## A collection of problems on mathematical physics |

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### Contents

auUxx+2aiixy+hiUyy+biUx+biUf+cu fxy 1 | 163 |

EQUATIONS OF HYPERBOLIC TYPE | 171 |

EQUATIONS OF PARABOLIC TYPE | 317 |

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arbitrary assuming axis boundary conditions boundary-value problem circular conductor Consider const convective heat exchange cosh cross-section cylinder D'Alembert's formula deflection density derived determined dielectric constant differential equation diffusion dipole eigenfunctions eigenvalues elastically electric equal to zero expression Find the temperature Find the vibrations formula Fourier given grad Green's function heat conduction heat exchange heat exchange takes homogeneous ideally conducting infinite inhomogeneous initial conditions initial temperature inside integral lamina Laplace's equation liquid longitudinal vibrations magnetic matching conditions medium membrane obtain the boundary-value origin of coordinates particular solution plane positive roots preceding problem pressure radiation region rigidly fixed satisfying the boundary semi-infinite semispace separation of variables sinh solution of problem Solve problem Solve the boundary-value Solve the preceding source function spherical steady-state string substitution system of coordinates thermally insulated transform transverse vibrations tube vector velocity potential wave z-axis