## Riemann's Method of Integration: Its Extensions with an Application, Issue 26 |

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### Contents

Examples of the Riemann function | 5 |

Application of the Method | 12 |

Remarks and Rigor | 29 |

1 other sections not shown

### Common terms and phrases

adjoint applied Arbitrary periodic initial arc AQ arc QB assumes the prescribed breakdown Cauchy problem change sign characteristic lines closed curve closed tube consider continuous functions correct initial values corresponding region direction of increasing equations 22 extrema finite number finite or infinite flow problem follows formula 11 gas dynamics Green's theorem Hence hypergeometric equation initial curve initial value problem interior point intersect inverse functions isentropic isothermal iteration method Jacobian large squares limit line line QE linear motion number of points obtain parametric partial differential equation periodic initial conditions physical plane prescribed initial values proof QB'E r-s plane region AQBDA region G replaced by rectangles respectively Riemann function Riemann's formula Riemann's method satisfy the equation sheeted surface single-valued branch single-valued function solution of L(w t)-plane defined takes the prescribed tangential third conditions unfolded diagram variables yields a solution zero