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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

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

View Full DocumentRight Arrow Icon
THE ALGEBRA OF ODD AND EVEN FUNCTIONS (odd)(odd) (odd)(even) (even)(even) WHAT ABOUT COSINE AND SINE?
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

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