..1ab9c43 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -1,8 +1,8 @@ -#Why Fourier series possible?</b> +#<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> +#<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: $1.\quad\sin^2(x) = ?$ @@ -78,7 +78,7 @@ Summing these two functions we get the following: <center></center> -#What is the Fourier series actually?</b> +#<b>What is the Fourier Series actually</b> ##Initial Hypothesis Now, to prove that the Fourier series is indeed true, we begin with the following hypothesis: Let $f : \mathbb I \rightarrow \mathbb C$ be a continuous, periodic function where $I$ is some time interval(period of the function). Then it can be expressed as : @@ -126,5 +126,5 @@ Extending this principle to the case of an n-dimensional vector: --> don't quite remember this part -#Why is Fourier series useful? </b> +#<b>Why is Fourier series useful? </b> Applications will be covered on Monday July 5, 2010. See you all soon!
\ No newline at end of file |