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Field Theory Handbook

Including Coordinate Systems, Differential Equations and Their Solutions

  • Book
  • © 1988

Overview

Authors:
  1. Parry Moon

    1. Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, USA

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  2. Domina Eberle Spencer

    1. Department of Mathematics, University of Connecticut, Storrs, USA

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VII
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  2. Eleven Coordinate Systems

    • Parry Moon, Domina Eberle Spencer
    Pages 1-48

  3. Transformations in the Complex Plane

    • Parry Moon, Domina Eberle Spencer
    Pages 49-76

  4. Cylindrical Systems

    • Parry Moon, Domina Eberle Spencer
    Pages 77-95

  5. Rotational Systems

    • Parry Moon, Domina Eberle Spencer
    Pages 96-135

  6. The Vector Helmholtz Equation

    • Parry Moon, Domina Eberle Spencer
    Pages 136-143

  7. Differential Equations

    • Parry Moon, Domina Eberle Spencer
    Pages 144-162

  8. Functions

    • Parry Moon, Domina Eberle Spencer
    Pages 163-216

  9. Back Matter

    Pages 217-236
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Keywords

About this book

Let us first state exactly what this book is and what it is not. It is a compendium of equations for the physicist and the engineer working with electrostatics, magne­ tostatics, electric currents, electromagnetic fields, heat flow, gravitation, diffusion, optics, or acoustics. It tabulates the properties of 40 coordinate systems, states the Laplace and Helmholtz equations in each coordinate system, and gives the separation equations and their solutions. But it is not a textbook and it does not cover relativistic and quantum phenomena. The history of classical physics may be regarded as an interplay between two ideas, the concept of action-at-a-distance and the concept of a field. Newton's equation of universal gravitation, for instance, implies action-at-a-distance. The same form of equation was employed by COULOMB to express the force between charged particles. AMPERE and GAUSS extended this idea to the phenomenological action between currents. In 1867, LUDVIG LORENZ formulated electrodynamics as retarded action-at-a-distance. At almost the same time, MAXWELL presented the alternative formulation in terms of fields. In most cases, the field approach has shown itself to be the more powerful.

Authors and Affiliations

  • Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, USA

    Parry Moon

  • Department of Mathematics, University of Connecticut, Storrs, USA

    Domina Eberle Spencer

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