## Mathematical Methods For PhysicsThis introduction to first-year graduate physics brings together mathematics and physics, using graphs and equations. |

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### Contents

1 | |

Separation of Variables and Ordinary Differential Equations | 28 |

Spherical Harmonics and Applications | 74 |

Bessel Functions and Applications | 122 |

Normal Mode Eigenvalue Problems | 154 |

Spherical Bessel Functions and Applications | 177 |

SUMMARY OF PART I | 207 |

Greens Functions and Integral Equations | 217 |

Integral Equations | 335 |

PART III Complex Variable Techniques | 381 |

Complex Variables Basic Theory | 383 |

Evaluation of Integrals | 448 |

Dispersion Relations | 475 |

Special Functions | 507 |

Integral Transforms in the Complex Plane | 564 |

Bibliography | 621 |

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All Together Now!: A Seriously Fun Collection of Training Games and Activities Lorraine L. Ukens No preview available - 1999 |

### Common terms and phrases

analytic continuation analytic function apply arbitrary assume asymptotic expansion atoms Bessel functions Bessel's equation boundary condition branch point Cauchy's theorem charge circle coefficients complex variable constant contour converges cosh curl cylinder defined delta function derivative dielectric dimensional drumhead dz f(z eigenfunctions electrostatic evaluate example exponential field finite formula Fourier transform function f(z given grad Green's function Helmholtz equation hypergeometric function imaginary indicial equation infinite inhomogeneous initial condition inside integral equation Laplace transform Laplace's equation Legendre polynomials Legendre's equation linear Liouville eigenvalue problem magnetic matrix Methods for Physics Neumann functions obtain orthogonality Poisson's equation poles potential power series radius real axis region regular singular point result Riemann series solution sheet single valued sinh solution of Laplace's solve sphere spherical harmonics Sturm Liouville eigenvalue Substituting surface Taylor series theory un(x vanish vector wave equation z-plane zero

### Popular passages

Page viii - Perseus Publishing's Frontiers in Physics series has, since 1961, made it possible for leading physicists to communicate in coherent fashion their views of recent developments in the most exciting and active fields of physics—- without having to devote the time and energy required to prepare a formal review or monograph. Indeed, throughout its nearly forty year existence, the series has emphasized informality in both style and content, as well as pedagogical clarity. Over time, it was expected...

Page viii - ... prepare a formal review or monograph. Indeed, throughout its nearly forty-year existence, the series has emphasized informality in both style and content, as well as pedagogical clarity. Over time, it was expected that these informal accounts would be replaced by more formal counterparts — textbooks or monographs — as the cutting-edge topics they treated gradually became integrated into the body of physics knowledge and reader interest dwindled. However, this has not proven to be the case...

Page vi - Superfluidity, ABC ppbk, ISBN 0-7382-0300-9 Ma: Modern Theory of Critical Phenomena, ABC ppbk, ISBN 0-7382-0301-7 Migdal: Qualitative Methods in Quantum Theory, ABC ppbk, ISBN 0-7382-0302-5...

Page vii - Nozieres: Theory of Interacting Fermi Systems, ABC ppbk, ISBN 0-201-32824-0 Parisi: Statistical Field Theory, ABC pphk, ISBN 0-7382-0051-4 Pines: Elementary Excitations in Solids, ABC pphk, ISBN 0-7382-01 1 5-4 Pines: The Many-Body Problem, ABC pphk, ISBN 0-201-32834-8 Quigg: Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, ABC...

Page 59 - ... piecewise continuous function defined in the fundamental domain with a square-integrable1 first derivative may 1 We say that the derivative is square-integrable if the integral of the square of the derivative is bounded for all the intervals of the fundamental domain in which the function is continuous. be expanded in an eigenfunction series which converges absolutely and uniformly in...

Page 257 - Solutions of these equations together with the boundary conditions that the normal component of B and the tangential component of H are continuous at the sample boundary yield the magnetostatic modes.4 The uniform precession mode.

Page 164 - Since we imposed the condition that the ends of the string are fixed at x = 0 and x - L for all time t, the displacement...

Page 122 - E = -A .-, sin 2-5 Show that the electrostatic potential at any point is equal to the average of the potential over the surface of any sphere centered at that point for the case where the sphere contains no charge. 2-6 Show by direct integration that the electric field at an external point p due to a uniformly charged cylindrical shell carrying charge density A of radius R is given by...

Page 367 - I. Stakgold, Boundary Value Problems of Mathematical Physics (Macmillan, New York, 1967), Vol. I, Chap. III. Jdxjdy [K(x,y)]2=||Kl|2...