notes 10-4

# notes 10-4 - SECTION 10.4 FUNCTIONS ON[0 L VIA ODD AND EVEN...

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SECTION 10.4 FUNCTIONS ON [0 , L ] VIA ODD AND EVEN EXTENSIONS Remember that to solve the heat/temperature problem that started all this, we needed to express a function f ( x ) as a sum of sine functions only, but only on the interval (0 , L ). So far we know how to ﬁnd a Fourier series that involves both sines and cosines for functions on ( - L, L ). The key to this problem lies in the idea of odd and even functions. A function is odd if it is like x or x 3 in that f ( - x ) = f ( x ), and a function is even if it is like x 2 or x 4 in that f ( - x ) = f ( x ). DRAW SOME ODD AND EVEN FUNCTIONS AND LOOK AT INTEGRALS.

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THE ALGEBRA OF ODD AND EVEN FUNCTIONS (odd)(odd) (odd)(even) (even)(even) WHAT ABOUT COSINE AND SINE?

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notes 10-4 - SECTION 10.4 FUNCTIONS ON[0 L VIA ODD AND EVEN...

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