## Elements of partial differential equations |

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### Contents

ORDINARY DIFFERENTIAL EQUATIONS IN MORE THAN Two VARIABLES | 1 |

Simultaneous Differential Equations of the First Order and the First Degree in Three Variables | 7 |

Methods of Solution of dxP dyQ dzjR | 10 |

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arbitrary constants arbitrary function axis boundary conditions boundary value problem canonical form Chap characteristic curve coefficients complete integral cone consider corresponding curl curve F cylinder Deduce defined denotes density determine diffusion equation Dirichlet problem dx dy dz envelope equation 11 equivalent Example expression finite first-order fluid Fourier transform function f given grad Green's function Green's theorem harmonic Hence independent variables initial condition integral curves integral surface integral transforms intersection Laplace's equation linear partial differential method obtain ordinary differential equation orthogonal parameter partial differential equation particular integral Pfaffian differential equation position vector potential function prescribed Prove readily shown reduces region relation satisfies the conditions satisfies the equation second-order separation of variables Show solution of equation Solve the equation sphere of radius string Substituting temperature theorem theory two-dimensional velocity potential wave equation xy plane zero