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--- math121a-f23:hw_8 [2023/10/20 22:08]
pzhou
+++ math121a-f23:hw_8 [2023/10/24 21:43] (current)
pzhou
@@ Line 5: / Line 5: @@
 Suppose you are given a function on an interval,  $f(x): [0, 1] \to \R$ . Such function  $f(x)$  can be expressed as a sum of 'sine waves' and cosine waves and constant
- f(x) = a_0 + \sum_{n=1}^\infty a_n \cos(n \pi x) + b_n \sin(n \pi x).
+ f(x) = a_0 + \sum_{n=1}^\infty a_n \cos(2n \pi x) + b_n \sin(2n \pi x).
 Can you figure out a way to determine the coefficients  $a_n$  and  $b_n$ ?
@@ Line 16: / Line 16: @@
 find  $a_0, a_1, b_1$  and plot the truncated Fourier series
- $a_0 + a_1 \cos(\pi x) + b_1 \sin(\pi x).$
+ a_0 + a_1 \cos(2 \pi x) + b_1 \sin(2 \pi x).
-How does the resemble your original given function?
+How does this resemble your original given function?

Lecture Notes