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FIRSTORDER DIFFERENTIAL EQUATIONS
SECONDORDER DIFFERENTIAL EQUATIONS
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50 gosub analytic apply approximation axis boundary conditions calculate called Cauchy residue theorem Chapter coefficients consider constant contour convergence coordinate system data points defined density determine diagonal differential equation distribution function divergence divergence theorem dx dy dy/dx eigenvalues eigenvectors elements equation 53 error evaluate exact Example Find first-order fluid force formula Fourier series frequency given gosub initial conditions initial value problem input integral integrand interval inverse Laplace transform Laplace's equation linear mass matrix multiply obtain orthogonal particular solution periodic function plot polynomial potential energy power series result rotation Runge-Kutta Runge-Kutta method scalar second-order Section separation of variables shown in Figure side of equation simple harmonic oscillator Simpson's rule solution of equation Step string subinterval subroutine Substitution into equation Suppose Taylor series tion vector field velocity wave equation x-y plane yields zero