(Sol.) =, = ==, = -ω→x and (simultaneously), and then a→b u→ω =, Summary Examples f(x) F(ω)= f(x)= , , , , etc. e-a|x| =, =, =, etc. =, =, =, =, etc. 5-2 Fourier Series of a Periodical Function Video Example of Fourier Series of Periodical Rectangular Function: Example of Fourier Series of Periodical Sawtooth Function: Fourier series: is a periodical function with period= and defined on an interval: f(x) and then where , , and f(x+)=f(x), f(x)=, In case is f(x) Parseval’s Identity for Fourier series: Orthogonalities: and Eg. Expand into Fourier series and f(x)=, f(x+4)=f(x) (Sol.) , , f(x+4)=f(x), Even function, =1 bn=0,
(Sol.) =, = ==, = -ω→x and a→b (simultaneously), and then u→ω =, Summary f(x) F(ω)= Examples f(x)= e-a|x| , , , , etc. =, =, =, etc. =, =, =, =, etc. 5-2 Fourier Series of a Periodical Function Video Example of Fourier Series of Periodical Rectangular Function: Example of Fourier Series of Periodical Sawtooth Function: Fourier series: f(x) is a periodical function with period= and defined on an interval: f(x+)=f(x), and then f(x)=, where , , and In case f(x) is Parseval’s Identity for Fourier series: Orthogonalities: and Eg. Expand f(x)=, f(x+4)=f(x) into Fourier series and (Sol.) , f(x+4)=f(x), , Even function, bn=0, =1
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