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Ordinary Differential Equations of the First Order
Linear Differential Equations
Introduction to Linear Algebra
17 other sections not shown
analytic applied assume axis boundary conditions characteristic equation characteristic values characteristic vectors coefficients column complete solution complex numbers components convergence Corollary corresponding cosh defined definition dependent variable derivatives determine diagonal displacement elements equal Euler-Lagrange equation EXAMPLE expansion expression factor finite formula Fourier series Green's function heat equation Hence hermitian Hint homogeneous identity interval inverse Laplace transform Laplace's equation line integral linear combination linear system linear transformation linearly independent motion multiply natural frequencies nonhomogeneous nonsingular obtain operator orthogonal parameters partial partial differential equation particular integral particular solutions periodic function plane polynomial positive problem Proof properties Prove real numbers region respect result of Exercise roots satisfy scalar Show shown in Fig sinh solve steady-state string substituting surface temperature Theorem uniform convergence vector function vector space velocity Verify wronskian zero
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