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FINDING THE FOURIER SERIES
FORCED SOLUTIONS OF ORDINARY
PARTIAL DIFFERENTIAL EQUATIONS
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2nkt amplitude approximating function arbitrary period attenuation boundary conditions choose circuit Confirm that eqn constant term convergence cosine components cosine function curve defined by eqn derivative engineering example exponential filter find the Fourier form of eqn Fourier components Fourier series given frequency full-range function defined function of Fig fundamental component Gibbs phenomenon given by eqn gives the Fourier half-range heat conduction higher harmonics initial conditions initial displacement initial velocity integrate interval kx dx look lx dx mathematics notation odd function ordinary differential equations Parseval's theorem partial differential equation periodic excitation periodic extension periodic function plotted in Fig problem pulse relationship resonance right-hand side RL circuit second harmonic Section shown in Fig side of eqn sine components sinusoidal solve square wave Substituting eqn symmetric temperature distribution third harmonic transmission line triangular function variables vibrating string waveform whence yielding