MATH 2ZZ3 Lecture Notes - Lecture 1: Hit106.9 Newcastle, Fourier Series, Britain Yearly Meeting

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3 x y z x y z k zk. Notation: u = u form a basis for. Symmetric: u v v u k u v k u v k u v. 0 u 0 u u u v w u w v w. 1 f and assume they are piecewise continuous on some interval [a, b]. Notation: ( x x d x f f. 1 f inner product a f on the interval [a, b] is the number: We now need to check to see that each of the four properties holds. f. This holds because you can take out constants from integrals. ( ) 0 f x = is our zero . Take the inner product of itself. x x x x x x x. 3 b a b a b a d f f x. We look at functions as if they were vectors with the dot product applied to them.

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