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Firstorder Ordinary Differential Equations
Higherorder Ordinary Differential Equations
The Laplace Transformation
9 other sections not shown
algebra analytic applied arbitrary constant boundary conditions boundary-value problem c2 exp called Cauchy-Euler equation characteristic equation coefficients complementary solution complex numbers compute Consider convergence cos2 cosh cosines curve defined definition derivative eigenfunctions eigenvalues eigenvectors evaluate Exercise exp 2x FIGURE Find first-order force formula Fourier series Gaussian elimination given Graph Hence Hint homogeneous initial conditions initial-value problem interval KEY WORDS Laplace transform Laplace's equation Legendre Legendre polynomials line integral linear transformation linearly independent mapping mathematical mathematician matrix method multiplying Note ordinary differential equations orthogonal partial differential equation particular solution plane polynomials problem of Example Prove real numbers result satisfies scalar Section separation of variables Show shown in Fig sinh Solve the following Solve the initial-value surface temperature Theorem tion vector field vector space velocity WORDS AND PHRASES zero