# Fourier formula sheet

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EE 261 The Fourier Transform and its Applications This Being an Ancient Formula Sheet Handed Down To All EE 261 Students Integration by parts: Z b a u(t)v0(t)dt = u(t)v(t) t= t= − Z b a u0(t)v(t)dt Even and odd parts of a function: Any function f(x) can be written as f(x)= f(x)+f(−x) 2 + f(x) − f(−x) 2 (even part) (odd part) Geometric series: XN n=0 rn = 1−rN+1 1− r XN n=M rn = Aug 12, 2016 · Fourier’s law states that “the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area.” Fourier’s equation of heat conduction: Take our target function, multiply it by sine (or cosine) and integrate (find the area) Do that for n=0, n=1, etc to calculate each coefficient; And after we calculate all coefficients, we put them into the series formula above. Each step is not that hard, but it does take a long time to do! But once you know how, it becomes fairly routine. Aug 12, 2016 · Fourier’s law states that “the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area.” Fourier’s equation of heat conduction: