Fourier Integral Fourier series of the function f [-p,p] The Fourier Integral of the function f.

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Presentation transcript:

Fourier Integral Fourier series of the function f [-p,p] The Fourier Integral of the function f

Fourier Integral Fourier series of the function f [-p,p] The Fourier Integral of the function f

Fourier Integral Find the Fourier integral representation of the piecewise- continuous function The Fourier Integral of the function f Example

Fourier integral can be used to evaluate integrals Find the Fourier integral representation of the piecewise- continuous function The Fourier Integral of the function f Example For example, at x = 1 Example

Fourier Cosine and Sine Integrals Find the Fourier integral representation of the function The Fourier integral of an even function on the interval (-oo, oo) is the cosine integral Example The Fourier integral of an odd function on the interval (-oo, oo) is the sine integral

Fourier Cosine and Sine Integrals Represent (a) by a cosine integral; (b) by a sine integral. The Fourier integral of an even function on the interval (-oo, oo) is the cosine integral Example The Fourier integral of an odd function on the interval (-oo, oo) is the sine integral cosine integral sine integral

Fourier Cosine and Sine Integrals The Fourier integral of an even function on the interval (-oo, oo) is the cosine integral The Fourier integral of an odd function on the interval (-oo, oo) is the sine integral The Fourier Integral of the function f complex form, or exponential form