fouries - Jan 7. Fourier Methods - What, How, and Why? In...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Jan 7. Fourier Methods - What, How, and Why? In the first decade of the 19th century, Jean Baptiste Joseph Fourier invented a technique using sums of trigonometric functions called ``Fourier Series'' to solve the differential equations of heat conduction. Today, physicists, astronomers, engineers, and many others use Fourier series to analyze functions of time and space, solve differential equations, and compress data, to name just a few applications. Periodic functions Definition. f ( x ) is periodic with period p if f ( x+p ) = f ( x ), for all x . For example. sin x and cos x both have period 2 π , sin λ x and cos ( λ x+ α ) both have period 2 π / λ , pulse functions are also periodic. Definition. Given any f ( x ) defined for a<x<b , we can define its periodic extension to all x by f ( x+nT ) = f ( x ), n = 0, ± 1, ± 2, . .., a<x<b. The extended function is not yet defined at x=a+nT ; if f ( a ) f ( b ), it will be discontinuous at x=a+nT . For allowing functions with discontinuities at any point
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

fouries - Jan 7. Fourier Methods - What, How, and Why? In...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online